## Final Report Summary - ATHENA (Advanced theories for functional oxides: new routes to handle the devices of the future)

Executive Summary:

The Eu-India ATHENA project has been carried out in a close partnership between three European and three Indian Institutes. The project has been completed in full, and the expected list of Tasks, Deliverables, and Milestones completed and uploaded according to the expected program and time schedule.

The project partners worked in tight collaboration, as testified by common publications, project meetings, exchange of students and researchers for short- and long-term (up to 3 weeks) periods.

The project had a specifically theoretical/methodological character. The fundamental scope was the building of an array of either radically new, or substantially improved and extended methodologies particularly suited for magnetic oxides, for materials with strong electron correlation and for their heterostructures. Those are materials of outstanding conceptual interest, and great potential for novel applications in microelectronics and spin-electronics.

Computational approaches, of the First-principles Density Functional type, and of model Hamiltonian type, were first separately developed and then interfaced to obtain a coherent description of test case materials covering a broad range of properties, from structural, electronic and magnetic properties to finite-temperature transport and thermodynamics. The developed theories were tested in relevant and paradigmatic classes of systems and the results confronted with experimental data or previous theoretical results. All our results confirm that the accuracy of our predictions overcomes, or at least matches, that obtained by precedent approaches, and it exceeds our initial expectations.

In brief, our major achievements include: a) the development of a novel First-principles density functional approach for the calculation of fundamental properties of oxides, which we named the variational pseudo-self interaction correction (VPSIC) method. The VPSIC has been tested on a variety of correlated oxides systems, including bulks, interfaces, and molecules, and implemented in two codes based on different methodological settings, and fully available to the community upon request. b) the development of a fully integrated approach based on the Hybrid Functional approach, as implemented in the VASP code, plus model tight-binding Hamiltonian built in the basis of maximally-localized Wannier-function basis set, as implemented in the Wannier90 code. c) the implementation of a novel model Hamiltonian approach based on the Hubbard-Stratonovich effective-field approach; this extension allows the treatment of the on-site repulsive interactions of the Hubbard model (typically problematic since very time consuming) thus overcoming usual single-band approximation used for the description of double-exchange manganites in the doping range corresponding to the colossal magnetoresistive behaviour. d) the implementation of Lanczos algorithm for the calculation of finite-temperature electronic spectral functions.

The outcome of the projects has been disseminated through talks and lectures given in a number of international conferences, a considerable list of publications spurring from the activity of all partners, (several of them in common), and a final, highly successful school held in Calcutta, which has seen an outstanding participation of students and young scientists, as well as internationally renowned lectures. The project has also established a tight synergy among the partners and close, durable scientific collaborations, which will be further pursued in the near future, possibly involving the hiring of students and post-docs. In summary, we can confidently attest the successful completion of aims and objectives of the ATHENA projects.

Project Context and Objectives:

The overall aim of the project was the investigation, through a synergy of advanced First-Principles (FP), density-functional based (DFT) methods, and Model Hamiltonian (MH) calculations suited for strong-correlated systems (SCS), of the properties and functionalities of transition metal oxides that may be viable candidates as building blocks of future micro- and nanoelectronic devices with enhanced capabilities. Despite the huge effort devoted to the field, a deep and complete understanding of these systems is hard to achieve. On the one hand, this is due to the complexity inherent to the physics of strong-correlated electrons, which includes a plethora of fascinating but overtly complex phenomena (e.g. charge and orbital ordering, polaronic formation, spin-charge separation, non-Fermi liquid behaviour, just to name a few). On the other hand, there is an unquestionable lack of coordinated effort devoted to share, integrate and develop the most advanced and powerful computational techniques nowadays available.

The ATHENA project is aimed at filling this gap by gathering in a synergic collaboration some of the most experienced groups in the subject, equipped with the most advanced methodologies for the theoretical study of strong-correlated phenomena in transition metal oxides. Specifically, the European units assembled vast competence in developments and applications of First-Principles methodologies, whereas the Indian partners are renowned experts on both First-Principles and model-based methodologies. The project pursued the idea of merging these two distinct but complementary viewpoints (First Principles and models) to tackle the study of strong-correlated oxides with the best possible efficiency and completeness.

In synthesis, ATHENAs specifics objectives include:

i) The development of novel or improved First-Principles and model approaches. Developed in the course of the first year of the project, this part was related to the work of WP1 and WP2, aimed at the development, refinement, and testing of both of ab-initio (WP1) and model (WP2) methodologies, the former within the EU consortium, the latter prevalently carried out by the Indian partners;

The outcome of the activity related to First-Principles method developments, carried out by EU partners, was highly successful. Indeed, we can claim that all our objectives in this context are achieved in full, even for what concern their most challenging aspects. We can mention three especially noteworthy achievements, in particular:

a) the development of a variational scheme for the pseudo-self-interaction correction method (VPSIC)

b) the development of a practicable and accurate algorithm for the Exact-exchange method (EEX)

c) the development of the Local Spin-Density plus Dynamical Mean Field Theory (LDA+DMFT).

All those are high-risk, far from standard implementations, whose possible failure could have hardly considered surprising. They required (at least in part) innovative formulations, which now represent, in our view, a solid intellectual and practical (software-type) value produced by the ATHENA project. All these methods are now implemented in efficient parallel-platform based codes (SIESTA, PWSIC, VASP, and other software) destined to enrich remarkably the computational condensed-matter community.

The activity of model Hamiltonian development (mainly carried out by Indian partners) was also highly successful, and allowed the extension of this method to previously untreatable systems. A case in point is the generalization of the double-exchange Hamiltonian (originally conceived for A-site doped perovskites of the ABO3 type with only one 3d eg electron per site at most) to the case of double perovskites, where two species of A-site cations (A and A') and/or transition metal ions (B and B') alternate in space to compose an exceptionally challenging phase diagrams. The new model Hamiltonian formulated by partner HRI was shown capable to describe several interesting aspects of the double perovskite phenomenology, in particular the influence of antisite disorder, that so much affect the properties of these systems favouring the vanishing of long-range magnetization and the transition towards an insulating state.

ii) The integration of First-Principles methods based on Density Functional Theory with many-body Model-Hamiltonian techniques suited for materials characterized by strongly electron correlation. Developed during first and second year of the project, this work is connected with WP2, WP3, and WP4

While general trends as a function of order parameters can be inferred exclusively relying on a model approaches, those are not sufficient to arrive at specific predictions for real systems. The spirit of the ATHENA project is setting up methodologies based on the merging of First-Principles and models, in order to be able to describe the materials phenomenology on a quantitatively predictive basis. The integration of these two major areas of computational materials science represent an outstanding advancement and bring major benefits to both fields: on the one hand, it helps to better understand the pitfalls of conventional Density Functional Theories, elaborate corrective solutions, and complement the zero-temperature description of Density Functionals with thermodynamic and disorder-related properties naturally accessible by model calculations. On the other hand, First-Principles calculations complement the model results with a fundamental understanding of the real materials in the ordered state, and the quantitative determination of parameters at the fundament of model Hamiltonians. The work of Indian members has functioned as guideline for our First-Principles plus model interface implementation.

The integration of First-Principles and model calculations was based on standard downfolding routes, i.e. projecting single-particles band energies calculated through different FP methodologies (VPSIC, Hybrid functionals, Exact-Exchange functionals) onto appropriate localized basis set in order to extract effective parameters suited for models (e.g. the very popular Hubbard Hamiltonians) and largely used by the theoretical community for the study of strong-correlated oxides. For the band downfolding we have followed two procedures: one consists in the transformation of Bloch states into maximally-localized Wannier Functions (MLWF), which is well established, and also simplified by the presence of freely available codes (Wannier90). In this case our work consisted in the creation of a software interface between Wannier90 and the First-Principles codes (i.e. SIESTA and VASP). Another procedure makes use of Lowdin-orthonormalized atomic orbitals instead of WFs, and was implemented in connection with the PWSIC code, which mounts the novel VPSIC approach. Test cases were selected according to guidelines and suggestions of the Indian members, which collaborated on specific application of the integrated First-Principles plus model approach.

iii) The investigation of microscopic mechanisms ruling the coexistence, the coupling, and the competition of magnetic, electronic, and structural properties in the bulk functional oxides. This part of the work was the subject of WP3 activity, devoted to gather the capabilities achieved in WP1 and WP2 and tackle complex problems by a combination of advanced ab-initio plus model Hamiltonian approach.

With the beginning of the work scheduled for WP3, the European and Indian sides have established a tight collaborative action, based on common lines of scientific investigation, which delivered results of strong scientific interest. Our optimised ab-initio plus model Hamiltonian approach equipment of methods and computing codes was applied to the study of the fundamental properties (structural, electronic, magnetic, thermodynamic) of strong-correlated systems. In order to demonstrate capabilities, accuracy, and functionalities of this approach, we have considered important test case materials, typically bulk magnetic oxides, with and without doping included, characterized by complex microscopic behaviour and a rich fundamental phenomenology. Those oxides are enabled with a range of special functionalities (e.g. magnetism, electric polarization, multiferroism, magnetoelectricity, magnetotransport, spin transport, thermoelectricity), which promote them as viable candidates for the microelectronic and spintronic devices of the futures.

Specific examples include a long series of magnetic materials: MnO and NiO as prototype of Mott-Hubbard insulators, CaMnO3 and LaMnO3 as parent compounds of colossal-magnetoresistive systems, the doped multiferroic perovskite PrxCa1-xMnO3, the double perovskite LaNi1-xMnxO3, diluted magnetic ferroelectrics, magnetic titanates YTiO3 and LaTiO3 as paramount examples of t2g electron systems. This excursus allowed us to achieve a thorough understanding, from a rigorous microscopic perspective, of the complicated mechanisms ruling the physics of these systems.

iv) The phenomenology of oxides heterojunctions, superlattices and multilayers designed to exploit and manipulate the coupling of different order parameters at the two sides of the interface. This work was entirely related to the objectives of WP4.

Oxide-base heterostructures are predicted to be the building blocks of a novel microelectronic age, due to their visionary functionalities enabled by the coexistence and interplay of orbital, charge, magnetic, and structural degrees of freedom at the interface. Several remarkable examples were thoroughly investigated during the WP4 activity, covering an extremely rich and vast phenomenology: the multiferroic tunnel junctions SrRuO3/BaTiO3/SrRuO3 and SrRuO3/SrTiO3/BaTiO3/SrRuO3, showing both magnetoresistance (MR) and tunneling electroresistance (TER); the spin-valve multilayers Fe/BaTiO3/Fe and Fe/MgO/BaTiO3/Fe with above-room critical temperatures, thus holding a real commercial potential; the LaNiO3/LaAlO3 superlattice, which offers a template to study controllable strain effects on the magnetic and transport properties of 2D oxides; the multiferroic and magnetoelectric (Insulator)/(LaMnO3)n/(SrMnO3)n/(Insulator) superlattice; the superconducting CuO/SrTiO3 interface.

The outcome of this extended investigation showed a substantial agreement with the experiments finding (whenever available), thus demonstrating the capability of our First-Principles plus model approaches to deliver quantitative predictions for a broad range of low-dimensional systems.

Deliverables and timing:

The work related to all the tasks of the four scientific workpackages was completed according to the original schedule, and all the deliverables were released according to the planned scientific action, with the only exception of Deliverable 2.4 originally planned at first year and delayed to the third year. No major difficulties or unforeseen drawback occurred during the duration of the project.

Project Meetings and exchange visits

Three intra-European meeting have been organized in Europe, plus a number of individual visits among the partners, functional to a dense schedule of collaborative work. Furthermore, three European-Indian project meeting were organized in India at the Indian Partners locations (Allahabad at month 6, Bangalore at month 18, Kolkata at month 35), attended by all the ATHENA members; these meetings were preparatory to specific collaborative plans between European and Indian members, and central to the work of WP3 and WP4. Two M18 review meetings, one held in Bruxelles in January 2011 (EU review) and the other in Bangalore in February 2011 (Indian DST review), were held. A dense calendar of student/post-doc reciprocal exchange visits among European and Indian Institutes (long up to 3 weeks) were activated. Finally, in April 2012 a highly successful ATHENA school were organized in Kolkata; the school, attended by about 50 among students and post-docs, was aimed at disseminating at the most foreground level themes and results developed during the project.

Partnership and Outcome

We believe that our EU-India collaboration will have the highest impact from both scientific and societal viewpoint, insofar as it implied development and sharing of knowledge, as well as human and technological resources.

From a technological viewpoint, the ATHENA project developed and released an outstanding armamentarium of computing tools, innovative methodologies, and experience in several areas of theoretical condensed matter, providing an unprecedented bulk of knowledge and understanding. This scientific activity was carried out in close synergy among the partners. The partnership resulted in a series of important common publications.

From the societal viewpoint, the EU-India integration allowed a series of long-term student/post-doc exchange visits which, beside the ordinary scientific output, will be also fruitful in the long run, as it will likely result in further collaborations which will be likely extended well beyond the 3-years limit of the project, and possibly in future hiring from EU groups of personnel coming from Indian partners. The successful outcome of the project was scientifically and socially celebrated by the end-of-project school, held in Kolkota in April 2012.

In summary, the majority of results obtained by the ATHENA project indicate that our work succeeded in delivering practical routes to the description of complex systems, overcoming the well-known limitations of standard Density Functional Theory approach commonly practiced so far. We expect that the outcome of our work will carry a tremendous potential impact in terms of fundamental knowledge of materials as well as applicative tool for prediction and design of systems with device capabilities, and as such it may impact the work of academy and industrial research alike.

Project Results:

The objectives of the project are grouped in 4 Workpackages. WP1 and WP2 were completed within the first year of the project, WP3 in the second and WP4 in the third. In what follows we report the description following the WP structure as originally listed in the Annex I of the GA.

WP1: Methodological development: First-Principles calculations.

Objectives and overall description

The objective of WP1, accomplished in synergy by the three EU members, consisted in the improvement, refinement, and confrontation of various First-Principles (FP) methodologies based on density-functional theory (DFT) and capable to deal with strong-correlated electron systems: namely the pseudo-self-interaction correction (PSIC), the hybrid functional approach (HSE), the local spin density functional plus dynamical mean-field theory (LSDA+DMFT). Part of the work was also devoted to improve the efficiency of available codes, e.g. the PWSIC and SIESTA codes which mount the PSIC approach, and the VASP codes performing HSE calculations. Our final aim was assembling the most effective array of FP-based computational techniques for the application to magnetic oxides and their properties. The WP1 has fully achieved its objectives. In brief:

A novel variational pseudo self-interaction corrected local density approach (VPSIC) was formulated and implemented in two versions: a) plane-wave plus ultrasoft pseudopotentials basis set in the framework of the PWSIC code; b) local-orbital plus norm-conserving pseudopotentials basis set implemented in the SIESTA code. The VPSIC was tested against the highly reliable hybrid HSE theory, implemented in the VASP code. Our work related to the Milestone at month 12 concerning the relative efficiency and the accuracy of the various FP approaches, certificate that a solid agreement between HSE and VPSIC results on the most fundamental aspects of various test materials was evidenced.

The compared approaches showed different inclinations, which make all of them worthy to be selectively applied according to the specific case: the fast and memory-cheap VPSIC/SIESTA implementation is especially useful for large-size systems and molecules; the computationally heavier VPSIC/PW is quite accurate for electronic properties and suited for smaller but highly complex orbital- and/or charge-ordered (OO/CO) systems; the HSE is the main reference for accuracy for both electronic and structural properties but it requires about an order of magnitude increase in computing effort with respect to VPSIC/PW.

Finally an approach based on local density plus dynamical mean field theory (LDA+DMFT) has been developed and tested as well. This approach, which includes dynamical correlation effects into the electronic properties, in principle overcomes VPISC and HSE in accuracy, although the extreme computational effort required by the method limits the applicability to small bulk systems. Given its recognized accuracy, it is the ideal approach for the determination of tight-banding parameters functional to the construction of model Hamiltonians.

Task 1.1. PSIC approach: development and parallel coding.

Improvements of the pSIC method: calculation of forces, implementation of the parallel version of the code, eventual generalization of the single-particle functional and search of alternative, possibly variational schemes. Test cases on metallic and insulating systems. Comparison with other approaches.

This task was fully successful even in the most challenging aspect, i.e. the search for a variational generalization of the pSIC approach. Indeed, a new variational pseudo-self-interaction correction approach (VPSIC) was formulated. The new method works as efficiently as the former (non-variational) for the electronic properties of generic crystalline systems, but in addition it allows the straightforward calculation of atomic forces (hence structural optimisation), clearly not attainable by the former non-variational version. The VPSIC was implemented in two different methodological setting: ultrasoft pseudopotential and plane-wave basis set (i.e. in the PWSIC code) by partner CNR; atomic-orbital local basis set (in the framework of SIESTA code) by partner TCD. Notice that SIESTA and PWSIC are highly complementary, insofar as, despite being both applicable to generic systems, they may be more efficient for different subjects (SIESTA for very large-size systems and molecules, PWSIC for periodic systems characterized by highly complex fundamental chemistry, including e.g. OO/CO states, polarons, mixture of localized and dispersed band energies).

The PWSIC code, previously available in serial mode only, has been modified in order to run on parallel platforms as well. The SIESTA code is fully optimised in parallel version. A full assessment of the VPSIC functional was carried out in synergy by TCD (for what concerns the SIESTA implementation) and CNR (for PWSIC implementation). Test cases have been produced for several magnetic titanates (YTiO3, LaTiO3) and manganites (LaMnO3), as well as non-magnetic oxides (SrTiO3, LaAlO3, TiO2 in Figure 1 of the Attachment). A close comparison with the hybrid functional approach (HSE) developed by Univie was also carried out, with very satisfying results, for structural, electronic, magnetic and thermodynamic properties of some transition metal monoxides MnO and NiO.

Results related to the development and testing of the VPSIC approach represent the basis for Deliverable D1.1 at month 12, The compared analysis of VPSIC and HSE results for TMO is basic for the work of Deliverables D3.123-1 and D3.123-2 due to M18, as well as instrumental to the resolution of Milestones M12 and M18.

Task 1.2: Hybrid functional and GW methods: development and testing.

Development and applications of HFT and HFT+GW methods to strong-correlated systems. Comparative analysis with other approaches. Test cases. (3-Univie).

Task 1.2 is fully accomplished. The hybrid functional theory in the HSE version, already implemented in the VASP code, was applied by partner Univie to a series of complex correlated oxides, and its efficiency and accuracy carefully checked and improved throughout a systematic comparison with the available experimental data. The implementation of several GW-based schemes was also finalized, and test cases carried out for a wide class of 'simple' compounds as well as for more complex materials such as CuO and BaBiO3. In order to achieve a better description of optical and electronic properties of the most challenging materials, we have optimized a scheme, which allows the combination of GW on top of pre-converged HSE wavefunctions.

A close comparison with the VPSIC approach developed in a tight collaboration among Univie, CNR and TCD members was put forth, with satisfying results, for the electronic and magnetic properties of transition metal monoxides (TMO) MnO, NiO, and CuO (see Figure 2 of the Attached PDF). Results related to the development and testing of HSE approach in the VASP framework are included in the Deliverable D1.2 due at month 12, The compared analysis of VPSIC and HSE results for TMO is reported in the Deliverables D3.123-1 and D3.123-2 due to M18, and central to the resolution of Milestones at month 12 and 18.

Task 1.3: LDA+DMFT approach: development and testing.

Development and applications to strong-correlated systems. Comparative analysis with other approaches, and test cases. (1-TCD,2-CNR).

The LSDA+DMFT approach combines DFT-LSDA [or generalized gradient approximation (GGA)] with dynamical mean-field theory (DMFT) for the treatment of strong electron correlation beyond the single-particle level. In practice the method interfaces existing DFT codes with a Quantum Monte Carlo impurity solver and a DMFT loop. From the full electronic structure calculated by DFT a subset of Wannier Functions (WF) relative to the most important strong-correlated states are extracted. These WFs are then used to formulate an effective lattice problem treated within DMFT. A new code has been written to calculate the dynamical mean-field, which described the effective bath for the single site problem, from the WFs. The Greens function of the resulting impurity problem is then calculated using an existing Quantum Monte Carlo code, and the resulting self-energy is used to construct a new estimate for the dynamic mean-field. The procedure is iterated until convergence is achieved. An additional code has been written to implement this self-consistent loop. This requires multiple transformations from the imaginary time formulation used by the Quantum Monte Carlo method to a formulation using Matsubara frequencies used to calculate the local Greens function and self-energy. Another code has been written to extract the electronic spectral function from the converged Greens function using the Maximum entropy method.

The schematic workflow of the method is illustrated in Figure 3 of the Attachment. Test calculations were performed to evaluate the stability and performance of the resulting computational scheme. Applications to selected prototype systems have been carried out, including benchmark system SrVO3, as well as p-electron magnet RbO2 and multilayer SrRuO3/CaRuO3. These results are the basis of Deliverable D1.3 due at month 12.

WP2: Model Hamiltonians and merging with First-Principles calculations

Overall description

Indian partners mastered a formidable array of computational tools based on model Hamiltonians ideal to investigate the coupling of charge, spin, orbital and lattice degrees of freedom in strong-correlated systems. These methods are capable to handle disorder and finite temperature effects, as well as spectral functions/dynamical response. However, in order to be predictive for real materials whose fundamental characteristics are not known from the beginning, or differ from ordinary situations, models need guidance and connection with First-Principles methods.

WP2, lead by Indian partners, was aimed at the development and integration of models and First-Principle methods elaborated in WP1. The construction of model Hamiltonians, carried out in particular by partner HRI, focused on specific phenomenologies (examples are B-site doped and double perovskites) to be then studied in detail in WP3 and WP4. In parallel, the development of downfolding procedures aimed at interfacing generic band spectra spurring from First-Principles calculations with the abovementioned model Hamiltonians was accomplished by several groups in the framework of different First-Principles codes (Univie for VASP, CNR for PWSIC, TCD for SIESTA). Those downfolding interfaces are either written from scratch or adapted from previously existing codes (such as, e.g. the Wannier90 code which constructs maximally localized Wannier Functions on the basis of First-Principles calculated single-particle Bloch states). They typically allow the determination of those essential parameters (typically hopping and on-site Coulomb energies) on which the fundamental phenomenology of magnetic and strong-correlated systems crucially depends.

The model Hamiltonian development carried out by HRI mainly relies on the strategy called Traveling Cluster Monte Carlo (TCM), an O(N) method, which can be applied to model systems of up to N~103 lattice sites (note that the scaling is linear, so that the maximum size of the system to investigate is simply limited to the computational resources available). The method solves Hamiltonians with a combination of (few) quantum degrees of freedom (typically related to eg orbitals), coupled to several classical parameters (e.g. JT displacements, t2g spins, etc.) and gives access to both ground state and finite temperature properties (transport, spectra, optics) at arbitrary coupling, including disorder. Notably the scheme fails if finite on-site Coulomb (U) interaction is introduced (at the mean field level the same scheme is possible but it becomes computationally extremely heavy). In order to circumvent the problem, HRI proposed a strategy based on the introduction of a Hubbard-Stratonovich effective field which accounts for the electronic coupling through the introduction of a classical field variable ?(x, t), thus making the TCM approach still applicable. In the following a concise description of the planned tasks of WP2 related to the downfolding procedures is reported.

Task 2.1: Merging FPC and MH: development and integration of HFT and HFT+GW with MH methods.

Development of an integrated FPC (HFT and HFT+GW implemented in VASP) plus MH scheme, and relative code implementation. Testing successful implementations on bulk materials (typically bulk manganites or transition metal oxides). (5-HRI, 3-Univie, 4-SNBNCBS).

Task 2.1 is devoted to the implementation and testing of a software interface between hybrid-functional (specifically the HSE version) plus GW calculations as implemented in the VASP code, and the model (Hubbard) Hamiltonian approach. This interface performs the construction, starting from HSE+GW-calculated electronic eigenstates, of the corresponding maximally localized Wannier functions (MLWF), according to the prescription of Marzari and Vanderbilt [Phys. Rev. B 56, 12847 (1997)], as implemented in the Wannier90 code, and the subsequent mapping into suitable tight-binding (TB) parameters. Since MLWF are defined in real space, they are in principle ideally suited to map the electronic ground state of the system in the real-space representation typical of model Hamiltonian; the MLWF matrix elements can be interpreted as hopping amplitudes within a TB picture. By constructing MLWF for a (small) set of bands suitably selected in a physically important energy window, one can construct a TB model, which reproduces the exact band dispersion, thus forming the basis for a model Hamiltonian analysis. In Figure 4 of the Attachment a scheme of the Method is reported.

In practice, the Wannier90 code requires as input (a) the overlap matrix elements between the cell periodic part of the Bloch states and (b) the initial projections of the Bloch states onto trial localized orbitals. The passage of these two ingredients from VASP to Wannier90 is operated by the newly written VASPtoWANNIER90 interface, now available in the VASP package for all members of the consortium. The interface is also included in the latest official release of the VASP package. Several test-case applications to e.g. MnO, LaMnO3, and graphene were carried out to prove the functioning of the method. The MLWF downfolding procedure was shown to be a solid approach to connect First-Principles and model Hamiltonians, and our results certificate the confidence in the method.

The VASPtoWANNIER90 interface included in the latest VASP official release package matches the software/object Deliverable 2.1 due at M12.

Task 2.2: Merging FPC and MH: development and integration of PSIC with MH methods.

Development of an integrated PSIC (implemented in PWSIC) plus MH scheme, and relative code implementation Testing successful implementations on bulk materials (typically bulk manganites or transition metal oxides). (5-HRI, 2-CNR, 4-SNBNCBS, 6-JNCASR).

The work of Task 2.2 was addressed to write an interface software added to the PWSIC code which mounts the new variational VPSIC approach developed in Task 1.1 to derive parameters necessary to build model Hamiltonians through band downfolding procedures. Two routes have been followed: the first performs the band manifold projection onto a Lowdin-orthonormalized atomic orbital (OAO) basis set. In this way a full set of tight-binding parameters is generated, including hopping and on-site energies, which can be directly transferred to a model Hamiltonian setting. The second is based on interfacing PWSIC and the Wannier90 code, analogously to what is done in Task 2.1 for VASP and Wannier90, in order to derive MLWF-based tight-binding parameters.

For what concerns the OAO-based downfolding procedure, we have performed a test calculation regarding the prototypical correlated Mott perovskite LaMnO3, in its antiferromagnetic, orbital-ordered, orthorhombic Pnma equilibrium structure, for which it is well known that only oxygen-mediated hopping between nearest-neighbor eg orbitals are substantial. We obtain results in agreement with other available downfolding approaches (such as the one based on MLWF), thus showing that the combined VPSIC+OAO downfolding procedure can produce reliable parameters for setting efficient Hubbard model Hamiltonians. Test cases for the PWSIC/Wannier90 interfaces have been also carried out for magnetic titanates (LaTiO3 and YTiO3), which are extremely interesting prototypes of t2g orbitals compounds.

The OAO-downfolding subroutine and the PWSICtoWANNIER90 interface are both included in the freely available PWSIC developmental version, and represent the software/object Deliverable 2.2 due at M12.

Task 2.3: Merging FPC and MH: development and integration of ASIC and EE with MH methods.

Development of an integrated ASIC and EE (implemented in SIESTA) plus MH scheme, and relative code implementation Testing successful implementations on bulk materials (typically bulk manganites or transition metal oxides). (6-JNCASR, 5-HRI, 1-TCD, 4-SNBNCBS).

The work of this Task proceeded along different directions, consisting in several code developments and testing, in the framework of the SIESTA code. Code development has been achieved in full, and the related software (ASIC and EE in SIESTA, and SIESTA-MH interface) is now ready to be used. Test cases assessing the quality of the codes are completed for the materials of relevance to the project. In the following we discuss the achievements of the task for each methodological development.

Full self-interaction correction (SIC) and Exact Exchange (EE) approach implemented in SIESTA.

In addition to the mean-field-like VPSIC scheme implemented in SIESTA (Task 1.1) a fully self-consistent version of the SIC-LDA functional, as originally proposed by Perdew and Zunger requiring the handling of a truly orbital-dependent functional, was also implemented in SIESTA. However, this is only available for finite systems and cannot be used for crystalline solids (unless they are cast in a finite cluster form). In brief our SIC-LDA implementation is based on the optimized effective potential (OEP) concept. Here an orbital dependent potential is recast, by variational principle, into an effective local functional leading to the same ground-state charge density and energy as the original orbital dependent functional. This is a common strategy used both for the SIC-LDA and the DFT exact exchange (DFT-EE) functionals (see next section). Also common to both SIC-LDA and DFT-EE is the reduction of the non-linear integral OEP equations to a set of linear equations, which can be solved by simple linear algebra. This is known as the Krieger-Li-Iafrate (KLI) method. Specific of the SIC-LDA method is the necessity of constructing the local potential from a set of localized orbitals related to the Kohn-Sham eigenfunctions by a unitary rotation, thus leaving the electron charge density invariant.

At variance with SIC-LDA, the DFT-EE functional is applicable to periodic system. The strategy closely follows that for the SIC-LDA scheme: the overall formulation is based on OEP and the problem is solved only approximately through the KLI scheme. Crucial to the Siesta implementation is the reduction of the 4-centre integral defining the EE potential to simplified 3- and 2-centre integrals. This effectively allows to achieve a computing cost scaling as N*nA4, instead of (N*nA)4 (where N is the number of unit cells and nA the number of basis functions per unit cell).

Mapping DFT to MH in Siesta

A tool for building maximally localized WFs from SIESTA-calculated band energies is now available [see R. Korytár et al. arXiv:0910.1748]. This has been constructed independently by the SIESTA team and essentially consists in an interface with the Wannier90 code [see wannier.org]. Importantly, the existing code is also interfaced with our private version of SIESTA, which includes ASIC, VPSIC and DFT-EE. Thus, the consortium members have now the capability of constructing MLWF from band energies calculated through a vast array of different functionals and of directly mapping the band energies obtained with these functionals onto know model Hamiltonians.

Test Cases

Several tests were performed to assess the correctness of the newly implemented DFT-EE functional for: 1) bulk solids, 2) supercells, 3) surfaces, and 4) molecules adsorbed to surfaces; while tests on the mapping of SIESTA band energies onto model Hamiltonians were carried out for MnO and RbO2.

For bulks, the DFT-EE give band gap in substantial agreement with the experiments, thus largely improving the LDA values. For supercells, the N*nA4 scaling of the code with the number of atoms has been demonstrated. As for surface properties, with the new DFT-EE scheme we have studied the Si (100) surface, which contains a well-known surface state splitting off from the Si bulk conduction band. The ~0.7 eV bandwidth of this surface state was perfectly reproduced. Furthermore such a surface state is offset by about 0.7 eV from the Si valence band, in agreement with experiments and at variance with the underestimated LDA/GGA offset of 0.4 eV. Finally we tested the DFT-EE scheme for molecules weakly coupled to metallic surfaces, in order to demonstrate the presence of the derivative discontinuity of the DFT potential in the EE approximation.

Task 2.4: Implementation of Lanczos algorithm for calculation of finite temperature spectral functions.

Calculation of relevant spectral functions for resonant x-ray scattering, especially at the transition metal L edge where both single particle effects as well as Coulomb interactions have to be handled simultaneously. The low temperature spectral functions will be calculated by finite temperature Lanczos algorithm. (4-SNBNCBS).

Task 2.4 (and its related Deliverable 2.4) has been partially accomplished since the method so far is implemented only for the case of zero-temperature; the development finite temperature algorithm is currently in progress at the Indian unit SNBNCBS, and it will be completed during the one-year no-cost extension of the Indian side of the consortium. We emphasize that this task is a single-participant beneficiary (Indian partner SNBNCBS) with a minimal connection with the rest of the project (i.e. it does not affect any deliverables subsequent to those of WP2), thus the delay had no impact either on the overall achievement of the Project objectives or on the resources originally planned.

The reason of the delay resides in the necessity for partner SNBNCBS to give priority to the development of software more directly preparatory to the common activity of European and Indian groups, rather than to the achievement of more individual interests. In the following we briefly describe the abundant code development carried out by SNBNCBS in the framework of Task 2.4.

Mean field decoupling of most general Coulomb interaction (SNBNCBS)

The most general form of the four-fermion Coulomb operator is evaluated for both p and d electrons. A computational scheme was implemented to carry out the mean-field decoupling and calculate the order parameters self-consistently. Such an implementation was carried out to treat a class of charge ordered ferromagnets and alkali metal oxides (both discussed later in applications).

Non perturbative determination of exchange interaction strengths (SNBNCBS)

The recent interest of the magnetism community has focussed on understanding the possibility of a magnetic order in p-shell materials. In this context, one desires a computational tool, which allows calculating the exchange interaction as the magnetic order of the p ions is altered. Unfortunately for these systems a perturbative approach fails. We have then implemented a non-perturbative treatment for determining the exchange paths, and subsequently applied to various p shell magnets.

Determination of magnetic anisotropy constants and spin-orbit interaction (SNBNCBS)

We implemented a computational scheme to determine the anisotropy constants for strongly correlated materials from model calculations. Similarly we implemented a model Hamiltonian based on the tight-binding formalism, which includes spin-orbit interaction. This is suitable for the description of 5d oxides.

Building the full multiplet Hamiltonian (SNBNCBS)

We built a full multiplet Hamiltonian, and solved it in within a mean-field decoupling for treating non-collinear magnetism. This opened the route to a more rigorous treatment of magnetism and an understanding of magnetization mechanism in greater detail.

WP3: Fundamental properties of bulk doped magnetic perovskites and transition metal oxides.

Objectives and overall description

This workpackage gathers together all the methodological capabilities and computational advancements spurred from WP1 and WP2 to attack the study of systems of interests, i.e. mainly magnetic oxides, with special emphasis on (doped/undoped) magnetic manganites and transition metal oxides (TMO). A comparative analysis of results obtained with different methodologies is aimed at tracing a rigorous account of the microscopic features of these systems in order to describe structural, electronic, and magnetic properties, as well as finite-temperature thermodynamic and transport properties, and phase diagrams as function of doping.

WP3 was scheduled to cover the whole 2nd year and a portion of the 3th year of the project. As expected and planned, WP3 required a huge amount of work and an intensive collaborations among the various EU and India members, which resulted in several published works and others currently submitted for publication.

Task 3.1: Study of Colossal-magnetoresistive Magnetic Perovskites by integrated FP+MH approaches.

M12-M24

Study of the fundamental properties of CMR manganese perovskites (e.g. LCMO, LSMO) and insulating manganese perovskites (e.g. Pr1-xCaxMnO3) carried out within FPC+MH approaches, where FPC may include PSIC, HFT (or HFT+GW), DMFT and EE. Investigations of electronic, magnetic, and structural properties both at equilibrium and under strain, as well as thermodynamic properties. Comparison with the available experimental results and previous theoretical results. (2-CNR, 5-HRI, 6-JNCASR, 3-Univie, 1-TCD).

The work inherent to this task, devoted to generic applications of the First-Principles plus model Hamiltonian approach to magnetic oxides is especially abundant and articulated, since all partners have largely contributed to it. The original proposition included as test materials well known A-site doped manganese perovskites families (LCMO and LSMO), and indeed an abundance of work was produced for those systems and their undoped parental compounds (i.e. CMO, LMO). On the other hand, the work also explored other magnetic oxide families, which gained special interest in recent times. This includes magnetic titanates (governed by 3d t2g electrons instead of the 3d eg types as in manganites) and the so-called superoxides (e.g. RbO2) where long-range magnetism can be induced by doping. The extension of our materials of interest is motivated by the need to verify the suitability of the methods set in the work of WP1 and WP2 for an as large as possible variety of applications.

A list of works inherent to this task include:

a) Study of undoped LaMnO3 carried out by hybrid functional HSE and GW, by partner Univie. This includes the determination of ground-state structural, electronic and magnetic properties, and the study of pressure-induced quenching of the cooperative Jahn-Teller (JT) distortions and the suppression of the orbital ordering leading to an insulator to metal transition accompanied by magnetic transitions. The very expensive First-Principles calculations with a variety of functionals (PBE, HSE and GW), and the full Tight-Binding parametrization, which is the essential ingredient for the model Hamiltonian analysis, were both accomplished.

In the framework of a collaboration involving partners Univie, HRI and TCD, the evolution of the spin- and orbital-ordered states in RMnO3 (R=La,Pr,Nd,...) by combined First-Principles plus model Hamiltonian approach was investigated. More specifically, we have determined the effect induced by a progressive decrease of the R-ion atomic radius on a) the enhancement of the cooperative GFO-like rotation of the MnO6 octahedra and the associated decrease of the Mn-O-Mn bond angle; b) the modulation of superexchange interaction between next-nearest Mn sites; c) the enhancement of the insulating character; d) the changes of the Jahn-Teller ordering temperature. In Fig.5 of the attached PDF file the effect of pressure on the Mn-O distances of LaMnO3 is reported.

b) Study of doped Ba1-xKxBiO3 (BKBO) by hybrid functional HSE. Carried out by partner Univie. The study of electronic and structural properties of this charge-ordered (CO) compound (with alternating Bi3+ and Bi5+ ions) was carried out in a wide range of A-site doping concentration, in order to investigate the interesting phase transition occurring from the insulating state at low-doping to the superconducting state at high doping. The properties change with hole doping are understood in terms of stabilization/interaction of bi-polarons consisting on Bi3+ ? Bi5+ plus local breathing distortions transformations occurring upon Ba? K substitutions. In Fig.6 of the Attachment the calculated and experimental volume is showed as a function of the k-dopant concentration, together with the indication of structural and transport phase stability at any doping.

c) Magnetism in 4d perovskites RTcO3. Carried out in cooperation by partners Univie, TCD & CNR. The evolution of the magnetic ordering temperature of the 4d3 perovskites RTcO3 (R=Ca, Sr, Ba) and its relation with electronic and structural properties was studied by means of hybrid density functional theory and Monte Carlo simulations. When compared to the most widely studied 3d perovskites the large spatial extent of the 4d shells and their relatively strong hybridization with oxygen weaken the tendency to form Jahn-Teller like orbital ordering. This strengthens the superexchange interaction. The resulting insulating G-type antiferromagnetic ground state is characterized by large superexchange coupling constants (26-35 meV) and Néel temperatures TN (750-1200 K). These monotonically increase as a function of the R ionic radius due to the progressive enhancement of the volume and the associated decrease of the cooperative rotation of the TcO6 octahedron. See Figure 7 of the Attachment for the results concerning calculated critical temperature and exchange interactions calculated as a function of the Tc-O-Tc angle.

d) Study of undoped magnetic titanates YTiO3 and LaTiO3 by VPSIC method. Partner CNR carried out the study of structural, electronic and magnetic properties of these two prototypical Mott insulators, with results in nice agreement with the observations, thus demonstrating the good accuracy of the variational VPSIC developed in the work of Task1.1.

As an example, in Fig.8 of the Attachment the calculated magnetization isosurface is showed for both systems, from which we can appreciate the ferromagnetic and antiferromagnetic ordering of YTO and STO, respectively, as well as their different orbital ordering: checkboard for YTO, ferro-orbital for LTO. Magnetic and orbital ordering depend on each other according to the superexchange rules. Our results nicely agree with previous theoretical results based on dynamical mean field, and with available photoemission experiments.

e) Electronic structure of Ferromagnetic Insulator K2Cr8O16. Accomplished in collaboration by partners SNBNCBS & Univie. Ferromagnetic insulators are rare in nature and the microscopic mechanism for their magnetic order is usually different from that invoked to explain ferromagnetism in metals. We studied the prototypical ferromagnetic insulator K2Cr8O16 within First Principles electronic structure calculations. Our work demonstrates that charge ordering transition is responsible for the insulating phase. Charge ordering is induced by K-doping and it is found to generate a super-exchange pathway that allows ferromagnetism to be stabilized. Calculations have been carried out with the LDA+U scheme, to account for on-site Coulomb repulsion at the Cr sites. The density of states of the ferromagnetic insulator K2Cr8O16 is presented in Fig.9 of the Attachment.

f) Magnetism in p-shell compounds: KO2 This work was realized by partner SNBNCBS. The community, which investigates magnetic materials showed a revival of interest for p-type magnetism, i.e. magnetism present in magnetic materials devoid of ions with partially filled d or f shells. Most of the effort has been devolved to defective oxides where defects can present an electronic structure sustaining a high spin state. However, we have identified an entire class of stoichiometric materials made of alkali-metal oxides, which can sustain a magnetic order. The elementary unit for such materials is the O2 molecule, whose ground state is a spin triplet. The long-range magnetic order however is the result of a subtle interplay between narrow band splitting and orbital ordering. In particular for the case of KO2 we find that orbital ordering (see figure) driven by electrostatic interaction precludes the possibility of high-temperature ferromagnetism. [Phys. Rev. Lett. 105, 056403 (2010).] The charge density isosurface of KO2 can be found in Fig.10 of the Attachment. Note that this work was related, and benefited from, a similar investigation carried out by TCD on RbO2 [Phys. Rev. B 86, 075130 (2012); Phys. Rev. B 80, 140411(R) (2009)].

g) Dual behaviour of excess electrons in TiO2. Carried out by partner Univie. Seemingly conflicting results have been reported for the behavior of electrons in TiO2. While high mobility have been observed, characteristic of delocalized electrons in the conduction band, excess electrons in TiO2 have long been described as localized small polarons. In this study we reconcile this apparent contradiction by showing that small polarons can coexist with delocalized electrons, and the dominant behavior depends on the type of experiment being conducted. By means of hybrid functional calculations we find that small polarons are energetically only slightly more favorable than delocalized electrons in n-type TiO2. The small polarons explain the optically-detected gap state near the conduction band, whereas the delocalized electrons give the high mobility observed in Hall measurements. We also find that small polarons can form complexes with oxygen vacancies and ionized shallow-donor impurities, explaining the rich spectrum of Ti3+ species observed in the electron paramagnetic resonance experiments. See Fig.11 in the Attached file.

h) Cation site-disorder, magnetic ordering and phonons in FeAlO3. Carried out by partner JNCASR. FeAlO3, reported to have ferrimagnetic and piezoelectric properties, has cation sites with both tetrahedral and octahedral coordination. Motivated by the rich set of its observed properties, we use first-principles density functional theory based calculations to determine the coupling between cation (Fe-Al) site-disorder and its magnetic ordering and vibrational properties. Using microscopic information available from our calculations, we investigated the possibility of magneto relaxor behavior with Ga substitution at the Al site. This work is in collaboration with experiments of C.N.R. Rao, A.K. Sood and A. Sundaresan at JNCASR. See Fig.12 in the attached file.

Task 3.2: Study of multiferroic magnetic perovskites and interplay of magnetic and electric polarization. M12-M24.

Study of ME coupling in MP: coexistence of CMR and CER effects (e.g. in Pr1-xCaxMnO3), and alternative forms of multiferroicity in MP. Investigations carried out within FPC+MH approaches, where FPC may include PSIC, HFT (or HFT+GW), DMFT and EE. Comparison with the available experimental results and previous theoretical results. (6-JNCASR, 1-TCD, 2-CNR, , 4-SNBNCBS, 3-Univie)

The study of magnetoelectric (ME) coupling in manganites in half-doped perovskites. Carried out by partner CNR. We investigated Pr1-xCaxMnO3 at half-doping (x=1/2), since at this concentration some form of ME behaviour was expected according to model calculations. VPSIC calculations of the electronic and magnetic properties of Pr1/2Ca1/2MnO3 indeed detected an electric polarization (P) in the insulating AF-CE magnetic phase, induced by the Pbnm ? P21nm structural distortion and the relative change in orbital ordering. The calculated P is purely electronic (i.e. Berry-phase determined) in the direction parallel to the spin-aligned chain direction, structurally determined orthogonally to the chains. See Fig.13 of the Attached file. The results related to this task have been published in Ref. G. Colizzi, et al, Phys. Rev. B 82, 140101(R) (2010). This work is also subject of Deliverable 3.2 due at month 24.

5) Use of Raman spectroscopy as a tool to find route to metal-insulator transition in Magnetoelectrics (JNCASR). Raman spectroscopy is a highly versatile and effective tool for the exploration of both bulk and nano-scale materials. We determined how a clear pathway to a metal-insulator transition in magnetoelectric materials is reflected in the anomaly of their Raman spectra, second order Raman spectral peaks being unexpectedly more pronounced than the first order ones. Using a combination of experiment and first-principles simulations, we demonstrate this behavior in a magneto-capacitive double perovskite La2NiMnO6, and in a well-known multiferroic BiFeO3. In the latter, our theory connects with an integer quantum ambiguity in polarization associated with path-dependent geometric phase, which often leads to puzzling interpretations of observed and theoretical values of polarization of multi-ferroics. Our work opened up the use of Raman spectroscopy in identifying the structural paths that lead to metal-insulator transitions that are fundamentally relevant to technological applications. This work was realized in collaboration with experiments of A.K. Sood and A. Sundaresan at JNCASR Institute.

Task 3.3: Study of diluted magnetic ferroelectrics by MH and FP+MH approaches.

M12-M24

Structural, electronic, and transport properties will be studied for the most promising diluted magnetic ferroelectrics through MH and FPC+MH approaches. Comparison with available experimental results and previous theoretical results. (4-SNBNCBS, 1-TCD)

In order to overcome the problem of the scarcity of multiferroic and magnetoelectric materials, one possible route is to plug into a ferroelectric host some magnetic dopants. Achieving a multiferroic system is however far from obvious, since the specificity of doping atomic species and the chemical environment surrounding the dopant must be fortunate enough to allow long-range magnetic ordering.

To explore this possibility in this task we studied the inclusion of magnetic atoms into a well-known ferroelectrics, BaTiO3, with inclusion of Ti-substitutional V and Mn at doping concentration of 5%. Ferroelectricity was found to be favored in the case of V and Mn doping in the GGA+U calculations. In the HSE calculations we found that all the doped transition metal atoms gave rise to filled impurity bands in the band gap of BaTiO3. Hence, ferroelectricity was found to be favored in all cases. This work is also the subject of Deliverable 3.3 due at month 24.

Task 3.4: Study of double perovskites: setting innovative MH and merging with FPC.

Period: 12-24

Construction of MH and then a many body/finite temperature theory, for the study of ground state, transport and thermodynamic properties of doped double perovskites by FPC (PSIC, HFT, HFT+GW) +MH approach. Comparison with available experimental results and previous theoretical results. (4-SNBNCBS, 5-HRI, 6-JNCASR).

Antisite disorder and domain formation in double perovskite ferromagnets A2BCO6 (e.g. La2NiMnO6, Sr2FeMnO6). Several double perovskite materials of the form A2BBO6 exhibit high ferromagnetic TC, and significant low field magnetoresistance. They are also a candidate source of spin-polarized electrons in spin-injection devices. The potential usefulness of these materials is, however, frustrated by misallocation of B and B ions, which are not ordered in the ideal alternating structure. The result is a strong dependence of the physical properties on preparative conditions, which reduces the magnetization and destroys the half-metallicity. Partner HRI provided the first study of the impact of spatially correlated antisite disorder (ASD), as observed experimentally, on the ferromagnetic double perovskites. The ASD suppresses magnetism and half-metallicity, as expected, but lead to a dramatic enhancement of the low field magnetoresistance (mostly due of magnetic variation of percolation paths). Calculations have been carried out at the level of electron/spin Hamiltonian and exact diagonalization Monte Carlo simulations for large disordered cells. See in Figures 14 and 15 of the Attached file the calculated maps of ASD configurations, and the calculated magnetization and resistivity as a function of temperature, respectively.

2) Antiferromagnetic Order and Phase Coexistence in Antisite Disordered Double Perovskites. Carried out by partner HRI. Much of the excitement in the investigation of double perovskites (DP) was due to the high ferromagnetic (FM) Tc, large magnetoresistance, and the possibility of spin-polarized conduction in materials like Sr2FeMoO6 (SFMO). However, it is also interesting to explore whether other non-FM orders (e.g. CE, A, C, and G type antiferromagnetic (AF) phases typical of single perovskites) may occur at some doping concentration range. Model Hamiltonian calculations shows that at low electron density the FM alignment of the core spins is favored since it leads to the maximum bandwidth. However, at sufficiently large band filling, antiferromagnetic (AF) states with A or G type order (in two dimensions) become successively favored. Nevertheless, electronically driven AF order continues to be elusive experimentally. One can envisage two reasons: (i) the AF phase occurs at (high) electron densities which have not been probed yet, or (ii) increasing electron density leads to a rapid growth in antisite disorder (ASD), strongly suppressing any signature of long range AF order.

The theoretical effort till now has focused on AF order in structurally ordered DP, but in real materials the B, B alternation between the two transition metal atoms is interrupted by an anti-phase boundary (APB) involving BB or BB nearest neighbors. This leads to a pattern of structural domains. The ASD not only destroys periodicity but also brings into play an additional AF superexchange coupling when two B ions (like Fe) adjoin each other. If this superexchange scale is sufficiently large, the BB anti-phase boundary also acts as a magnetic domain wall (MDW), leading to magnetic domain formation, suppression of magnetization, and a large enhancement of the resistivity. Our work provides a systematic exploration of the effect of increasing ASD on the AF phases in a two dimensional (2D) double DP model. We consider two electron densities relative to `A type' and `G type' ordering, and study magnetic order and transport for increasing antisite disorder.

Our principal results are: i) the suppression of magnetic order with ASD is slower in the AF than in the FM phase, and even with 30% mislocations there are clear signatures of long-range order. (ii) The Tc is not significantly affected, until strong disorder, although the `transition' is broadened. (iii) Both AF phases are metallic, and the increase in their resistivity with ASD is weaker than in the ferromagnet. (iv) The phase separation regime between the FM and A type phase is converted to a phase coexistence window in the presence of moderate ASD, and one observes the occurrence, locally, of both kinds of order in the same sample. In Fig.16 of the attachment maps of calculated magnetic correlations are reported.

Task 3.5: Study of B-site dopants: setting innovative MH for B-site dopants and merging with FPC. Period: 12-24

Construction of MH and then a many body/finite temperature theory, for the study of ground state, transport and thermodynamic properties of doped DP by FPC (PSIC, HFT, HFT+GW) +MH approach. Comparison with available experimental results and previous theoretical results. (5-HRI, 4-SNBNCBS, 6-JNCASR).

B-site doping in magnetic oxides is a subject of great interests for the possibility of radically changing the properties of the host material with a small amount of doping. While disorder on the active d element site is usually very disruptive for conduction and long-range order in perovskite transition metal oxide, in the background of phase competition it may also act to promote one ordered phase at the expense of another. This occurs either through valence change of the transition metal or via creation of defects in the parent magnetic state.

Partner HRI elaborated a model Hamiltonian written on the basis of few parameters thus providing a framework for understanding the complex variety of phenomena observed in B-sitedoped manganites, and identifying the key parameters that control the physics. However, to the aim of being predictive for practical cases, the generic Hamiltonian must be specified in terms of parameters drawn by First-Principles calculated electronic band structure. In Fig.17 of the attached file the schematic level diagram is reported.

The results of the work related to Tasks 3.4 and 3.5 are the subject of Deliverable 3.45 due at month 24. Publications related to these topics by HRI group are: V. N. Singh and P. Majumdar, Europhysics Letters 94, 47004 (2011); arXiv:1009.1709v1 [cond-mat.str-el] 9 Sep 2010. R. Tiwari and P. Majumdar (HRI), arXiv:1105.0148v2 [cond-mat.str-el] 3 May 2011.

WP4: Interfaces, multilayers, and devices

Objectives and overall description

WP4 is the most technologically oriented workpackage of the present project, as it deals with the study of interfaces, heterojunctions, and multilayers, with functional capabilities, such as magnetoelectric effects and spin-transport capabilities. The work performed in WP3 was largely instrumental to the WP4, since several bulk systems studied in WP3 are also building blocks of the examined multilayers. WP4 covered the whole 3rd year of the project, and was carried out in tight collaborative synergy among the consortium partners.

Task 4.1: Magnetic/ferro/piezoelectric interfaces: structural, electronic and transport properties. Period: 25-36

Calculation of the physical properties of several interfaces between different magnetic and ferro- piezoelectric materials carried out within both PSIC and PSIC+MH, HFT, HFT+GW and HFT(+GW)+MH methods. Investigations include determination of electronic, magnetic, structural and transport properties. The accuracy of our description was evaluated against available experimental and previous theoretical results.. (2-CNR, 6-JNCASR, 3-Univie, 5-HRI).

For this Task we selected a number of important cases of heterostructures and multilayers with special functionalities such as multiferroism, magnetoelectric coupling, magnetoresistance. In the following we briefly describe three relevant prototypes, the CuO/SrTiO3 interface, the multiferroic tunnel junction (MTJ) SrRuO3/BaTiO3/SrRuO3, (SRO/STO/SRO) and the LaNiO3/LaAlO3 (LNO/LAO) superlattice.

CuO/SrTiO3 interface: (Carried out by Univie). Hybrid Functionals are applied to study the evolution of the structural, electronic, and magnetic properties. The proper inclusion of substrate effects is crucial to understand the tetragonal expansion and to reproduce correctly the measured valence band spectrum for a CuO thickness of 3-3.5 unit cells (See Fig.18 of the attached PDF), in agreement with the experimentally estimated thickness. Our analysis explains the anomalously large Cu-O vertical distance observed in the experiments (2.7 A, see Fig.18): we find that the enormous structural anisotropy of the Cu-O sublattice --which determines the experimentally observed tetragonal symmetry-- can be understood in terms of a layer dependent evolution of the Cu ionicity which increases progressively towards the surface. Ultimately, the local structural and electronic Cu-O environment appears very frustrated as a results of the coexistence between two concurrent states attributable to an in-plane Cu2+-like and out-of-plane Cu3+-like arrangements. This work is Published in: C. Franchini, X.-Q. Chen & R. Podloucky, J. Phys.: Condens. Matter 23 045004 (2011).

For what concern transport properties, we have implemented a computational scheme to merge the VASP code with the BoltzTrap code, the computer program developed by G. Madsen and D. Singh for calculating the semi-classical transport coefficients. The VASP2BOLTZTRAP interface has been successfully applied to the calculation of the spin-polarizations in the Half-metallic FM regime realized in the CMR parent compound LaMnO3 at elevated pressure. We found values for the spin polarization very similar to those obtained for the CMR regime of doped LaMnO3 (La0.7Sr0.3MnO3). The interface is fully compatible with post-DFT methods such has HFT and GW. This work is published in: J. He, M.-X. Chen, X.-Q. Chen, and C. Franchini, Phys. Rev. B 85, 195135 (2012).

Multiferroic tunnel junction (MTJ) SrRuO3/BaTiO3/SrRuO3 (carried out by TCD). We performed an initial relaxation of bulk BaTiO3 and SrRuO3 under an in-plane compressive strain, emulating the common epitaxial growth on SrTiO3, to find the relaxed out-of-plane lattice constant. The relaxed cells were then used to construct the transport supercell, which comprises six BaTiO3 unit cells (?2.5 nm) sandwiched at either side by three SrRuO3 cells. The SrRuO3/BaTiO3 interface is SrO/TiO2 due to the experimentally observed volatility of the RuO2 termination. We consider two structures. In the first nonferroic (NFE) structure the atoms are frozen artificially in their centrosymmetric positions with the interfacial distance given by an average between the BaTiO3 and SrRuO3 c-lattice constant. In the second all positions in the supercell are completely relaxed out-of-plane until the forces are less than 10 meV/A, resulting in a stable ferroelectric ground state (FE structure). At the center of the BaTiO3 slab Ti displaces by 0.14 Å, which is significantly of bulk BaTiO3 experiencing smaller than the value of 0.23 Å the same strain. Note that GGA overestimates the volume and atomic distortions associated with ferro-electricity in BaTiO3 resulting in a supertetragonal structure. Such an over estimation, while resulting in a polarization greater than the experimental one, will not have a significant qualitative effect on our results. The interfacial SrRuO3 layers, as expected, also contribute to the polarization.

The symmetry of the electronic bands of both the ferromagnetic electrodes and the insulating spacer dictates the transport properties. Importantly, an incident Bloch state in the electrodes can couple to a given evanescent state in the insulator and then sustain a tunneling current, only if the two share the same symmetry.

The spin-polarized current for both the PA and AP configurations and for both the NFE (top panel) and FE (middle panel) structures are shown in Fig. 19 of the attached PDF, where we focus on the low voltage region in which the current is due entirely to tunneling (the broader I-V are displayed in the insets). The most distinctive feature emerging from the I-V curves is the presence of negative differential resistances (NDR) for the PA alignment, originating from the movement of the ?1? band edge with V. Because of the NDR the relative magnitude of the current for the parallel (IPA) and antiparallel alignment (IAP) can be reversed (i.e. the TMR changes sign with V). This work is published in: Phys. Rev. B 83, 125409 (2011).

Nickelate superlattice (carried out by CNR). Nickelates are nowadays among the most investigated oxides: their magnetization state is (even more than in manganites) sensibly influenced by small structural distortions and applied strain. When cast in heterostructures or superlattices, nickelates then provide potentially suited prototype systems whose structural, magnetic, and transport properties can be changed and manipulated by application of selected substrates, strains, and external fields. The LNO/LAO magnetic superlattice (MSL), recently grown and characterized, is one viable case where these functionalities can be implemented. Our calculations provide a description of the fundamental properties of this system in striking agreement with the experiments, and elucidate the mechanism at the basis of its phenomenology.

Our calculations describe the ground state as structurally dimerized, charge-ordered, insulating, and antiferromagnetic. This phase is energetically favorite with respect to metallic paramagnetic phase which characterize bulk LaNiO3. The transition is driven by valence disproportionation of Ni atoms at low T: in the insulating AF-CO phase the (nominally) Ni3+ sublattice splits in two separate sublattices occupied by magnetic Ni2+ and non-magnetic Ni4+ ions. Ni2+ ions have moment of 1.44 ?B (configuration t2g6eg2) while Ni4+ have zero moment (t2g6eg0). Within mean field approximation, the critical Neel temperature is TN ? 33 K, close to the experimental 40 K. All the above findings are consistent with the experiments. The concurrent action of dimerization and magnetic superstructure open an electronic gap of 1.3 eV in the AF-CO phase. Octahedral distortion is essential to obtain a gap: without distortion all simulated phases are metallic and not CO. However, only the Pauli-PM metal phase is stable in the non-CO configuration.

We use the calculated band structure to obtain transport properties through the Bloch-Boltzmann theory (BBT). We apply the BBT to evaluate the DC electron conductivity; in this work the ultrathin SLs (with 3 LNO units or less) appears as a correlated metal with anomalous hopping-like T-dependence, whereas thicker SLs behave as a normal metal but with large residual resistivity. Our working hypothesis is that the thick normal-metal SL corresponds to the PM phase, and the ultrathin SL to an electron-doped AF-CO insulating phase (typical impurities in wide-gap transition metal oxides, e.g. oxygen vacancies, are donors). Our results (see Fig.20 of the attached PDF) nicely fit the observations: at low-T the DC conductivity grows exponentially, then saturates to a more conventional metallic linear behaviour above T?150 K.

In summary: The work of Task 4.1 demonstrated the capability of our combined First-principles plus model approaches to investigate the fundamental properties of magnetic oxide heterostructures, from structural to electronic, magnetic, and transport properties. Our results describe several phenomenologies, in full agreement with the experimental studies. For what concern the examined all-oxide ferroelectric MTJ, we have detected huge TMR, the sign of which can be inverted as the applied bias increases. Furthermore, the sign inversion occurs at different voltages for different ferroic states of the barrier. Our finite-bias results are explained in terms of the electrodes and the barrier band structures. The possibility to control the TMR by manipulating the ferroic state of the barrier in an MTJ opens a potential avenue for the electrical control of magnetic devices. For what concern magnetic superlattices, we have studied LNO/LAO SL with ultra-short period, and found structurally- and valency-dimerized charge-ordered insulating ground state, undergoing a phase transitions to a metallic Pauli paramagnet. The magnetic and metal-insulator critical temperatures are estimated around 35 K and 80 K respectively. This interpretation is in good agreement with available experimental data. We have also described the SL transport properties in agreement with the observation.

Task 4.2: Merging models and First-Principles: setting model Hamiltonian for oxide interfaces.

Period: 25-36

Construction of model based on First-Principles parameters, and then a many body/finite temperature theory, for the study of oxide interfaces (especially manganese interfaces) and the related reconstruction effects on structural, electronic and magnetic properties. . The accuracy of our oxide interface description was evaluated against available experimental and previous theoretical results (5-HRI, 3-Univie).

This task, mainly based on the work of HRI is devoted to the construction of model Hamiltonians suited for oxide heterostructures. As a test case, the model is applied to describe the heterostructure made of differently doped manganites, which configures a prototype device with giant magnetoelectric effect, i.e. a system whose magnetization and/or magnetic ordering can be controlled by the application of an external electric field. Specifically, the interface is LaMnO3/SrMnO3 joining two antiferromagnetic bulk materials with different Mn nominal valence charge (3+ for LaMnO3, 4+ in SrMnO3), thus prefiguring an inhomogeneous distribution of eg-type valence charge along the direction orthogonal to the interface. Since the basic (in particular magnetic) properties of manganites are crucially dependent on the amount of the valence charge in the eg bands, control of this charge can directly lead to the control of the magnetic properties as well. As described in the Deliverable 4.2 related to this Task, charge control is achieved through an applied external potential at the back gates of the interface, thus envisioning the possibility of a controllable, general and robust magnetoelectric coupling mechanism.

The formulation developed by partner HRI is briefly described in the attached PDF file, while a more detailed description can be found in the Deliverable 4.2 report.

Task 4.3: Design of multilayered devices with enhanced capabilities.

Period: 25-36

Design and calculation of the physical properties of bi- and three-phase multi-layered systems showing potential applications in spintronic (e.g. spin-valve, magnetoelectric coupling, and others). The quality and reliability of our predictions are verified by synergic collaborations with a network of experimentalists. (6-JNCASR, 2-CNR, 1-TCD)

In tunneling magnetoresistance (TMR) the tunneling current through an insulating barrier is affected by the relative magnetization of the magnetic leads. This technology is currently used for read heads in the multi -billion dollar hard disks industry. The introduction of an active ferroelectric region offers the possibility of introducing additional functionalities in the same active element, such as non-destructive reading of ferroelectric RAM and four state resistance devices. To observe a tunneling electroresistance (TER) affect, using a ferroelectric material as insulating barrier is not sufficient, since the potential barrier of the two polarizations mirror each another and the resulting tunneling current for each electrically polarized states would be identical. Instead, the TER affect requires the asymmetry of the entire system. To the aim, the introduction of a non ferroelectric insulating layer into the system (FM/FE/Insulator/FM multilayer) is the most promising junction for device applications. Due to the long screening length in the insulating region and low carrier concentration the depolarization charge is not localized at the FM/FE but at the I/FM interface, thus switching the FE polarization has a dramatic affect on the potential barrier height of the insulating layer, and the TMR is large and tunable by the thickness of I and FE layers. In our work we show that the introduction of the wide band gap insulator SrTiO3 into the SrRuO3/BaTiO3/SrRuO3 junction creates an additional potential barrier that is switchable with the ferroelectric polarization. In doing so we propose the necessary components for a combined TER+TMR device.

We use a 6 unit cell thick BaTiO3 layer (? 2.5 nm), m=(0,1,2) unit cells of SrTiO3, and 3 unit cells for SrRuO3 left and right electrodes (the structure is described in detail in Del. 4.3-1). When BaTiO3 is included in the capacitor structure, the atomic displacements correspond to a polarization of 35.5?C/cm2 much reduced from the bulk value (43.8?C/cm2). The electronic properties of SrTiO3 and BaTiO3 are very similar: both real and complex band structure (which is a measure of the electronic tunneling coefficient) are almost identical, thus bulk properties alone we would not indicate any significant advantage in the introduction of the SrTiO3 into the junction. At zero bias, when a FE film is inserted within the leads, some charge accumulates at the interface to screen the electric field due to the FE and bring back to zero the electric potential in the leads. This can be seen in Figure 21 of the attached PDF file, where we plot the difference in the potential and charge profile between centrosymmetric and ferroelectric configurations, for the SrRuO3/SrTiO3/BaTiO3/SrRuO3 junction. The depolarization charge forms in the metallic SrRuO3 layer leaving the potential in SrTiO3 pinned at its STO/BTO value. Thus, inverting the BTO produces a rigid shift in the SrTiO3 potential. This configures a TER mechanism where the BTO region acts as a potential barrier with a constant gradient, and the STO side a square potential with a height matching the STO/BTO interface. We notice that some uncontrollable defect-driven TER contribution is always present, in practice, due to the difficulty in creating defect free structures. However, this can be made discardable with respect to the intrinsic TER, which can be tuned either by the thickness of BTO or STO.

Milestone M1: month 12

Comparison among First-Principles methodologies, assessment of respective accuracy and manageability. Verification of the correct realization of an integrated First-Principles plus model scheme, and relative code implementation.

Central to the Milestone is a collaboration of TCD, CNR, and Univie. These partners studied two relevant test case materials (MnO and NiO) with a number of different methods, including standard local density functionals (LDA) implemented in plane-wave basis set (LDAPW) and in local orbital basis set (LDALO), as well as generalized-gradient density functional approximation (PBE), and several beyond-local functionals: the newly developed VPSIC implemented in two versions, namely plane-wave basis set (VPSICPW) and local-orbital basis set (VPSICLO), and the hybrid functional HSE. In Figure 22 of the Attachment we report results concerning the relative energy stability for various magnetic orderings as a function of lattice parameter (i.e. under an applied pressure) and the related magnetic moments obtained with each of these methods.

Our work provided a comparative analysis of unprecedented variety and details. It testifies the consistency and the general reliability of structural, electronic, and magnetic properties for magnetic oxides obtained by the newly implemented VPSIC in comparison with HSE, considered the reference among First-Principles band theory approach for what concern accuracy. On the basis of these results our milestone decision consists in remaining actively working with all the 3 methods, selectively used according to their suitability for specific problems; specifically the VPSICLO is particularly suited for large-size systems and molecules, while the VPSICPW and HSE approaches are more indicated for very complex systems whose electronic properties have to be determined with the outmost precision. The correct realization of the model Hamiltonian integration with the First-Principle approach has been also verified, according to the original Milestone objectives.

Milestone M2: month 18

Assessment of the determination of ground state and thermodynamic properties of magnetic oxides by integrated First-Principles plus model Hamiltonian scheme. Comparison of FP plus model methodologies, decision on which method(s) are better suited to be fruitfully exploited in the project prosecution.

This Milestone is addressed to verify the correct realization of the model Hamiltonian integration with the First-Principle approach. The assessment concerning the determination of ground-state and thermodynamic properties of magnetic oxides is centered on the joint work of partners TCD, CNR, and Univie: in particular, the comparative analysis focused on the two Mott insulating prototypes MnO and NiO systems, tackled with an array of different approaches. In order to reach a resolution of virtues and weakness of the methods in question, the results for zero-temperature magnetic properties, previously discussed in the illustration of Milestione M1, are interfaced with calculations based on a newly developed Heisenberg Hamiltonian Monte Carlo procedure, which can deliver accurate finite-temperature magnetic properties for the systems of interests.

On the basis of the results obtained for the Nèel temperatures of MnO and NiO as a function of the lattice parameter (i.e. the volume), we confirm the excellent accuracy and the good accord of our beyond-standard functionals (VPSIC HSE) already verified for M1, and our determination to pursue the use of each functional in the remaining part of the project. See Fig. 23 of the attached file.

Milestone M3: month 24

Assessment on the capability of our method to describe ground state, transport and thermodynamic properties of bulk oxides, as well as several peculiar phenomenologies including ME effects in DMF, CMR and CER effects in MP, large magnetism in doped DP).

This Milestone is devoted to the verification of the quality of the newly developed approach in comparison to relevant phenomenological cases, such as those related to giant magnetoresistive or electroresistive effects (CMR, CER), large magnetoelectric coupling (ME), large ferromagnetic critical temperature. As a matter of fact, in the last few years most of these phenomenologies have been found full displayed in oxide heterostructures (interfaces, films, and superlattices) which represent the focus of Milestone M4. Thus, we can directly move to the description of M4, whose finding also encompasses the aims of Milestone M3.

Milestone M4: month 36

Assessment on the description of structural, electronic, and transport properties of MP/MP and MP/PZ interfaces by FP+MH approach. Assessment on the possibility to design bi- and three-phase multi-layers showing ME coupling with potential applications.

As described in the original Annex, this Milestone is to evaluate the quality of our newly developed approach in the description of a range of interfaces with diverse functionalities, such as large magnetoelectric coupling and spin-valve capability, with the aim of furnishing the final determination on the possibility to use integrated First-Principles plus model scheme to describe and eventually design oxide systems with improved functionalities, which represents the definitive, paramount achievement of the project. We considered a large array of bi-dimensional systems, including the multiferroic tunnel junctions SrRuO3/BaTiO3/SrRuO3 and SrRuO3/SrTiO3/BaTiO3/SrRuO3, the spin-valve multilayers Fe/BaTiO3/Fe and Fe/MgO/BaTiO3/Fe, the magnetic metal/non-magnetic insulating LaNiO3/LaAlO3 superlattice, the magnetic/non-magnetic insulating CuO/SrTiO3 interface, the magnetic/magnetic (LaMnO3)n/(SrMnO3)n superlattice.

The vast majority of our results indicate a favorable assessment to the Milestone. In all the cases, our calculations predicted interesting functionalities or characteristics potentially viable for device design. Whenever an experimental reference was available, calculations turned out to be in substantial agreement for what concern structural electronic, magnetic, and transport properties.

As an example, in Figure 23 of the attachment we show the k-resolved transmission coefficient calculated for the multiferroic tunnel junction. More detail of this work can be found in the Deliverable Report 4.1-1.

WP5: Project management

The management of the ATHENA project was carried out by the two Coordinators: Stefano Sanvito of TCD, was on duty for what concern all legal and scientific management and coordinating activities of the EU partners, while Priya Mahadevan of S.N. Bose of Kolkata managed the Indian side of the Consortium.

Management was carried out according to the original guidelines of the DoW, and form scientific viewpoint no specific problems have being encountered during the 3 years. In contrast, from the logistic viewpoint some uncertainty was caused by the difference in regulations and system management obligations required by the EU and the Indian Department of Science and Technology (DST). An example concerns the organization of the M18 review meeting, which was not possible to conduct as a joint EU-DST event. The problem was then solved by doubling the review meeting procedure, i.e. organizing two consecutive meetings (one in Bruxelles on January 2011, the second in Bangalore in April 2011 -- see the meeting list section later on). This of course is not ideal since travelling must be duplicated, without a clear benefit for the delivery of the project. As a suggestion for future projects, we believe that the best option will be having one single reporting body with common rules for the entire consortium (EU+DST). Such single reporting body may also correct issues related to the misalignment of the starting dates between the EU and India consortia, as well as the different policies for what concerns no cost extensions. We signalled these problems in occasion of the EU-India Coordinator meeting in Brussels in March 2011 (attended by both Stefano Sanvito and Priya Mahadevan).

We underline that no change occurred relative to the legal status of the members. A minor change regarded partner CNR of Cagliari, Italy: following a structural reorganization, the Institute formerly known as CNR-INFM (Istituto Nazionale di Fisica della Materia) and as such called in the original Project description, was renamed CNR-IOM (Consiglio-Nazionale delle Ricercha - Istituto Officina dei Materiali). Beside the name, no other change occurred in terms of either location (Cagliari, Italy), personnel, or scientific means, which might, on any regard, affect the scientific activity of this partner in the ATHENA project.

In the following we list the original Tasks with their objectives and a brief description of the related work.

Task 5.1: Administration and reporting. M1-M36

Administrative and reporting activities, including correct and timely distribution of the funds from the EU, communication with the EU, preparation of periodic reports for the EU, newsletters, meeting minutes (1-TCD, 4-SNBNCBS).

All administrative and reporting activities were duly accomplished along with the procedures required by the EU regulations and requirements. Distribution of funds to members occurred timely and without difficulties. Communication among partners was accomplished by meetings, e-mailing and an intensive use of teleconference tools. Preparation of project meetings was carried out with the help of local host institutions (see the meeting list below), which always ensured excellent conditions of work and highly successful scientific outcome.

Task 5.2: Website. M1-M36

Realization and maintenance of the project web sites. This will be a public site for dissemination of results and access of useful data and publications (1-TCD, 4-SNBNCBS).

The ATHENA project website was created in the first 6 months of the project as planned, and functions since the second half of 2009. Thomas Jochmann from INVITRONICS was appointed to design the website. The domain www.athenacomp.eu was purchased and it currently hosts the website. The site is divided into three parts, two public and one private, respectively. The public sections include a welcome page with news and description of the project and a materials page with list of publications, links to software, and summary of achievements to date. The private section serves as a forum for exchanging data and various scientific materials between the partners. The coordinator and his team updated the website (public section), while all the partners had access to the private section.

Task 5.3: Leaflets (CANCELLED)

Preparation and distribution of leaflets describing the objectives of the project and the main results obtained during the project (1-TCD, 4-SNBNCBS).

The preparation of leaflets were cancelled. Partners decided that the dissemination of project results during conferences and meeting could be more effectively carried out by digital modalities, whereas distribution of hard copies were not anymore necessary. This action was agreed at the midterm meeting by the EU project officer.

Task 5.4: Training School. M24-M36.

Organization of a training school on theoretical methods applied to strong-correlated materials open to public (1-TCD, 4-SNBNCBS).

The ATHENA project organized a highly successful school at the N.S. Bose Institute of Calcutta in April 2012. Lectures focused on the themes related to the research carried out in the ATHENA project, were held by scientists of the ATHENA project, complemented by several extra-project invited scientists. The School saw the participation of more than 50 among PhD students and Post-doctoral researcher, plus a qualified audience of professionals interest in condensed matter theory. More detail can be found in the related Deliverable Report 5.4.

Task 5.5: Interrelation with other WPs and meeting organization. M1-M36.

WP5 will strongly interact with all other workpackages to ensure the achievements of the goals of the project, organizing regular meetings among consortium members (one each 6 months for intra-European and intra-Indian separated sections, one each 12 months for the joint Euro-India consortium. (1-TCD, 4-SNBNCBS).

The originally planned meeting schedule was slightly varied (with the approval of EU) to better fit our scientific means. Specifically, the first general EU-India meeting originally expected at Month 12 was anticipated at Month 6, in order to establish an anticipated acquaintance among all the consortium members. Here is the list of project meetings held by the ATHENA project:

a) M0: June 22, 2009 Trinity College Dublin Kick-off Meeting of the European section.

b) M0: August 2009 Kolkata Kick-off Meeting of the Indian Section

c) M6: January 11-13, 2010 Harish-Chandra Research Institute, Allahabad 1th Joint EU-India Meeting.

d) M12: June 21-13 2010 Marina di Capitana, Sardinia, Italy First year Meeting of the European Section

e) M18: January 8-12, 2011 Brussels Midterm Review Meeting

f) M18: February 8-12, 2011 JNCASR, Bangalore Midterm Indian Review Meeting & 2nd Joint EU-India Meeting.

g) EU-India Project Coordinators Meeting: March 30-31, 2011 Brussels.

h) M24: June 2-3, 2011 Trinity College Dublin Second year Meeting of the European Section.

i) M30: April 9-14, 2012 - S. N. Bose, Kolkata - ATHENA School and 3th Joint EU-India Meeting.

j) M36: June 17-19, 2012 - University of Cagliari, Italy - Final Meeting of the European section.

Besides the official meetings listed above, a number of reciprocal visits between partners was organized to foster our common activity and collaborations on specific themes of the projects. These visits regarded WP leaders, students and post-docs. Here is a list of visits in the framework of ATHENA project:

October 2009: V. Fiorentini (CNR) visits TCD

November 2009: A. Filippetti (CNR) visits Univie.

November 2009: P. Mahadevan (SNBSCBS) visits HRI.

December 2009: P. Mahadevan (SNBSCBS) visits JNCASR.

January 2010: U. Waghmare (JNCASR) visits SNBSCBS

March 2010: C. Franchini (Univie), C. Ederer, R. Kovacik, S. Sanvito (TCD) meet in Portland

June 2010: C. Franchini (Univie) visit CNR Cagliari

August 2010: R. Kovacic (TCD) visits Univie

September 2010: C. Franchini (Univie), C. Ederer, R. Kovacik, S. Sanvito (TCD) meet in Berlin

October 2010: C. Ederer, R. Kovacik,(TCD) V. Fiorentini, A. Filippetti, D. Puggioni, (CNR) M. Marsman (Univie), S. Shirodkar (JNCASR) meet in LAquila, Italy.

November 2010: R. Kovacik (TCD) visits Univie.

December 2010: S. Bhattacharia (TCD) visits HRI;

December 2010: P. Mahadevan (SNBSCBS) and U. Waghmare (JNCASR) meet in Bhubhaneshwar

January 2011: R. Tiwari (HRI) visits CNR Cagliari.

January 2011: S. Datta (HRI) visits Univie.

January/February 2011: V. Singh (HRI) visits Dublin

March 2011: S. Sanvito (TCD) and P. Mahadevan (SNBNCBS) meet in Brusselles

April 2011: D. Puggioni and P. Delugas (CNR) visit JNCASR.

April 2011: P. Mahadevan (SNBNCBS) visits Vienna.

May 2011: S.S. Murthy (Univie) visits Dublin.

May 2011: C. Franchini visits CNR Cagliari.

October 2011: Saikat Debnath (SNBNCBS) visits Vienna.

May-June 2011: S. Murthy (Univie) visits Dublin.

Potential Impact:

We believe that the ATHENA project successfully matched the challenge to produce a strong impact from scientific, socio-economic, and societal viewpoint. ATHENA represents probably the first attempt towards the creation of an integrated network of theoretical scientists active in the development and testing of beyond the state-of the-art theories and software, with a sufficiently large critical mass of human resources and competences to create a serious impact in the condensed matter community.

The interaction between European and Indian academic and research institutions successfully achieved the sharing and integration of their respective intellectual and material resources, through an intense and reciprocal exchange of researchers and knowledge. Each one of the ATHENA consortium partners provided an environment of scientific excellence in their specific fields of activity in particular, thus ideal places where interactions of visiting (especially young) researchers could be fruitfully exploited to produce those scientific innovation generated by the project, and even more importantly, to establish and nurture those long-term scientific and social relations among our institutions and their respective scientists in order to create the critical mass of knowledge on the themes specific to the projects, and more in general, in the field of theoretical condensed matter.

Going to evaluate more specific scientific outcome, the ATHENA project was aimed at developing an inter Euro-Indian network of excellence in the field of theoretical/computational methods to investigate the properties of strong-correlated materials (transition metal oxides, with specific focus on the magnetic perovskites) which are candidate to be fundamental building blocks for future generation nanoelectronic devices. These systems have the characteristic to embody a formidable mix of technological promises and outstanding richness of unconventional, and for many aspects sill far from understood, fundamental physics. From a technological viewpoint, functional oxides are addressed as the potential basis of a whole new technology with enhanced and/or additional capabilities with respect to the actual Si-based technology. As such, they are subject of extraordinary appeal as much for academic environments as for visionary research industries, for physicists and material science engineers alike. It can be hardly confuted that no other investigative arena, at least within the material science framework, possess the same degree of versatility.

But reaching the border of the nanoscopic size limit necessarily requires the ability to understand (and thus predict and control) the quantum-mechanic behavior at the atomic level. In this light, the role of First-Principles theory becomes instrumental to the accurate description of the matter and the capability to make predictions on the functionalities of these systems should be regarded as a major investigative instrument, complementary and equally fundamental than the experiment itself.

The ATHENA project was conceived in order to pursue this aim not through the work of individual entities, which is the most common approach in the theoretical condensed matter world, but in terms of a structured collaborative network, which would coordinate their activities, sharing methodological knowledge, software (computing codes) and hardware equipment, and exchanging human resources, thus establishing a partnership whose ties could hopefully extend well beyond the time limit of the project itself. Establishing a tight collaboration between some of the leading European and Indian groups in the field, the ATHENA project paved the way for a durable collaboration and a stream of scientific work, which should engross and strengthen along the years, and bring Europe and India to the forefront of theoretical/computational investigations on strong-correlated electron systems. But the importance of the ATHENA project wan not just the sharing of existing capabilities, but first and foremost, in the creation of innovative theoretical resources; as mentioned above, strong-correlated oxides are extraordinary challenging systems from the theoretical/computational perspective as standard computational tools are not adequate to describe materials so rich of intertwined fundamental properties. To this aim, the ATHENA project was composed in order to get together the most advanced methodological tools and equipments based on First-Principles and model Hamiltonian approaches apt to describe the physics of strong-correlated systems, and in turn, the groups who better represent, in terms of expertise in development, mastering, and applications, these methodologies, respectively. As explained in detail in Sections 4.1 a), b), and c), we can affirm that these scientific objectives were achieved in full. During the project, the results dissemination has been carried out through participation of project partners to meetings and events, as well as to an intense publication activity. Coordination activities have proceeded through reciprocal visits and an intense activity of correspondence by on-line conferencing.

In synthesis, during the 3-years duration of the project our Task force has:

Produced a large amount of scientific works, disseminated during the 3 years of the project through a series of publications in international peer-reviewed journals, and national and international conference seminars, many of which resulting from invitations. This dissemination activity, mostly collected in our public website, might be useful to professional scientists in their research as well as to students and teachers of graduate classes to acquire knowledge of the arguments.

Developed outstanding new methods for calculations in condensed matter, and related software (codes) now available to the community by request and/or mutual collaborations.

Established an expertise environment devoted to theoretical/computational study of strong-correlated materials, built on an unprecedented amount of innovative, beyond state-of-the-art resources that will be made available for the solid state community.

Established a Euro-Indian school in methodologies devoted to optimization, development, and dissemination of the most advanced and efficient computing codes worldwide available and applicable to general strong-correlated systems.

Established a strong synergy with the experimental community in designing heterojunction and superlattice devices based on strong-correlation and proximity mechanisms.

Implemented a public website including a database periodically updated with the information collected during the 3 years project, giving access to all the publications and presentations resulting from the project as well as the information and results about the project that the consortium participants agreed to publicize.

Hold an ATHENA training School (Kolkata, April 2012) on strong-correlated materials and methods open to the public, and specifically addressed to PhD students and Post-Doc. The School, which saw the participation of more than 50 attendees and about 20 lecturers among coworkers of the ATHENA projects and several internationally renowned invited scientists external to the project, turned out to be highly successful and represented a formidable tool to disseminate the advancement carried out by the ATHENA project and to introduce young researchers to the most advanced state-of-the-art methodologies in the field of strong-correlated systems.

List of Websites:

www.athenacomp.eu

The Eu-India ATHENA project has been carried out in a close partnership between three European and three Indian Institutes. The project has been completed in full, and the expected list of Tasks, Deliverables, and Milestones completed and uploaded according to the expected program and time schedule.

The project partners worked in tight collaboration, as testified by common publications, project meetings, exchange of students and researchers for short- and long-term (up to 3 weeks) periods.

The project had a specifically theoretical/methodological character. The fundamental scope was the building of an array of either radically new, or substantially improved and extended methodologies particularly suited for magnetic oxides, for materials with strong electron correlation and for their heterostructures. Those are materials of outstanding conceptual interest, and great potential for novel applications in microelectronics and spin-electronics.

Computational approaches, of the First-principles Density Functional type, and of model Hamiltonian type, were first separately developed and then interfaced to obtain a coherent description of test case materials covering a broad range of properties, from structural, electronic and magnetic properties to finite-temperature transport and thermodynamics. The developed theories were tested in relevant and paradigmatic classes of systems and the results confronted with experimental data or previous theoretical results. All our results confirm that the accuracy of our predictions overcomes, or at least matches, that obtained by precedent approaches, and it exceeds our initial expectations.

In brief, our major achievements include: a) the development of a novel First-principles density functional approach for the calculation of fundamental properties of oxides, which we named the variational pseudo-self interaction correction (VPSIC) method. The VPSIC has been tested on a variety of correlated oxides systems, including bulks, interfaces, and molecules, and implemented in two codes based on different methodological settings, and fully available to the community upon request. b) the development of a fully integrated approach based on the Hybrid Functional approach, as implemented in the VASP code, plus model tight-binding Hamiltonian built in the basis of maximally-localized Wannier-function basis set, as implemented in the Wannier90 code. c) the implementation of a novel model Hamiltonian approach based on the Hubbard-Stratonovich effective-field approach; this extension allows the treatment of the on-site repulsive interactions of the Hubbard model (typically problematic since very time consuming) thus overcoming usual single-band approximation used for the description of double-exchange manganites in the doping range corresponding to the colossal magnetoresistive behaviour. d) the implementation of Lanczos algorithm for the calculation of finite-temperature electronic spectral functions.

The outcome of the projects has been disseminated through talks and lectures given in a number of international conferences, a considerable list of publications spurring from the activity of all partners, (several of them in common), and a final, highly successful school held in Calcutta, which has seen an outstanding participation of students and young scientists, as well as internationally renowned lectures. The project has also established a tight synergy among the partners and close, durable scientific collaborations, which will be further pursued in the near future, possibly involving the hiring of students and post-docs. In summary, we can confidently attest the successful completion of aims and objectives of the ATHENA projects.

Project Context and Objectives:

The overall aim of the project was the investigation, through a synergy of advanced First-Principles (FP), density-functional based (DFT) methods, and Model Hamiltonian (MH) calculations suited for strong-correlated systems (SCS), of the properties and functionalities of transition metal oxides that may be viable candidates as building blocks of future micro- and nanoelectronic devices with enhanced capabilities. Despite the huge effort devoted to the field, a deep and complete understanding of these systems is hard to achieve. On the one hand, this is due to the complexity inherent to the physics of strong-correlated electrons, which includes a plethora of fascinating but overtly complex phenomena (e.g. charge and orbital ordering, polaronic formation, spin-charge separation, non-Fermi liquid behaviour, just to name a few). On the other hand, there is an unquestionable lack of coordinated effort devoted to share, integrate and develop the most advanced and powerful computational techniques nowadays available.

The ATHENA project is aimed at filling this gap by gathering in a synergic collaboration some of the most experienced groups in the subject, equipped with the most advanced methodologies for the theoretical study of strong-correlated phenomena in transition metal oxides. Specifically, the European units assembled vast competence in developments and applications of First-Principles methodologies, whereas the Indian partners are renowned experts on both First-Principles and model-based methodologies. The project pursued the idea of merging these two distinct but complementary viewpoints (First Principles and models) to tackle the study of strong-correlated oxides with the best possible efficiency and completeness.

In synthesis, ATHENAs specifics objectives include:

i) The development of novel or improved First-Principles and model approaches. Developed in the course of the first year of the project, this part was related to the work of WP1 and WP2, aimed at the development, refinement, and testing of both of ab-initio (WP1) and model (WP2) methodologies, the former within the EU consortium, the latter prevalently carried out by the Indian partners;

The outcome of the activity related to First-Principles method developments, carried out by EU partners, was highly successful. Indeed, we can claim that all our objectives in this context are achieved in full, even for what concern their most challenging aspects. We can mention three especially noteworthy achievements, in particular:

a) the development of a variational scheme for the pseudo-self-interaction correction method (VPSIC)

b) the development of a practicable and accurate algorithm for the Exact-exchange method (EEX)

c) the development of the Local Spin-Density plus Dynamical Mean Field Theory (LDA+DMFT).

All those are high-risk, far from standard implementations, whose possible failure could have hardly considered surprising. They required (at least in part) innovative formulations, which now represent, in our view, a solid intellectual and practical (software-type) value produced by the ATHENA project. All these methods are now implemented in efficient parallel-platform based codes (SIESTA, PWSIC, VASP, and other software) destined to enrich remarkably the computational condensed-matter community.

The activity of model Hamiltonian development (mainly carried out by Indian partners) was also highly successful, and allowed the extension of this method to previously untreatable systems. A case in point is the generalization of the double-exchange Hamiltonian (originally conceived for A-site doped perovskites of the ABO3 type with only one 3d eg electron per site at most) to the case of double perovskites, where two species of A-site cations (A and A') and/or transition metal ions (B and B') alternate in space to compose an exceptionally challenging phase diagrams. The new model Hamiltonian formulated by partner HRI was shown capable to describe several interesting aspects of the double perovskite phenomenology, in particular the influence of antisite disorder, that so much affect the properties of these systems favouring the vanishing of long-range magnetization and the transition towards an insulating state.

ii) The integration of First-Principles methods based on Density Functional Theory with many-body Model-Hamiltonian techniques suited for materials characterized by strongly electron correlation. Developed during first and second year of the project, this work is connected with WP2, WP3, and WP4

While general trends as a function of order parameters can be inferred exclusively relying on a model approaches, those are not sufficient to arrive at specific predictions for real systems. The spirit of the ATHENA project is setting up methodologies based on the merging of First-Principles and models, in order to be able to describe the materials phenomenology on a quantitatively predictive basis. The integration of these two major areas of computational materials science represent an outstanding advancement and bring major benefits to both fields: on the one hand, it helps to better understand the pitfalls of conventional Density Functional Theories, elaborate corrective solutions, and complement the zero-temperature description of Density Functionals with thermodynamic and disorder-related properties naturally accessible by model calculations. On the other hand, First-Principles calculations complement the model results with a fundamental understanding of the real materials in the ordered state, and the quantitative determination of parameters at the fundament of model Hamiltonians. The work of Indian members has functioned as guideline for our First-Principles plus model interface implementation.

The integration of First-Principles and model calculations was based on standard downfolding routes, i.e. projecting single-particles band energies calculated through different FP methodologies (VPSIC, Hybrid functionals, Exact-Exchange functionals) onto appropriate localized basis set in order to extract effective parameters suited for models (e.g. the very popular Hubbard Hamiltonians) and largely used by the theoretical community for the study of strong-correlated oxides. For the band downfolding we have followed two procedures: one consists in the transformation of Bloch states into maximally-localized Wannier Functions (MLWF), which is well established, and also simplified by the presence of freely available codes (Wannier90). In this case our work consisted in the creation of a software interface between Wannier90 and the First-Principles codes (i.e. SIESTA and VASP). Another procedure makes use of Lowdin-orthonormalized atomic orbitals instead of WFs, and was implemented in connection with the PWSIC code, which mounts the novel VPSIC approach. Test cases were selected according to guidelines and suggestions of the Indian members, which collaborated on specific application of the integrated First-Principles plus model approach.

iii) The investigation of microscopic mechanisms ruling the coexistence, the coupling, and the competition of magnetic, electronic, and structural properties in the bulk functional oxides. This part of the work was the subject of WP3 activity, devoted to gather the capabilities achieved in WP1 and WP2 and tackle complex problems by a combination of advanced ab-initio plus model Hamiltonian approach.

With the beginning of the work scheduled for WP3, the European and Indian sides have established a tight collaborative action, based on common lines of scientific investigation, which delivered results of strong scientific interest. Our optimised ab-initio plus model Hamiltonian approach equipment of methods and computing codes was applied to the study of the fundamental properties (structural, electronic, magnetic, thermodynamic) of strong-correlated systems. In order to demonstrate capabilities, accuracy, and functionalities of this approach, we have considered important test case materials, typically bulk magnetic oxides, with and without doping included, characterized by complex microscopic behaviour and a rich fundamental phenomenology. Those oxides are enabled with a range of special functionalities (e.g. magnetism, electric polarization, multiferroism, magnetoelectricity, magnetotransport, spin transport, thermoelectricity), which promote them as viable candidates for the microelectronic and spintronic devices of the futures.

Specific examples include a long series of magnetic materials: MnO and NiO as prototype of Mott-Hubbard insulators, CaMnO3 and LaMnO3 as parent compounds of colossal-magnetoresistive systems, the doped multiferroic perovskite PrxCa1-xMnO3, the double perovskite LaNi1-xMnxO3, diluted magnetic ferroelectrics, magnetic titanates YTiO3 and LaTiO3 as paramount examples of t2g electron systems. This excursus allowed us to achieve a thorough understanding, from a rigorous microscopic perspective, of the complicated mechanisms ruling the physics of these systems.

iv) The phenomenology of oxides heterojunctions, superlattices and multilayers designed to exploit and manipulate the coupling of different order parameters at the two sides of the interface. This work was entirely related to the objectives of WP4.

Oxide-base heterostructures are predicted to be the building blocks of a novel microelectronic age, due to their visionary functionalities enabled by the coexistence and interplay of orbital, charge, magnetic, and structural degrees of freedom at the interface. Several remarkable examples were thoroughly investigated during the WP4 activity, covering an extremely rich and vast phenomenology: the multiferroic tunnel junctions SrRuO3/BaTiO3/SrRuO3 and SrRuO3/SrTiO3/BaTiO3/SrRuO3, showing both magnetoresistance (MR) and tunneling electroresistance (TER); the spin-valve multilayers Fe/BaTiO3/Fe and Fe/MgO/BaTiO3/Fe with above-room critical temperatures, thus holding a real commercial potential; the LaNiO3/LaAlO3 superlattice, which offers a template to study controllable strain effects on the magnetic and transport properties of 2D oxides; the multiferroic and magnetoelectric (Insulator)/(LaMnO3)n/(SrMnO3)n/(Insulator) superlattice; the superconducting CuO/SrTiO3 interface.

The outcome of this extended investigation showed a substantial agreement with the experiments finding (whenever available), thus demonstrating the capability of our First-Principles plus model approaches to deliver quantitative predictions for a broad range of low-dimensional systems.

Deliverables and timing:

The work related to all the tasks of the four scientific workpackages was completed according to the original schedule, and all the deliverables were released according to the planned scientific action, with the only exception of Deliverable 2.4 originally planned at first year and delayed to the third year. No major difficulties or unforeseen drawback occurred during the duration of the project.

Project Meetings and exchange visits

Three intra-European meeting have been organized in Europe, plus a number of individual visits among the partners, functional to a dense schedule of collaborative work. Furthermore, three European-Indian project meeting were organized in India at the Indian Partners locations (Allahabad at month 6, Bangalore at month 18, Kolkata at month 35), attended by all the ATHENA members; these meetings were preparatory to specific collaborative plans between European and Indian members, and central to the work of WP3 and WP4. Two M18 review meetings, one held in Bruxelles in January 2011 (EU review) and the other in Bangalore in February 2011 (Indian DST review), were held. A dense calendar of student/post-doc reciprocal exchange visits among European and Indian Institutes (long up to 3 weeks) were activated. Finally, in April 2012 a highly successful ATHENA school were organized in Kolkata; the school, attended by about 50 among students and post-docs, was aimed at disseminating at the most foreground level themes and results developed during the project.

Partnership and Outcome

We believe that our EU-India collaboration will have the highest impact from both scientific and societal viewpoint, insofar as it implied development and sharing of knowledge, as well as human and technological resources.

From a technological viewpoint, the ATHENA project developed and released an outstanding armamentarium of computing tools, innovative methodologies, and experience in several areas of theoretical condensed matter, providing an unprecedented bulk of knowledge and understanding. This scientific activity was carried out in close synergy among the partners. The partnership resulted in a series of important common publications.

From the societal viewpoint, the EU-India integration allowed a series of long-term student/post-doc exchange visits which, beside the ordinary scientific output, will be also fruitful in the long run, as it will likely result in further collaborations which will be likely extended well beyond the 3-years limit of the project, and possibly in future hiring from EU groups of personnel coming from Indian partners. The successful outcome of the project was scientifically and socially celebrated by the end-of-project school, held in Kolkota in April 2012.

In summary, the majority of results obtained by the ATHENA project indicate that our work succeeded in delivering practical routes to the description of complex systems, overcoming the well-known limitations of standard Density Functional Theory approach commonly practiced so far. We expect that the outcome of our work will carry a tremendous potential impact in terms of fundamental knowledge of materials as well as applicative tool for prediction and design of systems with device capabilities, and as such it may impact the work of academy and industrial research alike.

Project Results:

The objectives of the project are grouped in 4 Workpackages. WP1 and WP2 were completed within the first year of the project, WP3 in the second and WP4 in the third. In what follows we report the description following the WP structure as originally listed in the Annex I of the GA.

WP1: Methodological development: First-Principles calculations.

Objectives and overall description

The objective of WP1, accomplished in synergy by the three EU members, consisted in the improvement, refinement, and confrontation of various First-Principles (FP) methodologies based on density-functional theory (DFT) and capable to deal with strong-correlated electron systems: namely the pseudo-self-interaction correction (PSIC), the hybrid functional approach (HSE), the local spin density functional plus dynamical mean-field theory (LSDA+DMFT). Part of the work was also devoted to improve the efficiency of available codes, e.g. the PWSIC and SIESTA codes which mount the PSIC approach, and the VASP codes performing HSE calculations. Our final aim was assembling the most effective array of FP-based computational techniques for the application to magnetic oxides and their properties. The WP1 has fully achieved its objectives. In brief:

A novel variational pseudo self-interaction corrected local density approach (VPSIC) was formulated and implemented in two versions: a) plane-wave plus ultrasoft pseudopotentials basis set in the framework of the PWSIC code; b) local-orbital plus norm-conserving pseudopotentials basis set implemented in the SIESTA code. The VPSIC was tested against the highly reliable hybrid HSE theory, implemented in the VASP code. Our work related to the Milestone at month 12 concerning the relative efficiency and the accuracy of the various FP approaches, certificate that a solid agreement between HSE and VPSIC results on the most fundamental aspects of various test materials was evidenced.

The compared approaches showed different inclinations, which make all of them worthy to be selectively applied according to the specific case: the fast and memory-cheap VPSIC/SIESTA implementation is especially useful for large-size systems and molecules; the computationally heavier VPSIC/PW is quite accurate for electronic properties and suited for smaller but highly complex orbital- and/or charge-ordered (OO/CO) systems; the HSE is the main reference for accuracy for both electronic and structural properties but it requires about an order of magnitude increase in computing effort with respect to VPSIC/PW.

Finally an approach based on local density plus dynamical mean field theory (LDA+DMFT) has been developed and tested as well. This approach, which includes dynamical correlation effects into the electronic properties, in principle overcomes VPISC and HSE in accuracy, although the extreme computational effort required by the method limits the applicability to small bulk systems. Given its recognized accuracy, it is the ideal approach for the determination of tight-banding parameters functional to the construction of model Hamiltonians.

Task 1.1. PSIC approach: development and parallel coding.

Improvements of the pSIC method: calculation of forces, implementation of the parallel version of the code, eventual generalization of the single-particle functional and search of alternative, possibly variational schemes. Test cases on metallic and insulating systems. Comparison with other approaches.

This task was fully successful even in the most challenging aspect, i.e. the search for a variational generalization of the pSIC approach. Indeed, a new variational pseudo-self-interaction correction approach (VPSIC) was formulated. The new method works as efficiently as the former (non-variational) for the electronic properties of generic crystalline systems, but in addition it allows the straightforward calculation of atomic forces (hence structural optimisation), clearly not attainable by the former non-variational version. The VPSIC was implemented in two different methodological setting: ultrasoft pseudopotential and plane-wave basis set (i.e. in the PWSIC code) by partner CNR; atomic-orbital local basis set (in the framework of SIESTA code) by partner TCD. Notice that SIESTA and PWSIC are highly complementary, insofar as, despite being both applicable to generic systems, they may be more efficient for different subjects (SIESTA for very large-size systems and molecules, PWSIC for periodic systems characterized by highly complex fundamental chemistry, including e.g. OO/CO states, polarons, mixture of localized and dispersed band energies).

The PWSIC code, previously available in serial mode only, has been modified in order to run on parallel platforms as well. The SIESTA code is fully optimised in parallel version. A full assessment of the VPSIC functional was carried out in synergy by TCD (for what concerns the SIESTA implementation) and CNR (for PWSIC implementation). Test cases have been produced for several magnetic titanates (YTiO3, LaTiO3) and manganites (LaMnO3), as well as non-magnetic oxides (SrTiO3, LaAlO3, TiO2 in Figure 1 of the Attachment). A close comparison with the hybrid functional approach (HSE) developed by Univie was also carried out, with very satisfying results, for structural, electronic, magnetic and thermodynamic properties of some transition metal monoxides MnO and NiO.

Results related to the development and testing of the VPSIC approach represent the basis for Deliverable D1.1 at month 12, The compared analysis of VPSIC and HSE results for TMO is basic for the work of Deliverables D3.123-1 and D3.123-2 due to M18, as well as instrumental to the resolution of Milestones M12 and M18.

Task 1.2: Hybrid functional and GW methods: development and testing.

Development and applications of HFT and HFT+GW methods to strong-correlated systems. Comparative analysis with other approaches. Test cases. (3-Univie).

Task 1.2 is fully accomplished. The hybrid functional theory in the HSE version, already implemented in the VASP code, was applied by partner Univie to a series of complex correlated oxides, and its efficiency and accuracy carefully checked and improved throughout a systematic comparison with the available experimental data. The implementation of several GW-based schemes was also finalized, and test cases carried out for a wide class of 'simple' compounds as well as for more complex materials such as CuO and BaBiO3. In order to achieve a better description of optical and electronic properties of the most challenging materials, we have optimized a scheme, which allows the combination of GW on top of pre-converged HSE wavefunctions.

A close comparison with the VPSIC approach developed in a tight collaboration among Univie, CNR and TCD members was put forth, with satisfying results, for the electronic and magnetic properties of transition metal monoxides (TMO) MnO, NiO, and CuO (see Figure 2 of the Attached PDF). Results related to the development and testing of HSE approach in the VASP framework are included in the Deliverable D1.2 due at month 12, The compared analysis of VPSIC and HSE results for TMO is reported in the Deliverables D3.123-1 and D3.123-2 due to M18, and central to the resolution of Milestones at month 12 and 18.

Task 1.3: LDA+DMFT approach: development and testing.

Development and applications to strong-correlated systems. Comparative analysis with other approaches, and test cases. (1-TCD,2-CNR).

The LSDA+DMFT approach combines DFT-LSDA [or generalized gradient approximation (GGA)] with dynamical mean-field theory (DMFT) for the treatment of strong electron correlation beyond the single-particle level. In practice the method interfaces existing DFT codes with a Quantum Monte Carlo impurity solver and a DMFT loop. From the full electronic structure calculated by DFT a subset of Wannier Functions (WF) relative to the most important strong-correlated states are extracted. These WFs are then used to formulate an effective lattice problem treated within DMFT. A new code has been written to calculate the dynamical mean-field, which described the effective bath for the single site problem, from the WFs. The Greens function of the resulting impurity problem is then calculated using an existing Quantum Monte Carlo code, and the resulting self-energy is used to construct a new estimate for the dynamic mean-field. The procedure is iterated until convergence is achieved. An additional code has been written to implement this self-consistent loop. This requires multiple transformations from the imaginary time formulation used by the Quantum Monte Carlo method to a formulation using Matsubara frequencies used to calculate the local Greens function and self-energy. Another code has been written to extract the electronic spectral function from the converged Greens function using the Maximum entropy method.

The schematic workflow of the method is illustrated in Figure 3 of the Attachment. Test calculations were performed to evaluate the stability and performance of the resulting computational scheme. Applications to selected prototype systems have been carried out, including benchmark system SrVO3, as well as p-electron magnet RbO2 and multilayer SrRuO3/CaRuO3. These results are the basis of Deliverable D1.3 due at month 12.

WP2: Model Hamiltonians and merging with First-Principles calculations

Overall description

Indian partners mastered a formidable array of computational tools based on model Hamiltonians ideal to investigate the coupling of charge, spin, orbital and lattice degrees of freedom in strong-correlated systems. These methods are capable to handle disorder and finite temperature effects, as well as spectral functions/dynamical response. However, in order to be predictive for real materials whose fundamental characteristics are not known from the beginning, or differ from ordinary situations, models need guidance and connection with First-Principles methods.

WP2, lead by Indian partners, was aimed at the development and integration of models and First-Principle methods elaborated in WP1. The construction of model Hamiltonians, carried out in particular by partner HRI, focused on specific phenomenologies (examples are B-site doped and double perovskites) to be then studied in detail in WP3 and WP4. In parallel, the development of downfolding procedures aimed at interfacing generic band spectra spurring from First-Principles calculations with the abovementioned model Hamiltonians was accomplished by several groups in the framework of different First-Principles codes (Univie for VASP, CNR for PWSIC, TCD for SIESTA). Those downfolding interfaces are either written from scratch or adapted from previously existing codes (such as, e.g. the Wannier90 code which constructs maximally localized Wannier Functions on the basis of First-Principles calculated single-particle Bloch states). They typically allow the determination of those essential parameters (typically hopping and on-site Coulomb energies) on which the fundamental phenomenology of magnetic and strong-correlated systems crucially depends.

The model Hamiltonian development carried out by HRI mainly relies on the strategy called Traveling Cluster Monte Carlo (TCM), an O(N) method, which can be applied to model systems of up to N~103 lattice sites (note that the scaling is linear, so that the maximum size of the system to investigate is simply limited to the computational resources available). The method solves Hamiltonians with a combination of (few) quantum degrees of freedom (typically related to eg orbitals), coupled to several classical parameters (e.g. JT displacements, t2g spins, etc.) and gives access to both ground state and finite temperature properties (transport, spectra, optics) at arbitrary coupling, including disorder. Notably the scheme fails if finite on-site Coulomb (U) interaction is introduced (at the mean field level the same scheme is possible but it becomes computationally extremely heavy). In order to circumvent the problem, HRI proposed a strategy based on the introduction of a Hubbard-Stratonovich effective field which accounts for the electronic coupling through the introduction of a classical field variable ?(x, t), thus making the TCM approach still applicable. In the following a concise description of the planned tasks of WP2 related to the downfolding procedures is reported.

Task 2.1: Merging FPC and MH: development and integration of HFT and HFT+GW with MH methods.

Development of an integrated FPC (HFT and HFT+GW implemented in VASP) plus MH scheme, and relative code implementation. Testing successful implementations on bulk materials (typically bulk manganites or transition metal oxides). (5-HRI, 3-Univie, 4-SNBNCBS).

Task 2.1 is devoted to the implementation and testing of a software interface between hybrid-functional (specifically the HSE version) plus GW calculations as implemented in the VASP code, and the model (Hubbard) Hamiltonian approach. This interface performs the construction, starting from HSE+GW-calculated electronic eigenstates, of the corresponding maximally localized Wannier functions (MLWF), according to the prescription of Marzari and Vanderbilt [Phys. Rev. B 56, 12847 (1997)], as implemented in the Wannier90 code, and the subsequent mapping into suitable tight-binding (TB) parameters. Since MLWF are defined in real space, they are in principle ideally suited to map the electronic ground state of the system in the real-space representation typical of model Hamiltonian; the MLWF matrix elements can be interpreted as hopping amplitudes within a TB picture. By constructing MLWF for a (small) set of bands suitably selected in a physically important energy window, one can construct a TB model, which reproduces the exact band dispersion, thus forming the basis for a model Hamiltonian analysis. In Figure 4 of the Attachment a scheme of the Method is reported.

In practice, the Wannier90 code requires as input (a) the overlap matrix elements between the cell periodic part of the Bloch states and (b) the initial projections of the Bloch states onto trial localized orbitals. The passage of these two ingredients from VASP to Wannier90 is operated by the newly written VASPtoWANNIER90 interface, now available in the VASP package for all members of the consortium. The interface is also included in the latest official release of the VASP package. Several test-case applications to e.g. MnO, LaMnO3, and graphene were carried out to prove the functioning of the method. The MLWF downfolding procedure was shown to be a solid approach to connect First-Principles and model Hamiltonians, and our results certificate the confidence in the method.

The VASPtoWANNIER90 interface included in the latest VASP official release package matches the software/object Deliverable 2.1 due at M12.

Task 2.2: Merging FPC and MH: development and integration of PSIC with MH methods.

Development of an integrated PSIC (implemented in PWSIC) plus MH scheme, and relative code implementation Testing successful implementations on bulk materials (typically bulk manganites or transition metal oxides). (5-HRI, 2-CNR, 4-SNBNCBS, 6-JNCASR).

The work of Task 2.2 was addressed to write an interface software added to the PWSIC code which mounts the new variational VPSIC approach developed in Task 1.1 to derive parameters necessary to build model Hamiltonians through band downfolding procedures. Two routes have been followed: the first performs the band manifold projection onto a Lowdin-orthonormalized atomic orbital (OAO) basis set. In this way a full set of tight-binding parameters is generated, including hopping and on-site energies, which can be directly transferred to a model Hamiltonian setting. The second is based on interfacing PWSIC and the Wannier90 code, analogously to what is done in Task 2.1 for VASP and Wannier90, in order to derive MLWF-based tight-binding parameters.

For what concerns the OAO-based downfolding procedure, we have performed a test calculation regarding the prototypical correlated Mott perovskite LaMnO3, in its antiferromagnetic, orbital-ordered, orthorhombic Pnma equilibrium structure, for which it is well known that only oxygen-mediated hopping between nearest-neighbor eg orbitals are substantial. We obtain results in agreement with other available downfolding approaches (such as the one based on MLWF), thus showing that the combined VPSIC+OAO downfolding procedure can produce reliable parameters for setting efficient Hubbard model Hamiltonians. Test cases for the PWSIC/Wannier90 interfaces have been also carried out for magnetic titanates (LaTiO3 and YTiO3), which are extremely interesting prototypes of t2g orbitals compounds.

The OAO-downfolding subroutine and the PWSICtoWANNIER90 interface are both included in the freely available PWSIC developmental version, and represent the software/object Deliverable 2.2 due at M12.

Task 2.3: Merging FPC and MH: development and integration of ASIC and EE with MH methods.

Development of an integrated ASIC and EE (implemented in SIESTA) plus MH scheme, and relative code implementation Testing successful implementations on bulk materials (typically bulk manganites or transition metal oxides). (6-JNCASR, 5-HRI, 1-TCD, 4-SNBNCBS).

The work of this Task proceeded along different directions, consisting in several code developments and testing, in the framework of the SIESTA code. Code development has been achieved in full, and the related software (ASIC and EE in SIESTA, and SIESTA-MH interface) is now ready to be used. Test cases assessing the quality of the codes are completed for the materials of relevance to the project. In the following we discuss the achievements of the task for each methodological development.

Full self-interaction correction (SIC) and Exact Exchange (EE) approach implemented in SIESTA.

In addition to the mean-field-like VPSIC scheme implemented in SIESTA (Task 1.1) a fully self-consistent version of the SIC-LDA functional, as originally proposed by Perdew and Zunger requiring the handling of a truly orbital-dependent functional, was also implemented in SIESTA. However, this is only available for finite systems and cannot be used for crystalline solids (unless they are cast in a finite cluster form). In brief our SIC-LDA implementation is based on the optimized effective potential (OEP) concept. Here an orbital dependent potential is recast, by variational principle, into an effective local functional leading to the same ground-state charge density and energy as the original orbital dependent functional. This is a common strategy used both for the SIC-LDA and the DFT exact exchange (DFT-EE) functionals (see next section). Also common to both SIC-LDA and DFT-EE is the reduction of the non-linear integral OEP equations to a set of linear equations, which can be solved by simple linear algebra. This is known as the Krieger-Li-Iafrate (KLI) method. Specific of the SIC-LDA method is the necessity of constructing the local potential from a set of localized orbitals related to the Kohn-Sham eigenfunctions by a unitary rotation, thus leaving the electron charge density invariant.

At variance with SIC-LDA, the DFT-EE functional is applicable to periodic system. The strategy closely follows that for the SIC-LDA scheme: the overall formulation is based on OEP and the problem is solved only approximately through the KLI scheme. Crucial to the Siesta implementation is the reduction of the 4-centre integral defining the EE potential to simplified 3- and 2-centre integrals. This effectively allows to achieve a computing cost scaling as N*nA4, instead of (N*nA)4 (where N is the number of unit cells and nA the number of basis functions per unit cell).

Mapping DFT to MH in Siesta

A tool for building maximally localized WFs from SIESTA-calculated band energies is now available [see R. Korytár et al. arXiv:0910.1748]. This has been constructed independently by the SIESTA team and essentially consists in an interface with the Wannier90 code [see wannier.org]. Importantly, the existing code is also interfaced with our private version of SIESTA, which includes ASIC, VPSIC and DFT-EE. Thus, the consortium members have now the capability of constructing MLWF from band energies calculated through a vast array of different functionals and of directly mapping the band energies obtained with these functionals onto know model Hamiltonians.

Test Cases

Several tests were performed to assess the correctness of the newly implemented DFT-EE functional for: 1) bulk solids, 2) supercells, 3) surfaces, and 4) molecules adsorbed to surfaces; while tests on the mapping of SIESTA band energies onto model Hamiltonians were carried out for MnO and RbO2.

For bulks, the DFT-EE give band gap in substantial agreement with the experiments, thus largely improving the LDA values. For supercells, the N*nA4 scaling of the code with the number of atoms has been demonstrated. As for surface properties, with the new DFT-EE scheme we have studied the Si (100) surface, which contains a well-known surface state splitting off from the Si bulk conduction band. The ~0.7 eV bandwidth of this surface state was perfectly reproduced. Furthermore such a surface state is offset by about 0.7 eV from the Si valence band, in agreement with experiments and at variance with the underestimated LDA/GGA offset of 0.4 eV. Finally we tested the DFT-EE scheme for molecules weakly coupled to metallic surfaces, in order to demonstrate the presence of the derivative discontinuity of the DFT potential in the EE approximation.

Task 2.4: Implementation of Lanczos algorithm for calculation of finite temperature spectral functions.

Calculation of relevant spectral functions for resonant x-ray scattering, especially at the transition metal L edge where both single particle effects as well as Coulomb interactions have to be handled simultaneously. The low temperature spectral functions will be calculated by finite temperature Lanczos algorithm. (4-SNBNCBS).

Task 2.4 (and its related Deliverable 2.4) has been partially accomplished since the method so far is implemented only for the case of zero-temperature; the development finite temperature algorithm is currently in progress at the Indian unit SNBNCBS, and it will be completed during the one-year no-cost extension of the Indian side of the consortium. We emphasize that this task is a single-participant beneficiary (Indian partner SNBNCBS) with a minimal connection with the rest of the project (i.e. it does not affect any deliverables subsequent to those of WP2), thus the delay had no impact either on the overall achievement of the Project objectives or on the resources originally planned.

The reason of the delay resides in the necessity for partner SNBNCBS to give priority to the development of software more directly preparatory to the common activity of European and Indian groups, rather than to the achievement of more individual interests. In the following we briefly describe the abundant code development carried out by SNBNCBS in the framework of Task 2.4.

Mean field decoupling of most general Coulomb interaction (SNBNCBS)

The most general form of the four-fermion Coulomb operator is evaluated for both p and d electrons. A computational scheme was implemented to carry out the mean-field decoupling and calculate the order parameters self-consistently. Such an implementation was carried out to treat a class of charge ordered ferromagnets and alkali metal oxides (both discussed later in applications).

Non perturbative determination of exchange interaction strengths (SNBNCBS)

The recent interest of the magnetism community has focussed on understanding the possibility of a magnetic order in p-shell materials. In this context, one desires a computational tool, which allows calculating the exchange interaction as the magnetic order of the p ions is altered. Unfortunately for these systems a perturbative approach fails. We have then implemented a non-perturbative treatment for determining the exchange paths, and subsequently applied to various p shell magnets.

Determination of magnetic anisotropy constants and spin-orbit interaction (SNBNCBS)

We implemented a computational scheme to determine the anisotropy constants for strongly correlated materials from model calculations. Similarly we implemented a model Hamiltonian based on the tight-binding formalism, which includes spin-orbit interaction. This is suitable for the description of 5d oxides.

Building the full multiplet Hamiltonian (SNBNCBS)

We built a full multiplet Hamiltonian, and solved it in within a mean-field decoupling for treating non-collinear magnetism. This opened the route to a more rigorous treatment of magnetism and an understanding of magnetization mechanism in greater detail.

WP3: Fundamental properties of bulk doped magnetic perovskites and transition metal oxides.

Objectives and overall description

This workpackage gathers together all the methodological capabilities and computational advancements spurred from WP1 and WP2 to attack the study of systems of interests, i.e. mainly magnetic oxides, with special emphasis on (doped/undoped) magnetic manganites and transition metal oxides (TMO). A comparative analysis of results obtained with different methodologies is aimed at tracing a rigorous account of the microscopic features of these systems in order to describe structural, electronic, and magnetic properties, as well as finite-temperature thermodynamic and transport properties, and phase diagrams as function of doping.

WP3 was scheduled to cover the whole 2nd year and a portion of the 3th year of the project. As expected and planned, WP3 required a huge amount of work and an intensive collaborations among the various EU and India members, which resulted in several published works and others currently submitted for publication.

Task 3.1: Study of Colossal-magnetoresistive Magnetic Perovskites by integrated FP+MH approaches.

M12-M24

Study of the fundamental properties of CMR manganese perovskites (e.g. LCMO, LSMO) and insulating manganese perovskites (e.g. Pr1-xCaxMnO3) carried out within FPC+MH approaches, where FPC may include PSIC, HFT (or HFT+GW), DMFT and EE. Investigations of electronic, magnetic, and structural properties both at equilibrium and under strain, as well as thermodynamic properties. Comparison with the available experimental results and previous theoretical results. (2-CNR, 5-HRI, 6-JNCASR, 3-Univie, 1-TCD).

The work inherent to this task, devoted to generic applications of the First-Principles plus model Hamiltonian approach to magnetic oxides is especially abundant and articulated, since all partners have largely contributed to it. The original proposition included as test materials well known A-site doped manganese perovskites families (LCMO and LSMO), and indeed an abundance of work was produced for those systems and their undoped parental compounds (i.e. CMO, LMO). On the other hand, the work also explored other magnetic oxide families, which gained special interest in recent times. This includes magnetic titanates (governed by 3d t2g electrons instead of the 3d eg types as in manganites) and the so-called superoxides (e.g. RbO2) where long-range magnetism can be induced by doping. The extension of our materials of interest is motivated by the need to verify the suitability of the methods set in the work of WP1 and WP2 for an as large as possible variety of applications.

A list of works inherent to this task include:

a) Study of undoped LaMnO3 carried out by hybrid functional HSE and GW, by partner Univie. This includes the determination of ground-state structural, electronic and magnetic properties, and the study of pressure-induced quenching of the cooperative Jahn-Teller (JT) distortions and the suppression of the orbital ordering leading to an insulator to metal transition accompanied by magnetic transitions. The very expensive First-Principles calculations with a variety of functionals (PBE, HSE and GW), and the full Tight-Binding parametrization, which is the essential ingredient for the model Hamiltonian analysis, were both accomplished.

In the framework of a collaboration involving partners Univie, HRI and TCD, the evolution of the spin- and orbital-ordered states in RMnO3 (R=La,Pr,Nd,...) by combined First-Principles plus model Hamiltonian approach was investigated. More specifically, we have determined the effect induced by a progressive decrease of the R-ion atomic radius on a) the enhancement of the cooperative GFO-like rotation of the MnO6 octahedra and the associated decrease of the Mn-O-Mn bond angle; b) the modulation of superexchange interaction between next-nearest Mn sites; c) the enhancement of the insulating character; d) the changes of the Jahn-Teller ordering temperature. In Fig.5 of the attached PDF file the effect of pressure on the Mn-O distances of LaMnO3 is reported.

b) Study of doped Ba1-xKxBiO3 (BKBO) by hybrid functional HSE. Carried out by partner Univie. The study of electronic and structural properties of this charge-ordered (CO) compound (with alternating Bi3+ and Bi5+ ions) was carried out in a wide range of A-site doping concentration, in order to investigate the interesting phase transition occurring from the insulating state at low-doping to the superconducting state at high doping. The properties change with hole doping are understood in terms of stabilization/interaction of bi-polarons consisting on Bi3+ ? Bi5+ plus local breathing distortions transformations occurring upon Ba? K substitutions. In Fig.6 of the Attachment the calculated and experimental volume is showed as a function of the k-dopant concentration, together with the indication of structural and transport phase stability at any doping.

c) Magnetism in 4d perovskites RTcO3. Carried out in cooperation by partners Univie, TCD & CNR. The evolution of the magnetic ordering temperature of the 4d3 perovskites RTcO3 (R=Ca, Sr, Ba) and its relation with electronic and structural properties was studied by means of hybrid density functional theory and Monte Carlo simulations. When compared to the most widely studied 3d perovskites the large spatial extent of the 4d shells and their relatively strong hybridization with oxygen weaken the tendency to form Jahn-Teller like orbital ordering. This strengthens the superexchange interaction. The resulting insulating G-type antiferromagnetic ground state is characterized by large superexchange coupling constants (26-35 meV) and Néel temperatures TN (750-1200 K). These monotonically increase as a function of the R ionic radius due to the progressive enhancement of the volume and the associated decrease of the cooperative rotation of the TcO6 octahedron. See Figure 7 of the Attachment for the results concerning calculated critical temperature and exchange interactions calculated as a function of the Tc-O-Tc angle.

d) Study of undoped magnetic titanates YTiO3 and LaTiO3 by VPSIC method. Partner CNR carried out the study of structural, electronic and magnetic properties of these two prototypical Mott insulators, with results in nice agreement with the observations, thus demonstrating the good accuracy of the variational VPSIC developed in the work of Task1.1.

As an example, in Fig.8 of the Attachment the calculated magnetization isosurface is showed for both systems, from which we can appreciate the ferromagnetic and antiferromagnetic ordering of YTO and STO, respectively, as well as their different orbital ordering: checkboard for YTO, ferro-orbital for LTO. Magnetic and orbital ordering depend on each other according to the superexchange rules. Our results nicely agree with previous theoretical results based on dynamical mean field, and with available photoemission experiments.

e) Electronic structure of Ferromagnetic Insulator K2Cr8O16. Accomplished in collaboration by partners SNBNCBS & Univie. Ferromagnetic insulators are rare in nature and the microscopic mechanism for their magnetic order is usually different from that invoked to explain ferromagnetism in metals. We studied the prototypical ferromagnetic insulator K2Cr8O16 within First Principles electronic structure calculations. Our work demonstrates that charge ordering transition is responsible for the insulating phase. Charge ordering is induced by K-doping and it is found to generate a super-exchange pathway that allows ferromagnetism to be stabilized. Calculations have been carried out with the LDA+U scheme, to account for on-site Coulomb repulsion at the Cr sites. The density of states of the ferromagnetic insulator K2Cr8O16 is presented in Fig.9 of the Attachment.

f) Magnetism in p-shell compounds: KO2 This work was realized by partner SNBNCBS. The community, which investigates magnetic materials showed a revival of interest for p-type magnetism, i.e. magnetism present in magnetic materials devoid of ions with partially filled d or f shells. Most of the effort has been devolved to defective oxides where defects can present an electronic structure sustaining a high spin state. However, we have identified an entire class of stoichiometric materials made of alkali-metal oxides, which can sustain a magnetic order. The elementary unit for such materials is the O2 molecule, whose ground state is a spin triplet. The long-range magnetic order however is the result of a subtle interplay between narrow band splitting and orbital ordering. In particular for the case of KO2 we find that orbital ordering (see figure) driven by electrostatic interaction precludes the possibility of high-temperature ferromagnetism. [Phys. Rev. Lett. 105, 056403 (2010).] The charge density isosurface of KO2 can be found in Fig.10 of the Attachment. Note that this work was related, and benefited from, a similar investigation carried out by TCD on RbO2 [Phys. Rev. B 86, 075130 (2012); Phys. Rev. B 80, 140411(R) (2009)].

g) Dual behaviour of excess electrons in TiO2. Carried out by partner Univie. Seemingly conflicting results have been reported for the behavior of electrons in TiO2. While high mobility have been observed, characteristic of delocalized electrons in the conduction band, excess electrons in TiO2 have long been described as localized small polarons. In this study we reconcile this apparent contradiction by showing that small polarons can coexist with delocalized electrons, and the dominant behavior depends on the type of experiment being conducted. By means of hybrid functional calculations we find that small polarons are energetically only slightly more favorable than delocalized electrons in n-type TiO2. The small polarons explain the optically-detected gap state near the conduction band, whereas the delocalized electrons give the high mobility observed in Hall measurements. We also find that small polarons can form complexes with oxygen vacancies and ionized shallow-donor impurities, explaining the rich spectrum of Ti3+ species observed in the electron paramagnetic resonance experiments. See Fig.11 in the Attached file.

h) Cation site-disorder, magnetic ordering and phonons in FeAlO3. Carried out by partner JNCASR. FeAlO3, reported to have ferrimagnetic and piezoelectric properties, has cation sites with both tetrahedral and octahedral coordination. Motivated by the rich set of its observed properties, we use first-principles density functional theory based calculations to determine the coupling between cation (Fe-Al) site-disorder and its magnetic ordering and vibrational properties. Using microscopic information available from our calculations, we investigated the possibility of magneto relaxor behavior with Ga substitution at the Al site. This work is in collaboration with experiments of C.N.R. Rao, A.K. Sood and A. Sundaresan at JNCASR. See Fig.12 in the attached file.

Task 3.2: Study of multiferroic magnetic perovskites and interplay of magnetic and electric polarization. M12-M24.

Study of ME coupling in MP: coexistence of CMR and CER effects (e.g. in Pr1-xCaxMnO3), and alternative forms of multiferroicity in MP. Investigations carried out within FPC+MH approaches, where FPC may include PSIC, HFT (or HFT+GW), DMFT and EE. Comparison with the available experimental results and previous theoretical results. (6-JNCASR, 1-TCD, 2-CNR, , 4-SNBNCBS, 3-Univie)

The study of magnetoelectric (ME) coupling in manganites in half-doped perovskites. Carried out by partner CNR. We investigated Pr1-xCaxMnO3 at half-doping (x=1/2), since at this concentration some form of ME behaviour was expected according to model calculations. VPSIC calculations of the electronic and magnetic properties of Pr1/2Ca1/2MnO3 indeed detected an electric polarization (P) in the insulating AF-CE magnetic phase, induced by the Pbnm ? P21nm structural distortion and the relative change in orbital ordering. The calculated P is purely electronic (i.e. Berry-phase determined) in the direction parallel to the spin-aligned chain direction, structurally determined orthogonally to the chains. See Fig.13 of the Attached file. The results related to this task have been published in Ref. G. Colizzi, et al, Phys. Rev. B 82, 140101(R) (2010). This work is also subject of Deliverable 3.2 due at month 24.

5) Use of Raman spectroscopy as a tool to find route to metal-insulator transition in Magnetoelectrics (JNCASR). Raman spectroscopy is a highly versatile and effective tool for the exploration of both bulk and nano-scale materials. We determined how a clear pathway to a metal-insulator transition in magnetoelectric materials is reflected in the anomaly of their Raman spectra, second order Raman spectral peaks being unexpectedly more pronounced than the first order ones. Using a combination of experiment and first-principles simulations, we demonstrate this behavior in a magneto-capacitive double perovskite La2NiMnO6, and in a well-known multiferroic BiFeO3. In the latter, our theory connects with an integer quantum ambiguity in polarization associated with path-dependent geometric phase, which often leads to puzzling interpretations of observed and theoretical values of polarization of multi-ferroics. Our work opened up the use of Raman spectroscopy in identifying the structural paths that lead to metal-insulator transitions that are fundamentally relevant to technological applications. This work was realized in collaboration with experiments of A.K. Sood and A. Sundaresan at JNCASR Institute.

Task 3.3: Study of diluted magnetic ferroelectrics by MH and FP+MH approaches.

M12-M24

Structural, electronic, and transport properties will be studied for the most promising diluted magnetic ferroelectrics through MH and FPC+MH approaches. Comparison with available experimental results and previous theoretical results. (4-SNBNCBS, 1-TCD)

In order to overcome the problem of the scarcity of multiferroic and magnetoelectric materials, one possible route is to plug into a ferroelectric host some magnetic dopants. Achieving a multiferroic system is however far from obvious, since the specificity of doping atomic species and the chemical environment surrounding the dopant must be fortunate enough to allow long-range magnetic ordering.

To explore this possibility in this task we studied the inclusion of magnetic atoms into a well-known ferroelectrics, BaTiO3, with inclusion of Ti-substitutional V and Mn at doping concentration of 5%. Ferroelectricity was found to be favored in the case of V and Mn doping in the GGA+U calculations. In the HSE calculations we found that all the doped transition metal atoms gave rise to filled impurity bands in the band gap of BaTiO3. Hence, ferroelectricity was found to be favored in all cases. This work is also the subject of Deliverable 3.3 due at month 24.

Task 3.4: Study of double perovskites: setting innovative MH and merging with FPC.

Period: 12-24

Construction of MH and then a many body/finite temperature theory, for the study of ground state, transport and thermodynamic properties of doped double perovskites by FPC (PSIC, HFT, HFT+GW) +MH approach. Comparison with available experimental results and previous theoretical results. (4-SNBNCBS, 5-HRI, 6-JNCASR).

Antisite disorder and domain formation in double perovskite ferromagnets A2BCO6 (e.g. La2NiMnO6, Sr2FeMnO6). Several double perovskite materials of the form A2BBO6 exhibit high ferromagnetic TC, and significant low field magnetoresistance. They are also a candidate source of spin-polarized electrons in spin-injection devices. The potential usefulness of these materials is, however, frustrated by misallocation of B and B ions, which are not ordered in the ideal alternating structure. The result is a strong dependence of the physical properties on preparative conditions, which reduces the magnetization and destroys the half-metallicity. Partner HRI provided the first study of the impact of spatially correlated antisite disorder (ASD), as observed experimentally, on the ferromagnetic double perovskites. The ASD suppresses magnetism and half-metallicity, as expected, but lead to a dramatic enhancement of the low field magnetoresistance (mostly due of magnetic variation of percolation paths). Calculations have been carried out at the level of electron/spin Hamiltonian and exact diagonalization Monte Carlo simulations for large disordered cells. See in Figures 14 and 15 of the Attached file the calculated maps of ASD configurations, and the calculated magnetization and resistivity as a function of temperature, respectively.

2) Antiferromagnetic Order and Phase Coexistence in Antisite Disordered Double Perovskites. Carried out by partner HRI. Much of the excitement in the investigation of double perovskites (DP) was due to the high ferromagnetic (FM) Tc, large magnetoresistance, and the possibility of spin-polarized conduction in materials like Sr2FeMoO6 (SFMO). However, it is also interesting to explore whether other non-FM orders (e.g. CE, A, C, and G type antiferromagnetic (AF) phases typical of single perovskites) may occur at some doping concentration range. Model Hamiltonian calculations shows that at low electron density the FM alignment of the core spins is favored since it leads to the maximum bandwidth. However, at sufficiently large band filling, antiferromagnetic (AF) states with A or G type order (in two dimensions) become successively favored. Nevertheless, electronically driven AF order continues to be elusive experimentally. One can envisage two reasons: (i) the AF phase occurs at (high) electron densities which have not been probed yet, or (ii) increasing electron density leads to a rapid growth in antisite disorder (ASD), strongly suppressing any signature of long range AF order.

The theoretical effort till now has focused on AF order in structurally ordered DP, but in real materials the B, B alternation between the two transition metal atoms is interrupted by an anti-phase boundary (APB) involving BB or BB nearest neighbors. This leads to a pattern of structural domains. The ASD not only destroys periodicity but also brings into play an additional AF superexchange coupling when two B ions (like Fe) adjoin each other. If this superexchange scale is sufficiently large, the BB anti-phase boundary also acts as a magnetic domain wall (MDW), leading to magnetic domain formation, suppression of magnetization, and a large enhancement of the resistivity. Our work provides a systematic exploration of the effect of increasing ASD on the AF phases in a two dimensional (2D) double DP model. We consider two electron densities relative to `A type' and `G type' ordering, and study magnetic order and transport for increasing antisite disorder.

Our principal results are: i) the suppression of magnetic order with ASD is slower in the AF than in the FM phase, and even with 30% mislocations there are clear signatures of long-range order. (ii) The Tc is not significantly affected, until strong disorder, although the `transition' is broadened. (iii) Both AF phases are metallic, and the increase in their resistivity with ASD is weaker than in the ferromagnet. (iv) The phase separation regime between the FM and A type phase is converted to a phase coexistence window in the presence of moderate ASD, and one observes the occurrence, locally, of both kinds of order in the same sample. In Fig.16 of the attachment maps of calculated magnetic correlations are reported.

Task 3.5: Study of B-site dopants: setting innovative MH for B-site dopants and merging with FPC. Period: 12-24

Construction of MH and then a many body/finite temperature theory, for the study of ground state, transport and thermodynamic properties of doped DP by FPC (PSIC, HFT, HFT+GW) +MH approach. Comparison with available experimental results and previous theoretical results. (5-HRI, 4-SNBNCBS, 6-JNCASR).

B-site doping in magnetic oxides is a subject of great interests for the possibility of radically changing the properties of the host material with a small amount of doping. While disorder on the active d element site is usually very disruptive for conduction and long-range order in perovskite transition metal oxide, in the background of phase competition it may also act to promote one ordered phase at the expense of another. This occurs either through valence change of the transition metal or via creation of defects in the parent magnetic state.

Partner HRI elaborated a model Hamiltonian written on the basis of few parameters thus providing a framework for understanding the complex variety of phenomena observed in B-sitedoped manganites, and identifying the key parameters that control the physics. However, to the aim of being predictive for practical cases, the generic Hamiltonian must be specified in terms of parameters drawn by First-Principles calculated electronic band structure. In Fig.17 of the attached file the schematic level diagram is reported.

The results of the work related to Tasks 3.4 and 3.5 are the subject of Deliverable 3.45 due at month 24. Publications related to these topics by HRI group are: V. N. Singh and P. Majumdar, Europhysics Letters 94, 47004 (2011); arXiv:1009.1709v1 [cond-mat.str-el] 9 Sep 2010. R. Tiwari and P. Majumdar (HRI), arXiv:1105.0148v2 [cond-mat.str-el] 3 May 2011.

WP4: Interfaces, multilayers, and devices

Objectives and overall description

WP4 is the most technologically oriented workpackage of the present project, as it deals with the study of interfaces, heterojunctions, and multilayers, with functional capabilities, such as magnetoelectric effects and spin-transport capabilities. The work performed in WP3 was largely instrumental to the WP4, since several bulk systems studied in WP3 are also building blocks of the examined multilayers. WP4 covered the whole 3rd year of the project, and was carried out in tight collaborative synergy among the consortium partners.

Task 4.1: Magnetic/ferro/piezoelectric interfaces: structural, electronic and transport properties. Period: 25-36

Calculation of the physical properties of several interfaces between different magnetic and ferro- piezoelectric materials carried out within both PSIC and PSIC+MH, HFT, HFT+GW and HFT(+GW)+MH methods. Investigations include determination of electronic, magnetic, structural and transport properties. The accuracy of our description was evaluated against available experimental and previous theoretical results.. (2-CNR, 6-JNCASR, 3-Univie, 5-HRI).

For this Task we selected a number of important cases of heterostructures and multilayers with special functionalities such as multiferroism, magnetoelectric coupling, magnetoresistance. In the following we briefly describe three relevant prototypes, the CuO/SrTiO3 interface, the multiferroic tunnel junction (MTJ) SrRuO3/BaTiO3/SrRuO3, (SRO/STO/SRO) and the LaNiO3/LaAlO3 (LNO/LAO) superlattice.

CuO/SrTiO3 interface: (Carried out by Univie). Hybrid Functionals are applied to study the evolution of the structural, electronic, and magnetic properties. The proper inclusion of substrate effects is crucial to understand the tetragonal expansion and to reproduce correctly the measured valence band spectrum for a CuO thickness of 3-3.5 unit cells (See Fig.18 of the attached PDF), in agreement with the experimentally estimated thickness. Our analysis explains the anomalously large Cu-O vertical distance observed in the experiments (2.7 A, see Fig.18): we find that the enormous structural anisotropy of the Cu-O sublattice --which determines the experimentally observed tetragonal symmetry-- can be understood in terms of a layer dependent evolution of the Cu ionicity which increases progressively towards the surface. Ultimately, the local structural and electronic Cu-O environment appears very frustrated as a results of the coexistence between two concurrent states attributable to an in-plane Cu2+-like and out-of-plane Cu3+-like arrangements. This work is Published in: C. Franchini, X.-Q. Chen & R. Podloucky, J. Phys.: Condens. Matter 23 045004 (2011).

For what concern transport properties, we have implemented a computational scheme to merge the VASP code with the BoltzTrap code, the computer program developed by G. Madsen and D. Singh for calculating the semi-classical transport coefficients. The VASP2BOLTZTRAP interface has been successfully applied to the calculation of the spin-polarizations in the Half-metallic FM regime realized in the CMR parent compound LaMnO3 at elevated pressure. We found values for the spin polarization very similar to those obtained for the CMR regime of doped LaMnO3 (La0.7Sr0.3MnO3). The interface is fully compatible with post-DFT methods such has HFT and GW. This work is published in: J. He, M.-X. Chen, X.-Q. Chen, and C. Franchini, Phys. Rev. B 85, 195135 (2012).

Multiferroic tunnel junction (MTJ) SrRuO3/BaTiO3/SrRuO3 (carried out by TCD). We performed an initial relaxation of bulk BaTiO3 and SrRuO3 under an in-plane compressive strain, emulating the common epitaxial growth on SrTiO3, to find the relaxed out-of-plane lattice constant. The relaxed cells were then used to construct the transport supercell, which comprises six BaTiO3 unit cells (?2.5 nm) sandwiched at either side by three SrRuO3 cells. The SrRuO3/BaTiO3 interface is SrO/TiO2 due to the experimentally observed volatility of the RuO2 termination. We consider two structures. In the first nonferroic (NFE) structure the atoms are frozen artificially in their centrosymmetric positions with the interfacial distance given by an average between the BaTiO3 and SrRuO3 c-lattice constant. In the second all positions in the supercell are completely relaxed out-of-plane until the forces are less than 10 meV/A, resulting in a stable ferroelectric ground state (FE structure). At the center of the BaTiO3 slab Ti displaces by 0.14 Å, which is significantly of bulk BaTiO3 experiencing smaller than the value of 0.23 Å the same strain. Note that GGA overestimates the volume and atomic distortions associated with ferro-electricity in BaTiO3 resulting in a supertetragonal structure. Such an over estimation, while resulting in a polarization greater than the experimental one, will not have a significant qualitative effect on our results. The interfacial SrRuO3 layers, as expected, also contribute to the polarization.

The symmetry of the electronic bands of both the ferromagnetic electrodes and the insulating spacer dictates the transport properties. Importantly, an incident Bloch state in the electrodes can couple to a given evanescent state in the insulator and then sustain a tunneling current, only if the two share the same symmetry.

The spin-polarized current for both the PA and AP configurations and for both the NFE (top panel) and FE (middle panel) structures are shown in Fig. 19 of the attached PDF, where we focus on the low voltage region in which the current is due entirely to tunneling (the broader I-V are displayed in the insets). The most distinctive feature emerging from the I-V curves is the presence of negative differential resistances (NDR) for the PA alignment, originating from the movement of the ?1? band edge with V. Because of the NDR the relative magnitude of the current for the parallel (IPA) and antiparallel alignment (IAP) can be reversed (i.e. the TMR changes sign with V). This work is published in: Phys. Rev. B 83, 125409 (2011).

Nickelate superlattice (carried out by CNR). Nickelates are nowadays among the most investigated oxides: their magnetization state is (even more than in manganites) sensibly influenced by small structural distortions and applied strain. When cast in heterostructures or superlattices, nickelates then provide potentially suited prototype systems whose structural, magnetic, and transport properties can be changed and manipulated by application of selected substrates, strains, and external fields. The LNO/LAO magnetic superlattice (MSL), recently grown and characterized, is one viable case where these functionalities can be implemented. Our calculations provide a description of the fundamental properties of this system in striking agreement with the experiments, and elucidate the mechanism at the basis of its phenomenology.

Our calculations describe the ground state as structurally dimerized, charge-ordered, insulating, and antiferromagnetic. This phase is energetically favorite with respect to metallic paramagnetic phase which characterize bulk LaNiO3. The transition is driven by valence disproportionation of Ni atoms at low T: in the insulating AF-CO phase the (nominally) Ni3+ sublattice splits in two separate sublattices occupied by magnetic Ni2+ and non-magnetic Ni4+ ions. Ni2+ ions have moment of 1.44 ?B (configuration t2g6eg2) while Ni4+ have zero moment (t2g6eg0). Within mean field approximation, the critical Neel temperature is TN ? 33 K, close to the experimental 40 K. All the above findings are consistent with the experiments. The concurrent action of dimerization and magnetic superstructure open an electronic gap of 1.3 eV in the AF-CO phase. Octahedral distortion is essential to obtain a gap: without distortion all simulated phases are metallic and not CO. However, only the Pauli-PM metal phase is stable in the non-CO configuration.

We use the calculated band structure to obtain transport properties through the Bloch-Boltzmann theory (BBT). We apply the BBT to evaluate the DC electron conductivity; in this work the ultrathin SLs (with 3 LNO units or less) appears as a correlated metal with anomalous hopping-like T-dependence, whereas thicker SLs behave as a normal metal but with large residual resistivity. Our working hypothesis is that the thick normal-metal SL corresponds to the PM phase, and the ultrathin SL to an electron-doped AF-CO insulating phase (typical impurities in wide-gap transition metal oxides, e.g. oxygen vacancies, are donors). Our results (see Fig.20 of the attached PDF) nicely fit the observations: at low-T the DC conductivity grows exponentially, then saturates to a more conventional metallic linear behaviour above T?150 K.

In summary: The work of Task 4.1 demonstrated the capability of our combined First-principles plus model approaches to investigate the fundamental properties of magnetic oxide heterostructures, from structural to electronic, magnetic, and transport properties. Our results describe several phenomenologies, in full agreement with the experimental studies. For what concern the examined all-oxide ferroelectric MTJ, we have detected huge TMR, the sign of which can be inverted as the applied bias increases. Furthermore, the sign inversion occurs at different voltages for different ferroic states of the barrier. Our finite-bias results are explained in terms of the electrodes and the barrier band structures. The possibility to control the TMR by manipulating the ferroic state of the barrier in an MTJ opens a potential avenue for the electrical control of magnetic devices. For what concern magnetic superlattices, we have studied LNO/LAO SL with ultra-short period, and found structurally- and valency-dimerized charge-ordered insulating ground state, undergoing a phase transitions to a metallic Pauli paramagnet. The magnetic and metal-insulator critical temperatures are estimated around 35 K and 80 K respectively. This interpretation is in good agreement with available experimental data. We have also described the SL transport properties in agreement with the observation.

Task 4.2: Merging models and First-Principles: setting model Hamiltonian for oxide interfaces.

Period: 25-36

Construction of model based on First-Principles parameters, and then a many body/finite temperature theory, for the study of oxide interfaces (especially manganese interfaces) and the related reconstruction effects on structural, electronic and magnetic properties. . The accuracy of our oxide interface description was evaluated against available experimental and previous theoretical results (5-HRI, 3-Univie).

This task, mainly based on the work of HRI is devoted to the construction of model Hamiltonians suited for oxide heterostructures. As a test case, the model is applied to describe the heterostructure made of differently doped manganites, which configures a prototype device with giant magnetoelectric effect, i.e. a system whose magnetization and/or magnetic ordering can be controlled by the application of an external electric field. Specifically, the interface is LaMnO3/SrMnO3 joining two antiferromagnetic bulk materials with different Mn nominal valence charge (3+ for LaMnO3, 4+ in SrMnO3), thus prefiguring an inhomogeneous distribution of eg-type valence charge along the direction orthogonal to the interface. Since the basic (in particular magnetic) properties of manganites are crucially dependent on the amount of the valence charge in the eg bands, control of this charge can directly lead to the control of the magnetic properties as well. As described in the Deliverable 4.2 related to this Task, charge control is achieved through an applied external potential at the back gates of the interface, thus envisioning the possibility of a controllable, general and robust magnetoelectric coupling mechanism.

The formulation developed by partner HRI is briefly described in the attached PDF file, while a more detailed description can be found in the Deliverable 4.2 report.

Task 4.3: Design of multilayered devices with enhanced capabilities.

Period: 25-36

Design and calculation of the physical properties of bi- and three-phase multi-layered systems showing potential applications in spintronic (e.g. spin-valve, magnetoelectric coupling, and others). The quality and reliability of our predictions are verified by synergic collaborations with a network of experimentalists. (6-JNCASR, 2-CNR, 1-TCD)

In tunneling magnetoresistance (TMR) the tunneling current through an insulating barrier is affected by the relative magnetization of the magnetic leads. This technology is currently used for read heads in the multi -billion dollar hard disks industry. The introduction of an active ferroelectric region offers the possibility of introducing additional functionalities in the same active element, such as non-destructive reading of ferroelectric RAM and four state resistance devices. To observe a tunneling electroresistance (TER) affect, using a ferroelectric material as insulating barrier is not sufficient, since the potential barrier of the two polarizations mirror each another and the resulting tunneling current for each electrically polarized states would be identical. Instead, the TER affect requires the asymmetry of the entire system. To the aim, the introduction of a non ferroelectric insulating layer into the system (FM/FE/Insulator/FM multilayer) is the most promising junction for device applications. Due to the long screening length in the insulating region and low carrier concentration the depolarization charge is not localized at the FM/FE but at the I/FM interface, thus switching the FE polarization has a dramatic affect on the potential barrier height of the insulating layer, and the TMR is large and tunable by the thickness of I and FE layers. In our work we show that the introduction of the wide band gap insulator SrTiO3 into the SrRuO3/BaTiO3/SrRuO3 junction creates an additional potential barrier that is switchable with the ferroelectric polarization. In doing so we propose the necessary components for a combined TER+TMR device.

We use a 6 unit cell thick BaTiO3 layer (? 2.5 nm), m=(0,1,2) unit cells of SrTiO3, and 3 unit cells for SrRuO3 left and right electrodes (the structure is described in detail in Del. 4.3-1). When BaTiO3 is included in the capacitor structure, the atomic displacements correspond to a polarization of 35.5?C/cm2 much reduced from the bulk value (43.8?C/cm2). The electronic properties of SrTiO3 and BaTiO3 are very similar: both real and complex band structure (which is a measure of the electronic tunneling coefficient) are almost identical, thus bulk properties alone we would not indicate any significant advantage in the introduction of the SrTiO3 into the junction. At zero bias, when a FE film is inserted within the leads, some charge accumulates at the interface to screen the electric field due to the FE and bring back to zero the electric potential in the leads. This can be seen in Figure 21 of the attached PDF file, where we plot the difference in the potential and charge profile between centrosymmetric and ferroelectric configurations, for the SrRuO3/SrTiO3/BaTiO3/SrRuO3 junction. The depolarization charge forms in the metallic SrRuO3 layer leaving the potential in SrTiO3 pinned at its STO/BTO value. Thus, inverting the BTO produces a rigid shift in the SrTiO3 potential. This configures a TER mechanism where the BTO region acts as a potential barrier with a constant gradient, and the STO side a square potential with a height matching the STO/BTO interface. We notice that some uncontrollable defect-driven TER contribution is always present, in practice, due to the difficulty in creating defect free structures. However, this can be made discardable with respect to the intrinsic TER, which can be tuned either by the thickness of BTO or STO.

Milestone M1: month 12

Comparison among First-Principles methodologies, assessment of respective accuracy and manageability. Verification of the correct realization of an integrated First-Principles plus model scheme, and relative code implementation.

Central to the Milestone is a collaboration of TCD, CNR, and Univie. These partners studied two relevant test case materials (MnO and NiO) with a number of different methods, including standard local density functionals (LDA) implemented in plane-wave basis set (LDAPW) and in local orbital basis set (LDALO), as well as generalized-gradient density functional approximation (PBE), and several beyond-local functionals: the newly developed VPSIC implemented in two versions, namely plane-wave basis set (VPSICPW) and local-orbital basis set (VPSICLO), and the hybrid functional HSE. In Figure 22 of the Attachment we report results concerning the relative energy stability for various magnetic orderings as a function of lattice parameter (i.e. under an applied pressure) and the related magnetic moments obtained with each of these methods.

Our work provided a comparative analysis of unprecedented variety and details. It testifies the consistency and the general reliability of structural, electronic, and magnetic properties for magnetic oxides obtained by the newly implemented VPSIC in comparison with HSE, considered the reference among First-Principles band theory approach for what concern accuracy. On the basis of these results our milestone decision consists in remaining actively working with all the 3 methods, selectively used according to their suitability for specific problems; specifically the VPSICLO is particularly suited for large-size systems and molecules, while the VPSICPW and HSE approaches are more indicated for very complex systems whose electronic properties have to be determined with the outmost precision. The correct realization of the model Hamiltonian integration with the First-Principle approach has been also verified, according to the original Milestone objectives.

Milestone M2: month 18

Assessment of the determination of ground state and thermodynamic properties of magnetic oxides by integrated First-Principles plus model Hamiltonian scheme. Comparison of FP plus model methodologies, decision on which method(s) are better suited to be fruitfully exploited in the project prosecution.

This Milestone is addressed to verify the correct realization of the model Hamiltonian integration with the First-Principle approach. The assessment concerning the determination of ground-state and thermodynamic properties of magnetic oxides is centered on the joint work of partners TCD, CNR, and Univie: in particular, the comparative analysis focused on the two Mott insulating prototypes MnO and NiO systems, tackled with an array of different approaches. In order to reach a resolution of virtues and weakness of the methods in question, the results for zero-temperature magnetic properties, previously discussed in the illustration of Milestione M1, are interfaced with calculations based on a newly developed Heisenberg Hamiltonian Monte Carlo procedure, which can deliver accurate finite-temperature magnetic properties for the systems of interests.

On the basis of the results obtained for the Nèel temperatures of MnO and NiO as a function of the lattice parameter (i.e. the volume), we confirm the excellent accuracy and the good accord of our beyond-standard functionals (VPSIC HSE) already verified for M1, and our determination to pursue the use of each functional in the remaining part of the project. See Fig. 23 of the attached file.

Milestone M3: month 24

Assessment on the capability of our method to describe ground state, transport and thermodynamic properties of bulk oxides, as well as several peculiar phenomenologies including ME effects in DMF, CMR and CER effects in MP, large magnetism in doped DP).

This Milestone is devoted to the verification of the quality of the newly developed approach in comparison to relevant phenomenological cases, such as those related to giant magnetoresistive or electroresistive effects (CMR, CER), large magnetoelectric coupling (ME), large ferromagnetic critical temperature. As a matter of fact, in the last few years most of these phenomenologies have been found full displayed in oxide heterostructures (interfaces, films, and superlattices) which represent the focus of Milestone M4. Thus, we can directly move to the description of M4, whose finding also encompasses the aims of Milestone M3.

Milestone M4: month 36

Assessment on the description of structural, electronic, and transport properties of MP/MP and MP/PZ interfaces by FP+MH approach. Assessment on the possibility to design bi- and three-phase multi-layers showing ME coupling with potential applications.

As described in the original Annex, this Milestone is to evaluate the quality of our newly developed approach in the description of a range of interfaces with diverse functionalities, such as large magnetoelectric coupling and spin-valve capability, with the aim of furnishing the final determination on the possibility to use integrated First-Principles plus model scheme to describe and eventually design oxide systems with improved functionalities, which represents the definitive, paramount achievement of the project. We considered a large array of bi-dimensional systems, including the multiferroic tunnel junctions SrRuO3/BaTiO3/SrRuO3 and SrRuO3/SrTiO3/BaTiO3/SrRuO3, the spin-valve multilayers Fe/BaTiO3/Fe and Fe/MgO/BaTiO3/Fe, the magnetic metal/non-magnetic insulating LaNiO3/LaAlO3 superlattice, the magnetic/non-magnetic insulating CuO/SrTiO3 interface, the magnetic/magnetic (LaMnO3)n/(SrMnO3)n superlattice.

The vast majority of our results indicate a favorable assessment to the Milestone. In all the cases, our calculations predicted interesting functionalities or characteristics potentially viable for device design. Whenever an experimental reference was available, calculations turned out to be in substantial agreement for what concern structural electronic, magnetic, and transport properties.

As an example, in Figure 23 of the attachment we show the k-resolved transmission coefficient calculated for the multiferroic tunnel junction. More detail of this work can be found in the Deliverable Report 4.1-1.

WP5: Project management

The management of the ATHENA project was carried out by the two Coordinators: Stefano Sanvito of TCD, was on duty for what concern all legal and scientific management and coordinating activities of the EU partners, while Priya Mahadevan of S.N. Bose of Kolkata managed the Indian side of the Consortium.

Management was carried out according to the original guidelines of the DoW, and form scientific viewpoint no specific problems have being encountered during the 3 years. In contrast, from the logistic viewpoint some uncertainty was caused by the difference in regulations and system management obligations required by the EU and the Indian Department of Science and Technology (DST). An example concerns the organization of the M18 review meeting, which was not possible to conduct as a joint EU-DST event. The problem was then solved by doubling the review meeting procedure, i.e. organizing two consecutive meetings (one in Bruxelles on January 2011, the second in Bangalore in April 2011 -- see the meeting list section later on). This of course is not ideal since travelling must be duplicated, without a clear benefit for the delivery of the project. As a suggestion for future projects, we believe that the best option will be having one single reporting body with common rules for the entire consortium (EU+DST). Such single reporting body may also correct issues related to the misalignment of the starting dates between the EU and India consortia, as well as the different policies for what concerns no cost extensions. We signalled these problems in occasion of the EU-India Coordinator meeting in Brussels in March 2011 (attended by both Stefano Sanvito and Priya Mahadevan).

We underline that no change occurred relative to the legal status of the members. A minor change regarded partner CNR of Cagliari, Italy: following a structural reorganization, the Institute formerly known as CNR-INFM (Istituto Nazionale di Fisica della Materia) and as such called in the original Project description, was renamed CNR-IOM (Consiglio-Nazionale delle Ricercha - Istituto Officina dei Materiali). Beside the name, no other change occurred in terms of either location (Cagliari, Italy), personnel, or scientific means, which might, on any regard, affect the scientific activity of this partner in the ATHENA project.

In the following we list the original Tasks with their objectives and a brief description of the related work.

Task 5.1: Administration and reporting. M1-M36

Administrative and reporting activities, including correct and timely distribution of the funds from the EU, communication with the EU, preparation of periodic reports for the EU, newsletters, meeting minutes (1-TCD, 4-SNBNCBS).

All administrative and reporting activities were duly accomplished along with the procedures required by the EU regulations and requirements. Distribution of funds to members occurred timely and without difficulties. Communication among partners was accomplished by meetings, e-mailing and an intensive use of teleconference tools. Preparation of project meetings was carried out with the help of local host institutions (see the meeting list below), which always ensured excellent conditions of work and highly successful scientific outcome.

Task 5.2: Website. M1-M36

Realization and maintenance of the project web sites. This will be a public site for dissemination of results and access of useful data and publications (1-TCD, 4-SNBNCBS).

The ATHENA project website was created in the first 6 months of the project as planned, and functions since the second half of 2009. Thomas Jochmann from INVITRONICS was appointed to design the website. The domain www.athenacomp.eu was purchased and it currently hosts the website. The site is divided into three parts, two public and one private, respectively. The public sections include a welcome page with news and description of the project and a materials page with list of publications, links to software, and summary of achievements to date. The private section serves as a forum for exchanging data and various scientific materials between the partners. The coordinator and his team updated the website (public section), while all the partners had access to the private section.

Task 5.3: Leaflets (CANCELLED)

Preparation and distribution of leaflets describing the objectives of the project and the main results obtained during the project (1-TCD, 4-SNBNCBS).

The preparation of leaflets were cancelled. Partners decided that the dissemination of project results during conferences and meeting could be more effectively carried out by digital modalities, whereas distribution of hard copies were not anymore necessary. This action was agreed at the midterm meeting by the EU project officer.

Task 5.4: Training School. M24-M36.

Organization of a training school on theoretical methods applied to strong-correlated materials open to public (1-TCD, 4-SNBNCBS).

The ATHENA project organized a highly successful school at the N.S. Bose Institute of Calcutta in April 2012. Lectures focused on the themes related to the research carried out in the ATHENA project, were held by scientists of the ATHENA project, complemented by several extra-project invited scientists. The School saw the participation of more than 50 among PhD students and Post-doctoral researcher, plus a qualified audience of professionals interest in condensed matter theory. More detail can be found in the related Deliverable Report 5.4.

Task 5.5: Interrelation with other WPs and meeting organization. M1-M36.

WP5 will strongly interact with all other workpackages to ensure the achievements of the goals of the project, organizing regular meetings among consortium members (one each 6 months for intra-European and intra-Indian separated sections, one each 12 months for the joint Euro-India consortium. (1-TCD, 4-SNBNCBS).

The originally planned meeting schedule was slightly varied (with the approval of EU) to better fit our scientific means. Specifically, the first general EU-India meeting originally expected at Month 12 was anticipated at Month 6, in order to establish an anticipated acquaintance among all the consortium members. Here is the list of project meetings held by the ATHENA project:

a) M0: June 22, 2009 Trinity College Dublin Kick-off Meeting of the European section.

b) M0: August 2009 Kolkata Kick-off Meeting of the Indian Section

c) M6: January 11-13, 2010 Harish-Chandra Research Institute, Allahabad 1th Joint EU-India Meeting.

d) M12: June 21-13 2010 Marina di Capitana, Sardinia, Italy First year Meeting of the European Section

e) M18: January 8-12, 2011 Brussels Midterm Review Meeting

f) M18: February 8-12, 2011 JNCASR, Bangalore Midterm Indian Review Meeting & 2nd Joint EU-India Meeting.

g) EU-India Project Coordinators Meeting: March 30-31, 2011 Brussels.

h) M24: June 2-3, 2011 Trinity College Dublin Second year Meeting of the European Section.

i) M30: April 9-14, 2012 - S. N. Bose, Kolkata - ATHENA School and 3th Joint EU-India Meeting.

j) M36: June 17-19, 2012 - University of Cagliari, Italy - Final Meeting of the European section.

Besides the official meetings listed above, a number of reciprocal visits between partners was organized to foster our common activity and collaborations on specific themes of the projects. These visits regarded WP leaders, students and post-docs. Here is a list of visits in the framework of ATHENA project:

October 2009: V. Fiorentini (CNR) visits TCD

November 2009: A. Filippetti (CNR) visits Univie.

November 2009: P. Mahadevan (SNBSCBS) visits HRI.

December 2009: P. Mahadevan (SNBSCBS) visits JNCASR.

January 2010: U. Waghmare (JNCASR) visits SNBSCBS

March 2010: C. Franchini (Univie), C. Ederer, R. Kovacik, S. Sanvito (TCD) meet in Portland

June 2010: C. Franchini (Univie) visit CNR Cagliari

August 2010: R. Kovacic (TCD) visits Univie

September 2010: C. Franchini (Univie), C. Ederer, R. Kovacik, S. Sanvito (TCD) meet in Berlin

October 2010: C. Ederer, R. Kovacik,(TCD) V. Fiorentini, A. Filippetti, D. Puggioni, (CNR) M. Marsman (Univie), S. Shirodkar (JNCASR) meet in LAquila, Italy.

November 2010: R. Kovacik (TCD) visits Univie.

December 2010: S. Bhattacharia (TCD) visits HRI;

December 2010: P. Mahadevan (SNBSCBS) and U. Waghmare (JNCASR) meet in Bhubhaneshwar

January 2011: R. Tiwari (HRI) visits CNR Cagliari.

January 2011: S. Datta (HRI) visits Univie.

January/February 2011: V. Singh (HRI) visits Dublin

March 2011: S. Sanvito (TCD) and P. Mahadevan (SNBNCBS) meet in Brusselles

April 2011: D. Puggioni and P. Delugas (CNR) visit JNCASR.

April 2011: P. Mahadevan (SNBNCBS) visits Vienna.

May 2011: S.S. Murthy (Univie) visits Dublin.

May 2011: C. Franchini visits CNR Cagliari.

October 2011: Saikat Debnath (SNBNCBS) visits Vienna.

May-June 2011: S. Murthy (Univie) visits Dublin.

Potential Impact:

We believe that the ATHENA project successfully matched the challenge to produce a strong impact from scientific, socio-economic, and societal viewpoint. ATHENA represents probably the first attempt towards the creation of an integrated network of theoretical scientists active in the development and testing of beyond the state-of the-art theories and software, with a sufficiently large critical mass of human resources and competences to create a serious impact in the condensed matter community.

The interaction between European and Indian academic and research institutions successfully achieved the sharing and integration of their respective intellectual and material resources, through an intense and reciprocal exchange of researchers and knowledge. Each one of the ATHENA consortium partners provided an environment of scientific excellence in their specific fields of activity in particular, thus ideal places where interactions of visiting (especially young) researchers could be fruitfully exploited to produce those scientific innovation generated by the project, and even more importantly, to establish and nurture those long-term scientific and social relations among our institutions and their respective scientists in order to create the critical mass of knowledge on the themes specific to the projects, and more in general, in the field of theoretical condensed matter.

Going to evaluate more specific scientific outcome, the ATHENA project was aimed at developing an inter Euro-Indian network of excellence in the field of theoretical/computational methods to investigate the properties of strong-correlated materials (transition metal oxides, with specific focus on the magnetic perovskites) which are candidate to be fundamental building blocks for future generation nanoelectronic devices. These systems have the characteristic to embody a formidable mix of technological promises and outstanding richness of unconventional, and for many aspects sill far from understood, fundamental physics. From a technological viewpoint, functional oxides are addressed as the potential basis of a whole new technology with enhanced and/or additional capabilities with respect to the actual Si-based technology. As such, they are subject of extraordinary appeal as much for academic environments as for visionary research industries, for physicists and material science engineers alike. It can be hardly confuted that no other investigative arena, at least within the material science framework, possess the same degree of versatility.

But reaching the border of the nanoscopic size limit necessarily requires the ability to understand (and thus predict and control) the quantum-mechanic behavior at the atomic level. In this light, the role of First-Principles theory becomes instrumental to the accurate description of the matter and the capability to make predictions on the functionalities of these systems should be regarded as a major investigative instrument, complementary and equally fundamental than the experiment itself.

The ATHENA project was conceived in order to pursue this aim not through the work of individual entities, which is the most common approach in the theoretical condensed matter world, but in terms of a structured collaborative network, which would coordinate their activities, sharing methodological knowledge, software (computing codes) and hardware equipment, and exchanging human resources, thus establishing a partnership whose ties could hopefully extend well beyond the time limit of the project itself. Establishing a tight collaboration between some of the leading European and Indian groups in the field, the ATHENA project paved the way for a durable collaboration and a stream of scientific work, which should engross and strengthen along the years, and bring Europe and India to the forefront of theoretical/computational investigations on strong-correlated electron systems. But the importance of the ATHENA project wan not just the sharing of existing capabilities, but first and foremost, in the creation of innovative theoretical resources; as mentioned above, strong-correlated oxides are extraordinary challenging systems from the theoretical/computational perspective as standard computational tools are not adequate to describe materials so rich of intertwined fundamental properties. To this aim, the ATHENA project was composed in order to get together the most advanced methodological tools and equipments based on First-Principles and model Hamiltonian approaches apt to describe the physics of strong-correlated systems, and in turn, the groups who better represent, in terms of expertise in development, mastering, and applications, these methodologies, respectively. As explained in detail in Sections 4.1 a), b), and c), we can affirm that these scientific objectives were achieved in full. During the project, the results dissemination has been carried out through participation of project partners to meetings and events, as well as to an intense publication activity. Coordination activities have proceeded through reciprocal visits and an intense activity of correspondence by on-line conferencing.

In synthesis, during the 3-years duration of the project our Task force has:

Produced a large amount of scientific works, disseminated during the 3 years of the project through a series of publications in international peer-reviewed journals, and national and international conference seminars, many of which resulting from invitations. This dissemination activity, mostly collected in our public website, might be useful to professional scientists in their research as well as to students and teachers of graduate classes to acquire knowledge of the arguments.

Developed outstanding new methods for calculations in condensed matter, and related software (codes) now available to the community by request and/or mutual collaborations.

Established an expertise environment devoted to theoretical/computational study of strong-correlated materials, built on an unprecedented amount of innovative, beyond state-of-the-art resources that will be made available for the solid state community.

Established a Euro-Indian school in methodologies devoted to optimization, development, and dissemination of the most advanced and efficient computing codes worldwide available and applicable to general strong-correlated systems.

Established a strong synergy with the experimental community in designing heterojunction and superlattice devices based on strong-correlation and proximity mechanisms.

Implemented a public website including a database periodically updated with the information collected during the 3 years project, giving access to all the publications and presentations resulting from the project as well as the information and results about the project that the consortium participants agreed to publicize.

Hold an ATHENA training School (Kolkata, April 2012) on strong-correlated materials and methods open to the public, and specifically addressed to PhD students and Post-Doc. The School, which saw the participation of more than 50 attendees and about 20 lecturers among coworkers of the ATHENA projects and several internationally renowned invited scientists external to the project, turned out to be highly successful and represented a formidable tool to disseminate the advancement carried out by the ATHENA project and to introduce young researchers to the most advanced state-of-the-art methodologies in the field of strong-correlated systems.

List of Websites:

www.athenacomp.eu