Final Report Summary - FEMTOSPIN (Multiscale Modelling of Femtosecond Spin Dynamics)
Executive Summary:
The FemtoSpin project had the aim of understanding the basic processes involved in all-optical magnetization switching, to develop models at the electronic, atomistic and mesoscopic/continuum levels and to develop linking techniques to couple the models in a multiscale approach to calculations of ultrafast magnetization processes. The models were successfully developed, providing significant progress in the ab-initio determination of magnetic materials parameters and their incorporation into atomistic level models. The multiscale chain was completed by the development of advanced macrospin models based on the Landau-Lifshitz-Bloch equation of motion, in particular a model of 2-sublattice ferrimagnets. The models were developed and validated by comparison with state-of-the-art experiments in leading European laboratories. The project led to important advances in understanding of all-optical reversal processes; a field less than a decade old with considerable potential for applications in magnetic information storage and manipulation.
The scientific outputs from the project were outstanding, around 70 papers in high impact journals including Nature journals (7) and Physical Review Letters (2) and Scientific Reports (3), and some 68 invited papers at International conferences. Outreach activities included the organisation of a summer school in Nijmegen and the initiation of the Ultrafast Magnetism Conference (Rasing, Chantrell with Bigot and Huebner; first edition in Strasbourg in 2013 and second in Nijmegen in 2015). A review of the project output concluded that there was not a sufficient market for the commercialization of the software output. The main software output from the project is the VAMPIRE atomistic code, which has generated a user base of around 50 users and is currently being trialled in an industrial materials design context.
FemtoSpin has made a large impact in terms of generating the understanding of optomagnetic processes. The model development at all lengthscales has led to the production of a multiscale model chain taking magnetic parameters from ab-initio calculations into atomistic models which then provide parameterised information for macroscopic calculations. This process leads to macroscopic models with a strong physical basis for use in materials and device design. At the atomistic level we have developed the first approach taking into account the distinction between internal moments in Gd metal and studied the effects on the ultrafast dynamics. Atomistic model calculations also demonstrated the origin of the Thermally Induced Magnetisation Switching (TIMS) in the excitation of specific magnetic spin waves which transfer angular momentum between the transition metal and rare-earth sublattices leading to a transient ferromagnetic-like state which initiates the magnetisation reversal. This led to the prediction of a set of design rules for TIMS and the prediction of TIMS in synthetic ferrimagnets. This gives the promise of potential recording systems having no requirement for a magnetic reversing field to switch the polarity of the magnetic bit from ‘0’ to ‘1’. Calculations of specific materials design parameters enabled a Dutch patent (2008039). The patent process continuing in Europe (EP2795622 (A2)) and the United States (US2014368303).
Project Context and Objectives:
3.1 Publishable summary
3.1.1 Summary description
The FemtoSpin project has made rapid progress in a field of enormous scientific and technological importance. The scientific basis of the project is research in ultrafast magnetisation processes induced by the interaction of femtosecond laser light with magnetic materials. Experimentally, a light beam from a powerful-pulsed laser with a pulse width of around 50 femtoseconds is split into 2 beams. The first, high intensity (pump) beam is incident on the magnetic material, in the form of a thin film of thickness around 10nm, causing rapid heating. The second, low intensity (probe) beam is sent around a delay line, arriving at the sample with a controllable delay and used to measure the magnetisation of the film using a technique known as the Magneto-Optical Kerr or Faraday Effect. By means of such pump-probe experiments it has become possible to measure the magnetic response of a material on a timescale of tens of femtoseconds. This is a topic at the cutting edge of condensed matter and materials physics. In addition, for more detailed, element resolved, spin dynamics, similar experiments are done using femtosecond X-ray pulses that also give nanometer spatial resolution. FemtoSpin is predominantly aimed at developing models of the ultrafast magnetisation dynamics, but also has a core of leading experimental groups that provide validation as well as inspiration for the model development. The proven strong collaboration between the participants has led to a number of significant advances, including the explanation of the physical origin of a phenomenon known as Thermally Induced Magnetisation Switching (TIMS) in which magnetisation switching can be achieved by a heat pulse alone in the absence of an applied field. This astonishing result has triggered a major worldwide effort to provide a full understanding of the phenomenon and its translation into practical applications. The technical implications for information storage technology are extremely exciting, giving the possibility of increased data rates along with reduction of device complexity and power requirements.
The FemtoSpin project was carried out within a rapidly evolving industrial context. In terms of magnetic information storage, the drive to higher recording densities is based on Heat Assisted Magnetic Recording (HAMR), which uses laser pulses to heat the storage medium so as to allow reversal of the magnetisation. This relies on a combination of laser heating coupled with standard technology to generate a localised magnetic field to induce the magnetisation switching. Because of materials limitations, this field is limited in magnitude: a factor which will ultimately limit areal storage densities. Technologically, the complexity of manufacture of the write transducer is already slowing down the pace of development. The use of optical switching would remove the requirement for the inductive write transducer, significantly reducing both manufacturing costs and power requirements. At the same time, the field of spin electronics (or Spintronics), in which device functionality is dependent on the spin of the electron rather than simply the charge, is developing rapidly. Spintronics is a strong candidate to replace conventional electronics as this reaches its physical limitations. Again, optical reversal is a potential candidate for switching the magnetisation in spintronic devices.
3.1.2 Summary of objectives
• Obtain fundamental knowledge of dynamic processes on the fs timescale; this requires the development of new approaches to treat non-equilibrium electron dynamics, utilizing Density Functional Theory and applying these to understand the fundamental mechanisms underlying ultrafast spin dynamics.
• Advanced atomistic models; this includes spin models with equations of motion beyond Langevin dynamics; new approaches to induced spins and transport; integration of thermodynamic and quantum approaches
• Mesoscopic model development; this requires mesoscopic modelling using a generalised Landau-Lifshitz-Bloch (LLB) Equation; formulation for ferrimagnets and determination of LLB parameters from SDFT calculations and atomistic models.
• Multiscale calculations and link to experiments; verification of models against experiment; feedback from experiments to model development; material studies; large-scale calculations and device simulations.
• Detailed materials studies; candidate materials with especially promising properties on the femtosecond timescale will be investigated. This will encompass single-phase materials and alloys in addition to novel structured materials with engineered properties.
3.1.3 Work performed and major results achieved
The development of new technology based on opto-magnetic phenomena requires new models with a sufficiently strong physical basis. The models must be validated by comparison with state-of-the-art experiments. Within this background FemtoSpin has been highly successful, in particular in the following areas:
Multiscale model development. Optomagnetism is driven by the interaction between photons, conduction electrons, lattice vibrations and the atomic spins themselves. This is a complex problem involving the development and coupling of models on 3 fundamental lengthscales:
Electronic; theories of laser/spin interaction, predictions of important magnetic materials information. These have been investigated using Density Functional Theory (DFT) and analytical models, both for comparison with experiment and to link to atomistic models. Significant advances have been made in the understanding of the laser/spin interaction and in techniques for the determination of magnetic properties.
Atomistic models; using information from DFT, atomistic models introduce the thermodynamic aspects of the opto-magnetic phenomenon, allowing the heating effects of the laser pulse to be included.
Macrospin models; large scale simulations and device design rely on mesoscopic and continuum approaches based on macrospin models. Within FemtoSpin significant progress has been made in the development of macrospin models capable of simulating magnetic behaviour during the laser pulse. These models rely on input information from the atomistic approach to complete the multiscale formalism.
Model validation. The interaction between theoretical and experimental groups has been exemplary and has led to important model development and feedback to experiments.
Outputs
1. Calculations of specific materials design parameters enabling a Dutch patent (2008039). Patent process continuing in Europe (EP2795622 (A2)) and the United States (US2014368303).
2. Atomistic code (Vampire) on public release. Very good take-up by academia.
3. Preparing advanced optical and heat-assisted magnetic recording model (MARS) for public release.
Other Outputs
4. Publications; 70 papers in high impact journals including Nature journals (7) and Physical Review Letters (2) and Scientific Reports (3).
5. 68 invited papers at International conferences
6. Organisation of a summer school in Nijmegen
7. Initiation of the Ultrafast Magnetism Conference (Rasing, Chantrell with Bigot and Huebner; first edition in Strasbourg in 2013 and second in Nijmegen in 2015)
FemtoSpin has made a large impact in terms of generating the understanding of optomagnetic processes. The model development at all lengthscales has led to the production of a multiscale model chain taking magnetic parameters from ab-initio calculations into atomistic models which then provide parameterised information for macroscopic calculations. This process leads to macroscopic models with a strong physical basis for use in materials and device design. At the atomistic level we have developed the first approach taking into account the distinction between internal moments in Gd metal and studied the effects on the ultrafast dynamics. Atomistic model calculations also demonstrated the origin of the thermally assisted magnetisation reversal in the excitation of specific magnetic spin waves which transfer angular momentum between the transition metal and rare-earth sublattices leading to a transient ferromagnetic-like state which initiates the magnetisation reversal. This led to the prediction of a set of design rules for TIMS and the prediction of TIMS in synthetic ferrimagnets.
Scientific highlights
• Development of an ab-initio code for the calculation of the opto-magnetic field (i.e. the magnetization induced by circularly polarized laser light), on the basis of the derived quantum theory for the opto-magnetic field.
• A theoretical framework has been derived for demagnetization due to transfer of the spin of hot (laser-excited) electrons to the phonon system and the resulting demagnetization rates were ab-initio computed for 3d ferromagnets.
• Ultrafast demagnetization due to spin transport has been investigated and was shown to give rise to emission of THz radiation
• Understanding the TIMS phenomenon and its prediction in structured media
• Atomistic/ab-initio model of Gd – beyond the fixed spin model and successful validation by comparison with experiments.
• Studies of differential spin dynamics on FeNi. Full multi-scale modeling of the material and comparison with experiment.
Multiscaling and collaborative code development
• ab-initio determination of magnetic properties and parameterization of atomistic spin Hamiltonians (Budapest, Uppsala, Konstanz, York); automatic generation of spin model parameters for the Vampire atomistic code is almost complete.
• Macrospin simulations and atomistic testing/ parameterization (ICMM, Konstanz, York). This collaboration has produced a suite of models optimized for continuous and granular media. This collaboration has also developed a ferrimagnetic LLB equation for macrospin simulation.
• (ICMM, RU, York); atomistic and macrospin approaches have been combined to produce understanding of the dynamic behavior of ferrimagnetic materials during the thermally induced magnetization switching process.
Femtospin code development: public code release
– York atomistic code (Visual Atomistic Massively Parallel IntegRation Engine; VAMPIRE). On public release, Details available from vampire.york.ac.uk. Described in invited topical review; R. F. L. Evans, et. al., J. Phys.: Condens. Matter, 26, 103202 (2014) (23pp) (selected as one of the highlights of 2014 in J. Phys.: Condens. Matter). Code in trial use in industry
– MAgnetic Recording Simulator; MARS. Developed for advanced simulations of all-optical recording and HAMR in collaboration with Seagate/WD.
Future industrial prospects
Although technical difficulties remain to be overcome, Heat Assisted Magnetic Recording (HAMR) is closing in on providing the next generation of ultrahigh density recording systems. In May 2014 Seagate announced a 1.4Tbit/in2 areal density demonstration (the first to exceed conventional recording demonstrations) having previously shown 1000 hours of continuous write (the benchmark requirement). However, HAMR densities will be limited by the available write field (around 1Tesla) using inductive technology, due to the requirement of avoiding errors due to thermally induced back switching. Due to the physical and technical understanding within the FemtoSpin project, all-optical recording must be considered a realistic candidate for progress beyond HAMR. Here it must be noted that all candidate technologies face similar problems of writing and stability at extreme densities, and the large effective fields involved in all-optical technology could give it a strong advantage. Equally important could be the removal of inductive technology from the writing process in magnetic recording, leading to very significant design and process simplifications with important implications for cost reductions and reduced environmental impacts; that latter also enhanced by significantly reduced energy cost per bit in the write process. This represents an important potential advance for European industrial potential, supporting the major production centre of Seagate in Northern Ireland which produces around 25% of the world-wide total output (around 1 billion p.a.) of recording heads; an important European industrial resource.
Project Results:
3.1 Core of the report for the period: Project objectives, work progress and achievements, project management
Since the start of the project in 2012, the consortium has made great strives forward in the understanding of magnetization dynamics by developing high performance computing code capable of simulating complex materials. The array of skills within the consortium at the electronic, atomic and mesoscopic level, combined with advanced experimental techniques have paved the way in the first 18 months to develop multiscale models. During this period we also developed and validated a set of experimental techniques and began the process of testing and validating the theoretical and computational approaches.
The second phase of the project was aimed at further development of the models and a detailed comparison between theory and experiment. We made significant advances in the understanding of ultrafast magnetisation processes and released validated code into the public domain; the same code is also under test in industry. We determined design parameters for materials supporting ultrafast opto-magnetic phenomena and investigated candidate microstructures having significant potential for ultrafast field-free magnetic recording.
3.2.1 Project objectives for the period
• Obtain fundamental knowledge of dynamic processes on the fs timescale; this requires the development of new approaches to treat non-equilibrium electron dynamics, utilizing Density Functional Theory and applying these to understand the fundamental mechanisms underlying ultrafast spin dynamics.
• Advanced atomistic models; this includes spin models with equations of motion beyond Langevin dynamics; new approaches to induced spins and transport; integration of thermodynamic and quantum approaches
• Mesoscopic model development; this requires mesoscopic modelling using a generalised Landau-Lifshitz-Bloch (LLB) Equation; formulation for ferrimagnets and determination of LLB parameters from SDFT calculations and atomistic models.
• Multiscale calculations and link to experiments; verification of models against experiment; feedback from experiments to model development; material studies; large-scale calculations and device simulations.
• Detailed materials studies; candidate materials with especially promising properties on the femtosecond timescale will be investigated. This will encompass single phase materials and alloys in addition to novel structured materials with engineered properties.
3.2.2 Work progress and achievements during the period
Work Package 1: Femtosecond and ab-initio theory
Summary
The workpackage has been successfully completed and all deliverables have been submitted. All objectives as given in the DOW have been met. A delay of some tasks of partner P6 (UU) occurred due to recruitment difficulties in period I. Involving more manpower in period II counteracted this delay.
Highlights
• Development of an ab-initio code for the calculation of the opto-magnetic field (i.e. the magnetization induced by circularly polarized laser light), on the basis of the derived quantum theory for the opto-magnetic field.
• A theoretical framework has been derived for demagnetization due to transfer of the spin of hot (laser-excited) electrons to the phonon system and the resulting demagnetization rates were ab-initio computed for 3d ferromagnets.
• Ultrafast demagnetization due to spin transport has been investigated and was shown to give rise to emission of THz radiation (Kampfrath et al., Nature Nanotech. 8 (2013) 256–260).
• A theoretical investigation of optical modulation of the spin-spin exchange interaction together with measurements on an iron oxide will appear in Nature Communications.
Description of WP activities and results
The focus of WP1 is to develop analytical and ab-initio theory, aiming to obtain fundamental knowledge of dynamic processes on the femtosecond timescale. The description of such fast processes requires the development of new approaches to treat the occurring non-equilibrium electron dynamics as well as ab-initio implementation and modelling.
The modelling in WP1 is pursued along the following main lines: theory development for the description of electron and spin-dynamics on very short time scales (attoseconds to femtoseconds), theoretical investigations of the influence of energy and spin transfer channels in ultrafast demagnetization, development of new spin Hamiltonians for calculation of spin-dynamics (connected with ab-initio calculation of the required parameters), and lastly development of theory for spin-dynamics in the multi-orbital Hubbard model.
The work done in WP1 connects in a multi-scaling approach to that in WP2 and WP3 by providing ab-initio calculated parameters as input for simulations as well as by the development of new spin-Hamiltonians for simulations of specific materials (e.g. GdFeCo ferrimagnets, magnetically-hard FePt alloys). Also, tests of the developed models are provided through comparison (feed-back) with measurements in WP4.
Related to Task 1.1. Theory development for ultrafast, intensive light-matter interactions (partner P6, with P1 and P7).
To treat dynamical processes on ultrashort time scales (typically femtoseconds) theoretical underpinning and theory development is required. The underpinning has been provided in period I by the development of a theoretical framework capable of describing the interaction of the materials electrons with intensive, ultrashort radiation pulses (deliverable D1.1). The developed theory, which is based on the time evolution of the electron density matrix using the Liouville-Von Neumann equation, has been employed to derive a quantum theory for magnetization induced by a circularly polarized light pulse (the inverse Faraday effect).
It has been proposed by the Strasbourg group (Bigot and collaborators) that ultra-relativistic spin-photon interaction could contribute to an ultrafast laser-induced demagnetization. To examine the influence of such relativistic spin-photon interactions we have developed theory for such processes and performed ab-initio calculations of their influence on the magneto-optical response of Ni. We have derived an exact formulation of the ultra-relativistic terms on the basis of the Foldy-Wouthuysen transformation to the Dirac-Kohn-Sham Hamiltonian, and have treated the additional appearing relativistic terms within a response theory formulation. Performing an ab-initio calculation of the influence of relativistic light-induced spin-flip transitions on the magneto-optics, we find that these can give only a very small contribution (≤ 0.1%) to the laser-induced magnetization change in Ni (R. Mondal, M. Berritta, K. Carva, and P.M. Oppeneer, Phys. Rev. B 91 (2015) 174415).
Currently there does not exist a single model that incorporates all interaction channels between all quasi-particles within a non-equilibrium formulation. All theory development requires therefore validation against measurements. Within Task 1.1 a first comparison between theory and measurements of the spin (S) to orbital (L) moment ratio in a polycrystalline Fe film were undertaken. This was done with the electron magnetic circular dichroism (EMCD) which permits measurements with nanometer scale resolution. The measured ratio is in good agreement with the result from ab-initio calculations (S. Muto et al., Nat. Commun. 5 (2014) 3138).
Further comparisons with experiments were performed for the ultrafast non-equilibrium spin-dynamics of spins in different orbitals (4f, 5d) in Gd metal, and for the ultrafast demagnetization in Fe/Au and Fe/Ru films (see D1.3); these investigations are mentioned further below.
Related to Task 1.2. Theory for the inverse Faraday effect and origin of opto-magnetic field (partner P6).
In a material that is excited by an intense pulse of circularly polarized light a strong opto-magnetic field can be created through the inverse Faraday effect. This opto-magnetic field could provide a sizable contribution to generating an ultrafast magnetization reversal. A quantum theory of the light-induced magnetic polarization was developed in period I (D1.4). In period II we have coded the derived expressions and implemented these in an ab-initio electronic structure code on the basis of the density functional theory. Investigations of selected materials have been performed. Specifically, we have computed the light-imparted magnetization in the ferromagnets Fe, Co, Ni, in the hard-magnetic recording material FePt, and nonmagnetic metals such as Au. We have analysed the contributions to the opto-magnetic field as well as its dependence on the photon energy. In particular, we find large effects for materials with heavy elements (e.g. Au, Pt) (M. Berritta, R. Mondal, K. Carva, A. Aperis, P. Maldonado, and P.M. Oppeneer, to be published).
Related to Task 1.3. Energy and spin transfer channels in laser-induced demagnetization (partner P6, with P5, P7, P1).
The phenomenon of ultrafast all-optical demagnetization has been attributed previously to several different mechanisms, such as, Elliott-Yafet electron-phonon spin-flip scattering or ultrafast spin-transfer caused by laser-excited hot electrons. In this task we develop theory for these processes and perform ab-initio calculations to quantify the amount of demagnetization that can be achieved.
In the Elliott-Yafet model the spin of the electrons is transferred ultrafast to the lattice by electron-phonon spin-flip scatterings. We have developed a generalized, relativistic Eliashberg theory to describe this process and carried out ab-initio calculations to quantify the demagnetization induced by electron-phonon interaction in the transition-metal ferromagnets bcc Fe, fcc Co and fcc Ni. The developed formalism allows treating laser-created thermalized as well as non-equilibrium, non-thermal hot electron distributions. We found that in particular non-thermal distributions lead to a stronger demagnetization rate than hot, thermalized distributions, yet their demagnetizing effect is not enough to explain the experimentally observed demagnetization occurring within 300 fs. This implies that other mechanisms need to be considered (K. Carva, M. Battiato, D. Legut, and P.M. Oppeneer, Phys. Rev. B 87 (2013) 184425).
Another mechanism of ultrafast demagnetization could be direct, lateral transfer of spin-polarized laser-excited electrons. We have developed semi-classical transport theory to treat the energetics of such non-equilibrium, hot electrons. The developed theory can treat the presence of several different layers in the laser-irradiated material. The derived spin-dependent transport equation is solved numerically and the obtained results can be compared to experiments. The required input is ab-initio calculated hot electron lifetimes and velocities. For a ferromagnetic/non-magnetic metallic junction where the ferromagnetic layer is laser-excited, the computed spin dynamics shows that injection of a superdiffusive spin current in the non-magnetic layer is achieved. The injected spin current leads to a fast demagnetization of the ferromagnetic polarization in the ferromagnet. We have compared theoretical predictions of laser-induced demagnetization of Ni and Au/Ni films with measurements performed at the Helmholtz-Zentrum, Berlin (P7). Element-specific x-ray magnetic circular dichroism (XMCD) measurements reveal a clear time-delay in the demagnetization of the Au/Ni film as compared to the bare Ni film. This can be explained by the time needed for the hot electrons to traverse the Au film (30 nm) and reach the Ni film. A sizeable demagnetization of the Ni in the Au/Ni system is predicted to be caused by laser-excited hot electrons coming from the Au layer into the Ni film (A. Eschenlohr, M. Battiato, P. Maldonado, N. Pontius, T. Kachel, K. Holldack, R. Mitzner, A. Föhlisch, P.M. Oppeneer, and C. Stamm, Nat. Mater. 12 (2013) 322).
The superdiffusive spin transport model has also been used to study the terahertz radiation emission from Fe/Au and Fe/Ru heterostructures. A laser excitation of the Fe layer is used to create a spin current into the non-magnetic layer that has either low (Ru) or high (Au) electron mobility. The resulting transient spin current is detected by means of an ultrafast, contactless ampere meter based on the inverse spin Hall effect, which converts the spin flow into a terahertz electromagnetic pulse. A good agreement was achieved between theoretical predictions of the spin currents and the measured charge current (resulting from the inverse spin Hall effect). The spin current pulses and the resulting terahertz transients can be modified by tailoring the magnetic heterostructures (T. Kampfrath et al., Nat. Nanotech. 8 (2013) 256).
Related to Task 1.4. Theory for ab-initio parametrization of spin Hamiltonians.
Spin Cluster Expansion (partners P5 and P1): to obtain realistic spin-model parameters we applied the Relativistic Torque Method (RTM) and the Spin Cluster Expansion (SCE) technique to various exchange coupled composite layered systems, such as Fe/9(FePt)/Fe and MgO/Fe/MgO. We have combined the SCE technique with the Relativistic Disordered Local Moment (RDLM) scheme to compute site-resolved magnetic properties. We investigated the layer dependent effective exchange parameters and magnetic anisotropies through the systems, and found that the RTM and the SCE give very similar results for the layer resolved quantities; however, for Fe/FePt/Fe, due to the vanishing Pt magnetic moments in the paramagnetic phase, the SCE leads to reduced exchange couplings in the FePt slab. (C.J. Aas et al., Phys. Rev. B 88 (2013) 174409). For MgO/Fe/MgO, our calculations showed strong anti-ferromagnetic in-plane Fe-Fe exchange interactions near the MgO/Fe interface, but dominating ferromagnetic in-plane Fe-Fe interactions in the central Fe layers. A strong layer dependence of the on-site magnetic anisotropies was also computed, with a change of anisotropy energy from out-of-plane near the interface to in-plane in the central Fe layers. (R. Cuadrado and R. Chantrell, Phys. Rev. B 89 (2014) 94407).
The RDLM scheme combined with the RTM provides a technique that enables to calculate the spin-model parameters as a function of temperature, from the ferromagnetic to the paramagnetic state. Applications to Fe and FePt show non-monotonous temperature dependence for the nearest-neighbour exchange interactions, whereas more distant interactions can even undergo a transition from ferromagnetic to antiferromagnetic character. (A. Deák, Phys. Rev. B 89 (2014) 224401; A. Deák, PhD dissertation, BME 2015).
Ab-initio LDA+U calculations have furthermore been performed for ferrimagnetic 4f-transition metal compounds, such as DyCo5 and GdFe2, TbFe2, and Gd/Fe multilayers, for spin dynamics calculations in WP2 and WP3. (L. Oroszlány et al., arXiv:1503.08940 accepted to Phys. Rev. Lett. (2015); publication on DyCo5 is under preparation).
The influence of temperature-dependent exchange interactions has been computed for bulk Fe. The computed exchange parameters have been used in atomistic spin-dynamics simulations. The influence of the temperature-dependence is currently being investigated; its influence on the magnetization curve and Curie temperature is small. Systematic calculations of the exchange interactions up several thousands of K in both the spin- and electron temperatures have been performed. These interactions can then be directly used in atomistic simulations of ultrafast spin-dynamics induced by laser pulses. (A. Deák, PhD dissertation, BME 2015; D. Hinzke et al., to be published)
Orbital-resolved spin Hamiltonian (partners P3 and P6):
In an effort to improve the description of the ultrafast spin-dynamics in GdFeCo alloys, which contain the rare-earth element Gd, a novel spin model has been developed which treats separately the spin-dynamics of the 5d and 4f electron spins on Gd. As the 4f electrons are localized the 4f spin moment interacts only “on-site" with the 5d spin moment. Employing ab-initio calculated intra-atomic exchange in atomistic simulations provided a clear explanation of the transient ferromagnetic state and revealed conditions under which optical switching to a spin-reversed state could be achieved. The model allows the transfer of energy from the 5d to 4f electrons via the intra-atomic exchange.
This spin model - with all its parameters derived from first principles – has recently been applied to elemental Gd. It forecasts different dynamics for the spin moments of the d- and f-electrons on a time scale of several picoseconds. Such disparate dynamics of 4f and 5d spins has been confirmed by recent measurements of the group of M. Weinelt in Berlin. A joint manuscript was recently accepted for publication in Nature Communications.
Related to Task 1.5. Spin dynamics within the multi-band Hubbard model (partner P2, with P4).
We have developed a low-energy theory for the magnetic interactions occurring between electrons in the multi-band Hubbard model (MBHM) under non-equilibrium conditions, which are determined by an external time-dependent electric field, which simulates laser-induced spin dynamics [A. Secchi, S. Brener, A. I. Lichtenstein and M. I. Katsnelson, Ann. Phys. 333, 221-271 (2013)]. Using advanced many-body techniques (a path integral formulation of the Kadanoff-Baym-Schwinger-Keldysh non-equilibrium technique, combined with local time-dependent rotations of the spin quantization axes of the electrons), we have mapped the MBHM to an effective model of spin vectors coupled by exchange interaction and an additional effective interaction which we have named "twist exchange". Twist-exchange interaction depends on the vector product of the interacting spins, therefore being in competition with exchange interaction (the former favouring perpendicular alignment, the latter favouring parallel/anti-parallel alignment). Although the form is similar, it is not a Dzyaloshinskii-Moriya interaction, since it arises also when relativistic interactions (such as spin-orbit coupling) are neglected.
Our procedure gives the formulas needed to compute the coefficients of the spin-spin interaction terms from electronic non-equilibrium Green’s functions and self-energies. This is the essential distinctive trait of our theory, its power lying in the fact that we can rigorously map the dynamics of the electronic system to that of the spins: in other words, we can obtain the magnetic non-equilibrium properties from the electronic non-equilibrium properties of a given material. The needed electronic Green’s functions can be computed with the methods of Dynamical Mean-Field Theory (DMFT).
Since our theory fully includes electronic dynamics, it rigorously accounts for non-Heisenberg effects, i.e. variations of the lengths of the atomic magnetic moments, which are not captured by Landau-Lifshitz equations. It also accounts for the equilibrium temperature characterizing the initial state, and it provides the parameters of the magnetic interactions both in equilibrium and out of equilibrium. We have also obtained formulas for quantum noise. Importantly, the developed formalism allows to consider an external field varying on an arbitrary time scale, being therefore suitable for ultrafast magnetism, fully including non-adiabatic effects (which are accounted for by the electronic Green’s functions).
We have extended the theory of magnetic interactions within the MBHM to include orbital and relativistic effects, namely spin-orbit coupling, magnetic anisotropy, Zeeman coupling to external magnetic fields, which required an extension of the model to a “generalized” MBHM. Our work (A. Secchi, A. I. Lichtenstein and M. I. Katsnelson, Ann. Phys. 360, 61-97 (2015)) provides formulas for the complete exchange tensor in the relativistic regime and/or in the presence of spatial symmetry-breaking effects (such as interfaces), including Dzyaloshinskii-Moriya (anti-symmetric) exchange, the anisotropic components of exchange, as well as the effective local anisotropy parameters. We have fully included the orbital degrees of freedom of the electrons, without assuming quenching of the orbital moments; our theory allows (for the first time within the Green’s function formalism) to distinguish and compute separately the contributions to the whole exchange tensor arising from the interplay of spin-spin, spin-orbital, and orbital-orbital degrees of freedom. We have also provided the technical prescriptions for the implementation of these formulas within DMFT (A. Secchi, A. I. Lichtenstein and M. I. Katsnelson, arXiv 1506.06209 accepted for publication in J. Magn. Magn. Mater. (2015)).
We have studied the optical manipulation of the spin-spin exchange interaction in iron oxides. In this work we have showed that optical excitations indeed modify the iron-iron (super-) exchange interaction in iron oxides, which is mediated by electronic transfer via intermediate oxygen atoms. A joint publication with our experimental colleagues at the Radboud University and our collaborators in Hamburg (J. H. Mentink and M. Eckstein) is accepted for publication in Nature Communications (the preprint is available at arXiv 1412.7094).
Work Package 2: Atomistic Spin Models
Summary
This WP was on-track and met all objectives within the DOW. The resources have been used as planned.
Highlights
• Atomistic/ab-initio model of Gd – beyond the fixed spin model and successful validation by comparison with experiments. A manuscript was accepted for publication in Nature Communication.
• Studies of differential spin dynamics on FeNi. Full multi-scale modelling of the material and significant contribution to comparison with experiment. A manuscript was accepted to Phys. Rev. B.
Description of WP activities and results
The aim of WP2 was the development of new spin models for complex materials and microscopic equations of motion beyond the current state of the art, to link these spin models with ab-initio calculation in WP1 and with mesoscopic models in WP3 and to verify the approaches by comparison to experiments in WP4. In the following we summarize our achievements of the last 18 months split into tasks:
Task 2.1. Spinmodels for complex materials
In this task the focus was on spinmodels for magnets with more than one sublattice, like, e.g. the ferromagnet FeNi and the ferrimagnet FeCoGd. An important part of our multi-scale modelling procedure is to link spin model calculations with atomistic resolution - and hence large numerical effort - to mesoscopic models. The latter rest either a continuum theory or on macro-spin models with effective equations of motions that have less degrees of freedom and are capable of describing realistic sample sizes. In that context the central result that members of the consortium have obtained is the Landau-Lifshitz-Bloch (LLB) equation in a new version for complex magnetic materials with two sub-lattices. This equation has to be verified by comparison with spin model simulations. Furthermore, thermodynamic equilibrium input functions for the LLB approach have to be calculated in terms of spin model simulations.
Our work on the two-sublattice system (FeNi) used already a full multi-scale approach deriving first a spin model from ab-initio methods and then, in a second step, describing the spin-model with two macro-spins only following the LLB equation of motion. Although FeNi does not exhibit heat-driven magnetization reversal, it nonetheless exhibits distinct sublattice magnetization dynamics in form of different timescales for demagnetisation of each lattice. Our comparison of spin model and macro-spin dynamics verifies our multi-scale approach, where - in the LLB- approach - the dynamics can be successfully described with two macro-spins only. A joint manuscript on the mult-scale modelling of FeNi from groups in Uppsala, Madrid and Konstanz was recently accepted for publication in Phys. Rev. B.
Simulations of FeGd-ferrimagnetic resonance simulations revealed the complex temperature dependence of the ferrimagnetic resonance modes (ferromagnetic mode and exchange mode) in FeGd, currently the best investigated material for all-optical switching. A direct comparison of spin model simulations with analytical calculations based on the two-macrospin LLB approach shows very good agreement again underpinning the importance of the LLB approach.
This task ended in month 24. In was concluded on-time with Deliverable 2.2 “Macroscopic calculations; comparison with spin model“ which details our work which was summarized above.
Task 2.2. Models beyond fixed spin length
While many magnetic materials can be described with a simple Heisenberg exchange as leading part of the Hamiltonian, in some cases more complex models beyond the assumption of fixed spin length are needed. We extended our collaboration between the Konstanz and Uppsala groups in an effort to develop models beyond fixed spin length by a distinct treatment of different types of electrons and their role for the excitation process. The model separates the 5d and 4f electron spins of the Gd, i.e. the orbital character of the spin is introduced. The model then allows the transfer of energy from the 5d to 4f electrons via the intra-atomic exchange. This spin model - with all its parameters derived from first principles - forecasts different dynamics for the magnetization of d- and f-electron on a time scale of several picoseconds, a result that is well confirmed by recent experiments performed at the Free University in Berlin. A joint manuscript of our groups in Uppsala and Konstanz with the group of M. Weinelt in Berlin was recently accepted for publication in Nature Communications.
In another project for models beyond fixed-spin length we focused on a detailed understanding of the temperature dependence of magnetic material properties. The temperature dependence of macroscopic physical quantities is due to thermal fluctuations of the microscopic degrees of freedom, which --- for magnetic systems --- is the atomic magnetic moments. The Hamiltonian of the system is then parameterized in the form of a spin model. However, the question arises as to how far the parameters of the spin model itself are temperature dependent due to temperature dependent changes of the electronic structure. In collaboration between Budapest and Konstanz we calculated the temperature dependence of the Heisenberg exchange from first-principles in order to investigate the influence of their temperature dependence on magnetic phenomena at finite temperatures. We focus on the understanding of the interplay between these two types of temperature dependence --- coming from thermal fluctuations of the spin degrees of freedom on the one hand and changes in the electronic structure leading to temperature dependent spin model parameters on the other. As a test system Fe was modelled in the bcc phase. Finite temperature spin-fluctuations are taken into account using the Relativistic Disordered Local Moment scheme as implemented in the Korringa-Kohn-Rostoker method (see WP1). From these calculations the electronic structure is obtained as a function of the magnetization from the ferromagnetic state down to the paramagnetic state. For a given value of the magnetization, the exchange parameters are evaluated by using the relativistic torque method in as much the statistical average of the exchange coupling is performed in terms of the Coherent Potential Approximation. Then we use Langevin dynamics simulations and compare simulations where we either assume constant ground state spin model parameters (exchange interactions and atomic magnetic moments) or m-dependent spin model parameters where we use a self- consistent scheme for the calculation of the temperature dependence of m while taking into account the m-dependent spin model parameters. The equilibrium magnetization curve is clearly affected by the temperature dependence of the exchange and we continued our investigation towards the dynamic behavior under the assumption of time-varying spin model parameters. Our temperature dependent parameters went into the FEMTOSPIN database and a final publication is in preparations.
Upon femtosecond laser excitation of a metallic trilayer or bilayer system fast spin transport can occur from the excited layer to the adjacent layers, which leads to a nonthermal magnetisation redistribution in the layers. Subsequently a fast longitudinal spin evolution occurs, attempting to bring the material back to its spin equilibrium; the appearing spin evolution cannot be captured with fixed-spin length models. Therefore a theoretical formulation on the basis of the Landau-Lifshitz-Bar'yakhtar equation was developed as well. Effectively the longitudinal spin evolution is concurrent with a strong spin current owing between the layers.
This task was concluded in month 24, details are given in Deliverable 2.3 “Models beyond fixed spin length; underlying theory“ which was submitted in month 24 and Deliverable 2.4 “Advanced models beyond fixed spin length“ submitted in month 36.
Task 2.3. Beyond Langevin Dynamics
In most of our atomistic and micromagnetic simulations use a Langevin dynamics approach, where stochastic fields are introduced in the Landau-Lifshitz-Gilbert equation of motion with a strength calculated from near-equilibrium properties. The damping term is rather phenomenological and is a result of the averaging over instantaneous bath degrees of freedom. This approach may fail for the modelling of ultra fast dynamics where the phonon, electron and spin dynamics occurs at the same timescale. To go beyond the standard Langevin dynamics we explore two approaches:
First, in the classical approach we simulate the lattice degrees of freedom explicitly as energy and angular momentum reservoir for the spin system. To follow the flow of energy as well as angular momentum we derive and use coupled equations of motion for both subsystems on an atomistic level. These equations avoid the phenomenological Landau-Lishitz (or Gilbert) damping paving the way for a new type of spin-molecular dynamics simulations. As a first application the dynamics of the Einstein-deHaas-Effect was investigated, where the angular momentum flow from spin- into the lattice degrees of freedom was calculated microscopically.
Second, a quasi-classical approach where we propose a method to study the finite-temperature behaviour of small magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert equations, where the effective magnetic field is calculated directly during the solution of the dynamical equations from first principles instead of relying on an effective spin Hamiltonian. Different numerical solvers for the dynamical equation were investigated. As an example of this new type of dynamics we performed detailed investigations for a monatomic chain of ten Co atoms on top of Au(001) surface.
This task was concluded in month 33. Details are given in Deliverable 2.5 “Beyond Langevin Dynamics”, which was submitted in month 24
Task 2.4. Heat-bath models of ultrafast processes
In the most common approaches for the study of magnetization dynamics the heat bath is added phenomenologically as damping term in the equation of motion. Physically the heat-bath for the spin system is provided by the electron system and the lattice degrees of freedom. In this task an improved model of the coupled spin and lattice dynamics has been developed to explore the effect of the lattice acting as a heat bath. An example system of bcc Fe was modelled and was tested for the energy conservation and the phonon dispersion. With thermal noise and damping incorporated on both the spin and lattice system the equilibrium magnetisation and susceptibility showed a Curie temperature of 1050 K and the calculated magnon dispersion showed typical ferromagnetic bands. The range dependent exchange interaction does not provide a suitable coupling due to the symmetry of the equations of motion and so a specific coupling term is also included based on the spin-orbit coupling. By including this term with out thermal noise for the spin system magnon modes are excited at the edge of the Brillouin zone and relax into longer wavelength modes.
This task was concluded in month 36. Details are given in Deliverable 2.6 “Heat-bath models of ultrafast processes”.
Work Package 3: Mesoscopic model development
Summary
The work within this WP was delivered on-time and met most of objectives within the DOW. Each partner as planned has used the resources outlined in the consortium agreement. The goal of this work package was to provide a platform for incorporating atomistic scale detail and providing a means for comparison with experiment. This has been broadly achieved resulting in a number of cross WP publications.
Highlight
• Creation of large-scale micromagnetic framework and programs (MARS and VAMPIRE) for modelling of high-temperature ultra fast magnetisation dynamics for ferro and ferromagnetic continuous and granular materials and multilayers.
• Articles published in Nature Scientific Reports and Physical Review Letters.
Description of WP activities and results
The aim of WP3 was the development of new types of micromagnetics, suitable for modeling of ultra-fast magnetization dynamics at large scale. For this purpose we further developed the theoretical framework based on the Landau-Lifshitz-Bloch (LLB) equation for ferro and ferrimagnetic materials. The WP3 completes the multi-scale modelling scheme since it uses the information from WP1 and WP2, it also connects with WP4 through the direct comparison with the experimental data.
Our achievements of the last 18 months split into tasks:
Task 3.1. Mesoscopic multi-scale models for ferromagnetic materials
In this task multi-scale models for one-component materials such as Ni, Co, FePt and several bilayers such as Gd/Fe have been created. The diluted magnetic semiconductors were excluded from consideration by the decision of the consortium. To incorporate miscroscopic scattering mechanism, the quantum LLB equation was derived (published recently in Phys.Rev.B) incorporating phonon and electron scattering The coloured noise was also incorporated into the LLB equation. The LLB equation has been used to model the ultra-fast dynamics (including the domain wall and bubbles) in FePt and vortices and domain walls in FeNi and multiferroics (recently accepted at Physical Review Letters).
Task 3.2. Development of novel models for ferrimagnets and antiferromagnets
In this task we derived a novel LLB equation for two-component systems in classical and quantum cases. The models were applied for RE-TM alloys such as GdFeCo, TbFe and CoFe. The ab-initio information from Budapest group was incorporated for GdFe, TbFe and FeRh large-scale modelling. The use of the ferrimagnetic LLB equation has allowed us to achieve theoretical understanding of many important characteristics of the ultra-fast dynamics in two-component systems. Namely, we predicted that (i) the switching in small dots becomes precessional (ii) the switching is defined by different demagnetisation speeds of materials, consequently in highly coupled materials such as TbFe Laves phase, deterministic switching does not take place (iii) at high temperatures the demagnetisation in Gd may become faster than that of Fe in GdFeCo, and the polarity of the transient-like state may change (iv) while Fe experiences a slowing critical down at high temperatures in GdFeCo, Gd – does not, this explains that high temperatures are not good for switching (v) the dependence on RE concentration is highly non-trivial and one can find different situations: for small intersublattice coupling, the switching is more effective when Gd concentration is larger and for large coupling the situation is the opposite. All this findings have been published in series of articles in Physical Review B between several groups (and workpackages) in the consortium.
The large-scale modelling has been also applied for modelling of ultra-fast dynamics in Gd/Fe multilayers achieving understanding of several experimental situations (collaboration between Madrid, Nijmegen and York groups), particularly a non-trivial occurrence of precession when going through the magnetisation compensation point.
Task 3.3 Development of models for granular and polycrystalline materials
The models of granular and polycrystalline materials based on the Voronoi construction were developed in the first part of the project by Madrid and York groups. In the second part, the work involved the incorporation of the models into the software MARS and VAMPIRE
Task 3.4 Development of the optimized code for advanced material and device design
Several in-house codes for LLB micromagnetics have been created in York, Konstanz and Madrid groups. These were developed in collaboration but optimised for different purposes. The optimised MPI parallel code (MARS), working on GPU, which will be suitable for public release has been created in York. The database for several materials was created and maintained in the Femtospin webpage with the input from all theoretical partners. Without these codes development steps the work carried out in this WP would not have been possible. Whilst the codes were developed as part of the FemtoSpin project for ultrafast magnetisation dynamics, the codes will have a lasting impact for the members of the consortium going forward and are already finding appropriate uses for research beyond ultrafast dynamics (e.g. vortex core dynamics in composite multiferroics).
Task 3.5 Micromagnetic and multiscale modelling of heat-assisted all-optical magnetic recording.
Both York and Madrid groups were using the large-scale models to investigate the possibility of ultra-fast all-optical magnetic recording. Particularly, we have investigated the magnitude and the duration of the field coming from the inverse Faraday effect to explain recent experimental data and to make predictions in FePt. Large-scale micromagnetic program was used for this purpose and the laser pulse intensity was varied. We have found that the inverse Faraday field either of the magnitude above 10T or duration more than several picoseconds is necessary for all-optical recording. The switching speed may be fast (below 0.5 ps) depending on the magnitude of the field and the temperature, defined by the laser pulse intensity (to be published).
Work Package 4: Experiments and link to multiscale calculations
Summary
This WP has met all objectives within the DOW. The materials preparation aspects were initially delayed but has eventually delivered the necessary samples for the optical and X-ray experiments. The resources have been used as planned.
Highlights:
• Measurements of differential demagnetisation in NiFe and comparison with theoretical predictions.
• Development of element specific optical microscopy and measurements on TbFeCo
• Demonstration of angular momentum transport between Gd and Fe sublattices with fs time and nm spatial resolution, using fs-Xray scattering
• Demonstration of AOS in Gd/Fe multilayers, as predicted by the model of AOS in antiferromagnetically coupled multilayers.
Description of WP activities and results
The aim of WP4 was to develop and apply novel experimental tools on validated nanostructured test samples to obtain fundamental input parameters for models and to test the output of the mesoscopic models with time resolved optical, THz and X-ray experiments.
Task 4.1: Fs-XMCD
For the fs-XMCD experiments we made use of two facilities: the fs-slicing facility at BESSY-II at the Helmholtz-Zentrum Berlin and the Linac Coherent Light Source (LCLS) at SLAC, Stanford. We have demonstrated that the element specific demagnetization proportional to the magnetic moment (I. Radu et al, Nature 472, 205 (2011)) is a very general phenomenon that appears in both anti-ferromagnetically and ferromagnetically coupled sublattices (I. Radu et al, SPIN, 2015). We have determined the demagnetization times for a large number of elements, both in their pure form and in various alloys. These results support the recent theoretical models of ultrafast all-optical demagnetization and switching.
The experiments at the LCLS have led to the surprising results that the FeGdCo samples that have been shown all-optical switching are inhomogeneous on the nanoscale. The time and q-dependent XMCD data demonstrate that there is angular momentum exchange between these areas, as evidenced by the time delay in the dynamics at larger q values (C. Graves et al, Nature Mat 12, 293-298(2013). These unique results directly support the theoretical models of intersublattice exchange.
Several Gd/Fe and Gd/FeCo multilayer samples grown by the Belfast group have been measured using element-specific XMCD technique as a function of temperature. All the investigated samples Ta(5nm)/[Gd(0.5nm)/Fe90Co10(2nm)]8/Ta(5nm) Ta(5nm)/[Gd(3nm)/Fe90Co10(2nm)]4/Ta(5nm) and Ta(5nm)/[Gd(1nm)/Fe(1nm)]10/Ta(5nm) are showing an in-plane anisotropy. We have observed a magnetization compensation temperature of ~250K for [Gd(3nm)/Fe90Co10(2nm)]4 sample, while for [Gd(1nm)/Fe(1nm)]10 and [Gd(0.5nm)/Fe90Co10(2nm)]8 the compensation temperature were below 10K or above Tc, respectively. The Task was successfully finished with deliverable D4.1.2 Fs X-ray spectroscopy
Task 4.2: fs X-ray microscopy
Several experiments with holographic imaging have been attempted at the LCLS, using a FeGd sample on specifically designed membranes made of SiN. Single shot switching has been observed, with smallest structures in the tens of nm regime, showing the potential of all-optical switching on the nanoscale. We have also attempted to use plasmonic antennas to focus the optical laser beam and achieve controlled switching at nanometer length scales. Unfortunately these experiments were not very successful, presumably due to the quality of the antennas. The Task was finished with deliverable D4.4: Fs Xray microscopy.
Task 4.3: fs optical spectroscopy
We have developed a new femtosecond pump-probe set-up that allows to probe the spin dynamics in magnetic thin films and heterostructures in fields up to 7Tesla and at temperatures down to 4K. With this system we have probed the d–f exchange interaction in EuTe using pump-probe experiments and the spin interactions in ferromagnetic (In,Mn)As (R. R. Subkhangulov,et al, Laser-induced spin dynamics in ferromagnetic (In,Mn)As at magnetic fields up to 7 T; Phys.Rev. B 89, 060402(R) (2014); R. R. Subkhangulov, et al, All-optical manipulation and probing of the d–f exchange interaction in EuTe, Scientific Reports 2014).
We have demonstrated element specific probing with visible lasers, using the frequency dependence of their magneto-optical response (A. R. Khorsand, et al, Phys. Rev. Lett. 110, 107205 (2013), showing a similar transient ferromagnetic state as was seen in FeGdCo before using Xrays. In particular, we demonstrated that in FeTb one can study the dynamics of the Tb- and Fe-spins individually, by choosing the wavelength of light above and below 600 nm, respectively, as presented in Fig. 4.3.1(Left). The possibility of using visible laser light also increases significantly the signal-to-noise ratio in the element-specific measurements compared with other techniques. Exploiting this feature, we were able to investigate with extremely high reproducibility and low noise the demagnetization rate as a function of the impinging pump fluence. Surprisingly we found that this rate of demagnetization presents a piecewise behavior, as presented in Fig.4.3.1(Right). A
Fig. 4.3.1. (Left) Ultrafast sublattice magnetization dynamics of TbFe at λFe = 800 nm and λTb = 500 nm, corresponding to dominantly the Fe and Tb sublattices, respectively. A long lasting ferromagnetic state is excited, with a fluence of F = 8 mJ/cm2[4]. (Right) Demagnetization rate as a function of pump laser fluence; a clear super-linear trend is measured for fluences above 4 mJ/cm2.
linear trend, typical for magnetic metals, is followed by an enhanced (super-linear) demagnetization rate. Atomistic models (York) give rise to a similar behaviour but do not as yet completely explain this phenomenon. We have also looked at the details of the Gd-Fe spin interactions in the demagnetization and clarified the role of the intersublattice exchange interaction and the compensation point in this process (A. Mekonnen, et al, Phys. Rev. B 87, 180406 (2013); R. Medapalli, et al, Phys. Rev. B 86 054442 (2012)).
As simulations have shown that AOS should be possible in FePt/Fe exchange coupled multilayers, we have started dynamic studies of highly anisotropic granular FePt films in their L1(0) phase. Experiments were done in a newly developed pump-probe set up at the Nijmegen High Field Magnet Laboratory, allowing the study of the static and dynamic properties of magnetic thin film samples in fields up to 38Tesla. Samples were provided by HGST-Hitachi. The first results have shown large inherent resonance frequencies in the THz regime and a damping parameter of 0.1 (J. Becker, et al, Laser induced spin precession in highly anisotropic granular L1(0) FePt. Appl. Phys. Lett., 104 (2014)).
We have also performed stroboscopic pump-probe measurements on Fe/Gd multilayer samples, both above and below TM (for the description of the samples, see Task4.4). We show that we are able to induce a switching event with a single optical pulse both below and above TM. In particular, all-optical switching is possible up to about TM + 100 K. At higher temperature is not possible anymore to ignite the switching event.
This Task was successfully finished and yielded the deliverables D4.6 - femtosecond optical spectroscopy (heterostructures): determination of the coupling of the dynamics in magnetic heterostructures (AFM/FM); Because of the discovery of TIMS, we did not further pursuit the determination of the dependence of pulse parameters and frequency dependence for the Inverse Faraday Effect, which was part of the original deliverable.
Task 4.4: fs optical microscopy
We have dramatically improved our optical microscopy capabilities. Single shot imaging now allows pump-probe experiments to look at the temporal development of magnetic domains in optically excited thin magnetic films with fs time and one micron spatial resolution. We have also improved the speed and stability of our magneto-optical microscope, by a combination of mechanical and software improvements. The latter allow for automatic control and corrections for drift (Y. Hashimoto, et al, Review of Scientific Instruments, 85(6). 10.1063/1.4880015 (2014). We have also demonstrated that optical interference can greatly enhance the efficiency of all-optical switching (M. Savoini et al. ,Phys. Rev. B 86, 140404, 2012).
In the past 10 years, all-optical switching has been demonstrated in GdFeCo amorphous alloys. With a deepening understanding of the underling mechanism driving the magnetization reversal process, theoretical predictions of other possible system in which the switching could occur have been made. In particular a synthetic ferrimagnetic structure (even rare-earth free) has been proposed within the FemtoSpin consortium. We have investigated the magnetic properties of an intermediate step, where the transition metal and the rare-earth elements are separate in a multilayer stack. Thus we have deposited 4 different samples through sputtering, varying the thickness of the single layers. Figure 4.4.1 shows a schematic of the magnetic layers in the different samples, where n represents the total number of layers and t the thickness of the layers (equal for Gd and Fe, unless otherwise specified). The total thickness of the magnetic sample is kept constant (tTot=20 nm).
We have investigated the magnetic properties of the 4 samples as a function of the temperature, down to liquid nitrogen temperature (T=70 K). Samples A, B, C showed in-plane anisotropy. D instead was out-of-plane magnetized. An increase of the coercivity at lower temperatures is apparent for all the samples, but only for C a clear magnetization compensation temperature is measurable at TM=175 K (sample B might present it at T=0 K). A similar value of TM has been found for sample D (out-of-plane anisotropy). All these sample were designed to have a composition percentage similar to the amorphous alloy Gd25[FexCo(1-x)]75. It is remarkable that by tuning the number of layers, thus the interaction between the elements, we are able to tune both the magnetic anisotropy and the magnetization compensation temperature. Another important point is that the amorphous alloy with the mentioned composition generally shows TM>300 K, double than the one measured for C or D.
Using a single-shot pump-probe imaging technique, a strongly spatially inhomogeneous magnetization reversal process is observed (see Fig. 1) as a function of the local excitation. At certain experimental conditions the excited domain shows a periodic change of the magnetic contrast accompanied by a gradual shrinking of the oscillating part with a linear velocity of the shrinking equal to 30 km/s. This observation, together with a high amplitude magnetization precession makes this magnetization dynamics very different from the one observed in RE-TM amorphous alloys.
Figure 1: Spatially inhomogeneous magnetization reversal process in Gd/FeCo multilayers. Insets show the magneto-optical contrasts after a single ultra-short laser pump illuminates the sample. After a certain delay the magnetization state is probed and the magneto-optical images are obtained. Evolution of the illuminated area cross-section is plotted as a function of time. Spatially inhomogeneous ultrafast magnetization reversal with the magnetization precession is accomplished by a gradual shrinking of the oscillating part. The speed of such a shrinking is indicated as 30 km/s.
The study reveals changes of the effective magnetization precession damping within the laser-illuminated area, where the temperature gradient is suggested to be responsible for this dynamics [3]. The Task was successfully finished with deliverable D4.6.
Task 4.5 Materials and Nanostructuring
The task was to provide materials customised to meet the various requirements of the consortium in pursuit of the project objectives regarding material studies. A number of systems ranging from RETM alloys and multilayers, to complex transition metal based ferrimagnetic structures were developed and fabricated. Materials were sent to P2 and P7 for the study of switching dynamics on the femtosecond scale.
Partners required the materials in most cases to be ferrimagnetic, exhibiting magnetic compensation near to or below room temperature. There was no specific requirement regarding direction of magnetic anisotropy (although a practical media is expected to be perpendicular to the film plane) and some systems exhibited in-plane magnetic anisotropy and others were out-of-plane. Method of preparation was planar magnetron sputtering in ultra high vacuum and substrates were typically silicon or glass wafers. Process temperatures were in the range 300K to 750K. Validation was carried out using Vibrating Sample Magnetometry and Magneto-optical Kerr Effect measurements.
The materials produced fell into three main categories: rare earth transition metal (RETM) materials, synthetic ferrimagnets, and ordered FePt based materials with high anisotropy. RETM materials were mainly alloys and multilayers of Gd and Fe or FeCo, where the compensation temperatures were controllable through the relative concentration of rare earth to transition metal in the films. Synthetic ferrimagnets were transition metal based multilayered systems involving ferromagnetic layers such as Fe, Co and Ni or their alloys, coupled antiferromagnetically through an appropriate spacer layer. Compensation points were achieved through the matching of the magnetic properties of the component layers.
Materials for P7 were subject to a number of constraints specific to the requirements of their femtoslicing and XMCD experiments. For this work, it was necessary to have the coupled layers made of different magnetic elements so their switching characteristics could to distinguished. In addition there were restrictions on film thickness, a preference for compensation temperatures below room temperature, and the need for films to be grown on a special aluminium foil, which was a very different type of substrate to the silicon and glass used during material development and also limited the process temperatures used. Consequently, it was not possible to fabricate a synthetic ferrimagnet with perpendicular magnetic anisotropy that was compatible with the experimental techniques of P7, and the most promising materials for P7 were RETM multilayers or transition metal based synthetic ferrimagnets with in-plane magnetic anisotropy.
Materials for the thermally induced switching scheme proposed by P1 require high anisotropy and strong coupling to be effective. Efforts were made toward producing a suitable structure based on the calculations of P1, which were for L10 FePt antiferromagnetically coupled to Fe through a suitable spacer. Much work was done on achieving the ordered L10 phase of FePt at temperatures attainable on our tools, which are lower than is typical for L10 FePt production. Antiferromagnetic coupling between L10 FePt and Fe was demonstrated using an Ir spacer and was found to be affected by the thickness of the L10 FePt and Fe layers.
A general problem for synthetic ferrimagnetic materials was the loss of properties due to elevated temperatures applied either during deposition or by post annealing. This had implications for the longevity of the materials and also imposed serious limits on the type of structures that could be grown. It was a particular issue for perpendicular materials or materials with high anisotropy, where alloys such as L10 FePt are a necessary component of the structure, and require significant temperatures during manufacture. We were able to demonstrate that a possible solution exists in the use of thinner layers in repeated multilayer structures, which could improve both ferrimagnetic properties and thermal stability. This provides a basis for further study on how heating affects certain properties such as microstructure and the integrity of the ultrathin spacer layer responsible for strong antiferromagnetic coupling essential for a ferrimagnet. The latter may also be important in the development of future theoretical models, where microstructure is often neglected and materials are assumed to be perfectly formed and orientated monolayer stacks. This task was completed with deliverable D4.10 Materials and nanostructuring.
Task 4.6: THz control
The goal of this task was to demonstrate the possibility to control the magnetic state and properties using THz pulses. We have shown the possibility to resonantly pump a lattice mode to trigger a structural phase transition (A. D. C Aviglia et al, Phys. Rev. Lett. 108,136801 (2012). Using femtosecond resonant soft X-ray diffraction at the LCLS free electron laser, we demonstrated that the resonant optical excitation of an infrared-active phonon mode in a LaAlO3 substrate induces melting of the antiferromagnetic order in a NdNiO3 thin film, epitaxially grown on top of it. The magnetization dynamics in the thin film involve a supersonic phase front propagation, triggered by the lattice distortion at the substrate-film interface (M. Först. A.D. Caviglia et al., in preparation).
In addition, experiments were carried out on the lattice control of magnetic excitations in bulk orthoferrites. Our preliminary data indicate that the resonant excitation of an optical phonon mode in ErFeO3 (at multi-THz frequencies) drives a coherent magnon, as observed via time-resolved Faraday rotation.
Potential Impact:
Potential impact
The FemtoSpin project was carried out within a rapidly evolving industrial context. In terms of magnetic information storage, the drive to higher recording densities is based on Heat Assisted Magnetic Recording (HAMR), which uses laser pulses to heat the storage medium so as to allow reversal of the magnetisation. This relies on a combination of laser heating coupled with standard technology to generate a localised magnetic field to induce the magnetisation switching. Because of materials limitations, this field is limited in magnitude: a factor which will ultimately limit areal storage densities. Technologically, the complexity of manufacture of the write transducer is already slowing down the pace of development. The use of optical switching would remove the requirement for the inductive write transducer, significantly reducing both manufacturing costs and power requirements. At the same time, the field of spin electronics (or Spintronics), in which device functionality is dependent on the spin of the electron rather than simply the charge, is developing rapidly. Spintronics is a strong candidate to replace conventional electronics as this reaches its physical limitations. Again, optical reversal is a potential candidate for switching the magnetisation in spintronic devices.
Although technical difficulties remain to be overcome, Heat Assisted Magnetic Recording (HAMR) is closing in on providing the next generation of ultrahigh density recording systems. In May 2014 Seagate announced a 1.4Tbit/in2 areal density demonstration (the first to exceed conventional recording demonstrations) having previously shown 1000 hours of continuous write (the benchmark requirement). However, HAMR densities will be limited by the available write field (around 1Tesla) using inductive technology, due to the requirement of avoiding errors due to thermally induced back switching. Due to the physical and technical understanding within the FemtoSpin project, all-optical recording must be considered a realistic candidate for progress beyond HAMR. Here it must be noted that all candidate technologies face similar problems of writing and stability at extreme densities, and the large effective fields involved in all-optical technology could give it a strong advantage. Equally important could be the removal of inductive technology from the writing process in magnetic recording, leading to very significant design and process simplifications with important implications for cost reductions and reduced environmental impacts; that latter also enhanced by significantly reduced energy cost per bit in the write process. This represents an important potential advance for European industrial potential, supporting the major production centre of Seagate in Northern Ireland which produces around 25% of the world-wide total output (around 1 billion p.a.) of recording heads; an important European industrial resource.
Scientific highlights
• Development of an ab-initio code for the calculation of the opto-magnetic field (i.e. the magnetization induced by circularly polarized laser light), on the basis of the derived quantum theory for the opto-magnetic field.
• A theoretical framework has been derived for demagnetization due to transfer of the spin of hot (laser-excited) electrons to the phonon system and the resulting demagnetization rates were ab-initio computed for 3d ferromagnets.
• Ultrafast demagnetization due to spin transport has been investigated and was shown to give rise to emission of THz radiation
• Understanding the TIMS phenomenon and its prediction in structured media
• Atomistic/ab-initio model of Gd – beyond the fixed spin model and successful validation by comparison with experiments.
• Studies of differential spin dynamics on FeNi. Full multi-scale modeling of the material and comparison with experiment.
Multiscaling and collaborative code development
In magnetic materials the problem of linking lengthscales is compounded by the complex dynamical behaviour of spin systems and the difficulty of obtaining accurate values for magnetic materials properties from ab-initio calculations since the quantities of interest (the exchange energy and magnetic anisotropy values) are very small components of the total energy of the systems and require specialized techniques as well as fully relativistic models. Femtospin has made great strides in improving multiscale magnetic calculations and developing them into an integrated formalism. In particular,
• ab-initio determination of magnetic properties and parameterization of atomistic spin Hamiltonians (Budapest, Uppsala, Konstanz, York); automatic generation of spin model parameters for the Vampire atomistic code is almost complete.
• Macrospin simulations and atomistic testing/ parameterization (ICMM, Konstanz, York). This collaboration has produced a suite of models optimized for continuous and granular media. This collaboration has also developed a ferrimagnetic LLB equation for macrospin simulation.
• (ICMM, RU, York); atomistic and macrospin approaches have been combined to produce understanding of the dynamic behavior of ferrimagnetic materials during the thermally induced magnetization switching process.
Femtospin code development: public code release
– York atomistic code (Visual Atomistic Massively Parallel IntegRation Engine; VAMPIRE). On public release, Details available from vampire.york.ac.uk. Described in invited topical review; R. F. L. Evans, et. al., J. Phys.: Condens. Matter, 26, 103202 (2014) (23pp) (selected as one of the highlights of 2014 in J. Phys.: Condens. Matter). This paper has had almost 1000 downloads and already VAMPIRE has a user base of around 50. The code is in trial use in industry to support the development of advanced media structures for HAMR.
– MAgnetic Recording Simulator; MARS. Developed for advanced simulations of all-optical recording and HAMR in collaboration with Seagate/WD.
Document Database
Throughout the project a number of documents, files and articles have been produced.
The vast majority of the material produced has been stored in the private (member) area of the project website. A significant effort has also been made to create a database of the material properties calculated during the project. This website will remain for the short to medium term, managed by the University of York. The main code developed under the remit of the project is the VAMPIRE code which is publicly available at vampire.york.ac.uk where new versions are uploaded upon new release. The visualisation code developed in Konstanz (IMAGIN) is located on the internal pages of the FemtoSpin website for use within the consortium. The database will be placed on the outward facing pages of the Femtospin website, which will be maintained for the foreseeable future.
Dissemination
A huge number of publications have been published through the efforts of the members of the consortium in prestigious journals such as Nature Communications, Nature Materials, Physical Review Letters and Scientific Reports, to name but a few.
Outputs
1. Calculations of specific materials design parameters enabling a Dutch patent (2008039). Patent process continuing in Europe (EP2795622 (A2)) and the United States (US2014368303).
2. Atomistic code (Vampire) on public release. Very good take-up by academia.
3. Preparing advanced optical and heat-assisted magnetic recording model (MARS) for public release.
Other Outputs
4. Publications; 70 papers in high impact journals including Nature journals (7) and Physical Review Letters (2) and Scientific Reports (3).
5. 68 invited papers at International conferences
6. Organisation of a summer school in Nijmegen
7. Initiation of the Ultrafast Magnetism Conference (Rasing, Chantrell with Bigot and Huebner; first edition in Strasbourg in 2013 and second in Nijmegen in 2015)
Through regular meetings or the members of the consortium various channels for circulating the key results of the project and their impact have been planned and executed to great success. Assisted by the leading role of the members of the consortium in this field a large number of prestigious invited papers have been central to disseminating results to the magnetism community within the EU and beyond.
The leading role of the members of the consortium in theoretical and experimental magnetism has provided excellent opportunities throughout the project for engaging with the community to demonstrate the cutting edge techniques used within the consortium. Through workshops and other outreach activities the progress made in theoretical and experimental techniques has been shared with other scientists. We were also instrumental in the establishment of a new conference series, the Ultrafast Magnetism Conference.
A further aim of the FemtoSpin project was to increase the profile of ultrafast magnetization dynamics for data storage applications, as well as to raise awareness of the theoretical and experimental techniques used and developed by the consortium. By engaging with industrial partners through joint workshops and by making regular visits to various members of industry the project has succeeded in part in achieving these goals.
List of Websites:
www.femtospin.eu
Prof. Roy Chantrell
Dept. of Physics
The University of York
Heslington
York
North Yorkshire
UK
Email: roy.chantrell@york.ac.uk
The FemtoSpin project had the aim of understanding the basic processes involved in all-optical magnetization switching, to develop models at the electronic, atomistic and mesoscopic/continuum levels and to develop linking techniques to couple the models in a multiscale approach to calculations of ultrafast magnetization processes. The models were successfully developed, providing significant progress in the ab-initio determination of magnetic materials parameters and their incorporation into atomistic level models. The multiscale chain was completed by the development of advanced macrospin models based on the Landau-Lifshitz-Bloch equation of motion, in particular a model of 2-sublattice ferrimagnets. The models were developed and validated by comparison with state-of-the-art experiments in leading European laboratories. The project led to important advances in understanding of all-optical reversal processes; a field less than a decade old with considerable potential for applications in magnetic information storage and manipulation.
The scientific outputs from the project were outstanding, around 70 papers in high impact journals including Nature journals (7) and Physical Review Letters (2) and Scientific Reports (3), and some 68 invited papers at International conferences. Outreach activities included the organisation of a summer school in Nijmegen and the initiation of the Ultrafast Magnetism Conference (Rasing, Chantrell with Bigot and Huebner; first edition in Strasbourg in 2013 and second in Nijmegen in 2015). A review of the project output concluded that there was not a sufficient market for the commercialization of the software output. The main software output from the project is the VAMPIRE atomistic code, which has generated a user base of around 50 users and is currently being trialled in an industrial materials design context.
FemtoSpin has made a large impact in terms of generating the understanding of optomagnetic processes. The model development at all lengthscales has led to the production of a multiscale model chain taking magnetic parameters from ab-initio calculations into atomistic models which then provide parameterised information for macroscopic calculations. This process leads to macroscopic models with a strong physical basis for use in materials and device design. At the atomistic level we have developed the first approach taking into account the distinction between internal moments in Gd metal and studied the effects on the ultrafast dynamics. Atomistic model calculations also demonstrated the origin of the Thermally Induced Magnetisation Switching (TIMS) in the excitation of specific magnetic spin waves which transfer angular momentum between the transition metal and rare-earth sublattices leading to a transient ferromagnetic-like state which initiates the magnetisation reversal. This led to the prediction of a set of design rules for TIMS and the prediction of TIMS in synthetic ferrimagnets. This gives the promise of potential recording systems having no requirement for a magnetic reversing field to switch the polarity of the magnetic bit from ‘0’ to ‘1’. Calculations of specific materials design parameters enabled a Dutch patent (2008039). The patent process continuing in Europe (EP2795622 (A2)) and the United States (US2014368303).
Project Context and Objectives:
3.1 Publishable summary
3.1.1 Summary description
The FemtoSpin project has made rapid progress in a field of enormous scientific and technological importance. The scientific basis of the project is research in ultrafast magnetisation processes induced by the interaction of femtosecond laser light with magnetic materials. Experimentally, a light beam from a powerful-pulsed laser with a pulse width of around 50 femtoseconds is split into 2 beams. The first, high intensity (pump) beam is incident on the magnetic material, in the form of a thin film of thickness around 10nm, causing rapid heating. The second, low intensity (probe) beam is sent around a delay line, arriving at the sample with a controllable delay and used to measure the magnetisation of the film using a technique known as the Magneto-Optical Kerr or Faraday Effect. By means of such pump-probe experiments it has become possible to measure the magnetic response of a material on a timescale of tens of femtoseconds. This is a topic at the cutting edge of condensed matter and materials physics. In addition, for more detailed, element resolved, spin dynamics, similar experiments are done using femtosecond X-ray pulses that also give nanometer spatial resolution. FemtoSpin is predominantly aimed at developing models of the ultrafast magnetisation dynamics, but also has a core of leading experimental groups that provide validation as well as inspiration for the model development. The proven strong collaboration between the participants has led to a number of significant advances, including the explanation of the physical origin of a phenomenon known as Thermally Induced Magnetisation Switching (TIMS) in which magnetisation switching can be achieved by a heat pulse alone in the absence of an applied field. This astonishing result has triggered a major worldwide effort to provide a full understanding of the phenomenon and its translation into practical applications. The technical implications for information storage technology are extremely exciting, giving the possibility of increased data rates along with reduction of device complexity and power requirements.
The FemtoSpin project was carried out within a rapidly evolving industrial context. In terms of magnetic information storage, the drive to higher recording densities is based on Heat Assisted Magnetic Recording (HAMR), which uses laser pulses to heat the storage medium so as to allow reversal of the magnetisation. This relies on a combination of laser heating coupled with standard technology to generate a localised magnetic field to induce the magnetisation switching. Because of materials limitations, this field is limited in magnitude: a factor which will ultimately limit areal storage densities. Technologically, the complexity of manufacture of the write transducer is already slowing down the pace of development. The use of optical switching would remove the requirement for the inductive write transducer, significantly reducing both manufacturing costs and power requirements. At the same time, the field of spin electronics (or Spintronics), in which device functionality is dependent on the spin of the electron rather than simply the charge, is developing rapidly. Spintronics is a strong candidate to replace conventional electronics as this reaches its physical limitations. Again, optical reversal is a potential candidate for switching the magnetisation in spintronic devices.
3.1.2 Summary of objectives
• Obtain fundamental knowledge of dynamic processes on the fs timescale; this requires the development of new approaches to treat non-equilibrium electron dynamics, utilizing Density Functional Theory and applying these to understand the fundamental mechanisms underlying ultrafast spin dynamics.
• Advanced atomistic models; this includes spin models with equations of motion beyond Langevin dynamics; new approaches to induced spins and transport; integration of thermodynamic and quantum approaches
• Mesoscopic model development; this requires mesoscopic modelling using a generalised Landau-Lifshitz-Bloch (LLB) Equation; formulation for ferrimagnets and determination of LLB parameters from SDFT calculations and atomistic models.
• Multiscale calculations and link to experiments; verification of models against experiment; feedback from experiments to model development; material studies; large-scale calculations and device simulations.
• Detailed materials studies; candidate materials with especially promising properties on the femtosecond timescale will be investigated. This will encompass single-phase materials and alloys in addition to novel structured materials with engineered properties.
3.1.3 Work performed and major results achieved
The development of new technology based on opto-magnetic phenomena requires new models with a sufficiently strong physical basis. The models must be validated by comparison with state-of-the-art experiments. Within this background FemtoSpin has been highly successful, in particular in the following areas:
Multiscale model development. Optomagnetism is driven by the interaction between photons, conduction electrons, lattice vibrations and the atomic spins themselves. This is a complex problem involving the development and coupling of models on 3 fundamental lengthscales:
Electronic; theories of laser/spin interaction, predictions of important magnetic materials information. These have been investigated using Density Functional Theory (DFT) and analytical models, both for comparison with experiment and to link to atomistic models. Significant advances have been made in the understanding of the laser/spin interaction and in techniques for the determination of magnetic properties.
Atomistic models; using information from DFT, atomistic models introduce the thermodynamic aspects of the opto-magnetic phenomenon, allowing the heating effects of the laser pulse to be included.
Macrospin models; large scale simulations and device design rely on mesoscopic and continuum approaches based on macrospin models. Within FemtoSpin significant progress has been made in the development of macrospin models capable of simulating magnetic behaviour during the laser pulse. These models rely on input information from the atomistic approach to complete the multiscale formalism.
Model validation. The interaction between theoretical and experimental groups has been exemplary and has led to important model development and feedback to experiments.
Outputs
1. Calculations of specific materials design parameters enabling a Dutch patent (2008039). Patent process continuing in Europe (EP2795622 (A2)) and the United States (US2014368303).
2. Atomistic code (Vampire) on public release. Very good take-up by academia.
3. Preparing advanced optical and heat-assisted magnetic recording model (MARS) for public release.
Other Outputs
4. Publications; 70 papers in high impact journals including Nature journals (7) and Physical Review Letters (2) and Scientific Reports (3).
5. 68 invited papers at International conferences
6. Organisation of a summer school in Nijmegen
7. Initiation of the Ultrafast Magnetism Conference (Rasing, Chantrell with Bigot and Huebner; first edition in Strasbourg in 2013 and second in Nijmegen in 2015)
FemtoSpin has made a large impact in terms of generating the understanding of optomagnetic processes. The model development at all lengthscales has led to the production of a multiscale model chain taking magnetic parameters from ab-initio calculations into atomistic models which then provide parameterised information for macroscopic calculations. This process leads to macroscopic models with a strong physical basis for use in materials and device design. At the atomistic level we have developed the first approach taking into account the distinction between internal moments in Gd metal and studied the effects on the ultrafast dynamics. Atomistic model calculations also demonstrated the origin of the thermally assisted magnetisation reversal in the excitation of specific magnetic spin waves which transfer angular momentum between the transition metal and rare-earth sublattices leading to a transient ferromagnetic-like state which initiates the magnetisation reversal. This led to the prediction of a set of design rules for TIMS and the prediction of TIMS in synthetic ferrimagnets.
Scientific highlights
• Development of an ab-initio code for the calculation of the opto-magnetic field (i.e. the magnetization induced by circularly polarized laser light), on the basis of the derived quantum theory for the opto-magnetic field.
• A theoretical framework has been derived for demagnetization due to transfer of the spin of hot (laser-excited) electrons to the phonon system and the resulting demagnetization rates were ab-initio computed for 3d ferromagnets.
• Ultrafast demagnetization due to spin transport has been investigated and was shown to give rise to emission of THz radiation
• Understanding the TIMS phenomenon and its prediction in structured media
• Atomistic/ab-initio model of Gd – beyond the fixed spin model and successful validation by comparison with experiments.
• Studies of differential spin dynamics on FeNi. Full multi-scale modeling of the material and comparison with experiment.
Multiscaling and collaborative code development
• ab-initio determination of magnetic properties and parameterization of atomistic spin Hamiltonians (Budapest, Uppsala, Konstanz, York); automatic generation of spin model parameters for the Vampire atomistic code is almost complete.
• Macrospin simulations and atomistic testing/ parameterization (ICMM, Konstanz, York). This collaboration has produced a suite of models optimized for continuous and granular media. This collaboration has also developed a ferrimagnetic LLB equation for macrospin simulation.
• (ICMM, RU, York); atomistic and macrospin approaches have been combined to produce understanding of the dynamic behavior of ferrimagnetic materials during the thermally induced magnetization switching process.
Femtospin code development: public code release
– York atomistic code (Visual Atomistic Massively Parallel IntegRation Engine; VAMPIRE). On public release, Details available from vampire.york.ac.uk. Described in invited topical review; R. F. L. Evans, et. al., J. Phys.: Condens. Matter, 26, 103202 (2014) (23pp) (selected as one of the highlights of 2014 in J. Phys.: Condens. Matter). Code in trial use in industry
– MAgnetic Recording Simulator; MARS. Developed for advanced simulations of all-optical recording and HAMR in collaboration with Seagate/WD.
Future industrial prospects
Although technical difficulties remain to be overcome, Heat Assisted Magnetic Recording (HAMR) is closing in on providing the next generation of ultrahigh density recording systems. In May 2014 Seagate announced a 1.4Tbit/in2 areal density demonstration (the first to exceed conventional recording demonstrations) having previously shown 1000 hours of continuous write (the benchmark requirement). However, HAMR densities will be limited by the available write field (around 1Tesla) using inductive technology, due to the requirement of avoiding errors due to thermally induced back switching. Due to the physical and technical understanding within the FemtoSpin project, all-optical recording must be considered a realistic candidate for progress beyond HAMR. Here it must be noted that all candidate technologies face similar problems of writing and stability at extreme densities, and the large effective fields involved in all-optical technology could give it a strong advantage. Equally important could be the removal of inductive technology from the writing process in magnetic recording, leading to very significant design and process simplifications with important implications for cost reductions and reduced environmental impacts; that latter also enhanced by significantly reduced energy cost per bit in the write process. This represents an important potential advance for European industrial potential, supporting the major production centre of Seagate in Northern Ireland which produces around 25% of the world-wide total output (around 1 billion p.a.) of recording heads; an important European industrial resource.
Project Results:
3.1 Core of the report for the period: Project objectives, work progress and achievements, project management
Since the start of the project in 2012, the consortium has made great strives forward in the understanding of magnetization dynamics by developing high performance computing code capable of simulating complex materials. The array of skills within the consortium at the electronic, atomic and mesoscopic level, combined with advanced experimental techniques have paved the way in the first 18 months to develop multiscale models. During this period we also developed and validated a set of experimental techniques and began the process of testing and validating the theoretical and computational approaches.
The second phase of the project was aimed at further development of the models and a detailed comparison between theory and experiment. We made significant advances in the understanding of ultrafast magnetisation processes and released validated code into the public domain; the same code is also under test in industry. We determined design parameters for materials supporting ultrafast opto-magnetic phenomena and investigated candidate microstructures having significant potential for ultrafast field-free magnetic recording.
3.2.1 Project objectives for the period
• Obtain fundamental knowledge of dynamic processes on the fs timescale; this requires the development of new approaches to treat non-equilibrium electron dynamics, utilizing Density Functional Theory and applying these to understand the fundamental mechanisms underlying ultrafast spin dynamics.
• Advanced atomistic models; this includes spin models with equations of motion beyond Langevin dynamics; new approaches to induced spins and transport; integration of thermodynamic and quantum approaches
• Mesoscopic model development; this requires mesoscopic modelling using a generalised Landau-Lifshitz-Bloch (LLB) Equation; formulation for ferrimagnets and determination of LLB parameters from SDFT calculations and atomistic models.
• Multiscale calculations and link to experiments; verification of models against experiment; feedback from experiments to model development; material studies; large-scale calculations and device simulations.
• Detailed materials studies; candidate materials with especially promising properties on the femtosecond timescale will be investigated. This will encompass single phase materials and alloys in addition to novel structured materials with engineered properties.
3.2.2 Work progress and achievements during the period
Work Package 1: Femtosecond and ab-initio theory
Summary
The workpackage has been successfully completed and all deliverables have been submitted. All objectives as given in the DOW have been met. A delay of some tasks of partner P6 (UU) occurred due to recruitment difficulties in period I. Involving more manpower in period II counteracted this delay.
Highlights
• Development of an ab-initio code for the calculation of the opto-magnetic field (i.e. the magnetization induced by circularly polarized laser light), on the basis of the derived quantum theory for the opto-magnetic field.
• A theoretical framework has been derived for demagnetization due to transfer of the spin of hot (laser-excited) electrons to the phonon system and the resulting demagnetization rates were ab-initio computed for 3d ferromagnets.
• Ultrafast demagnetization due to spin transport has been investigated and was shown to give rise to emission of THz radiation (Kampfrath et al., Nature Nanotech. 8 (2013) 256–260).
• A theoretical investigation of optical modulation of the spin-spin exchange interaction together with measurements on an iron oxide will appear in Nature Communications.
Description of WP activities and results
The focus of WP1 is to develop analytical and ab-initio theory, aiming to obtain fundamental knowledge of dynamic processes on the femtosecond timescale. The description of such fast processes requires the development of new approaches to treat the occurring non-equilibrium electron dynamics as well as ab-initio implementation and modelling.
The modelling in WP1 is pursued along the following main lines: theory development for the description of electron and spin-dynamics on very short time scales (attoseconds to femtoseconds), theoretical investigations of the influence of energy and spin transfer channels in ultrafast demagnetization, development of new spin Hamiltonians for calculation of spin-dynamics (connected with ab-initio calculation of the required parameters), and lastly development of theory for spin-dynamics in the multi-orbital Hubbard model.
The work done in WP1 connects in a multi-scaling approach to that in WP2 and WP3 by providing ab-initio calculated parameters as input for simulations as well as by the development of new spin-Hamiltonians for simulations of specific materials (e.g. GdFeCo ferrimagnets, magnetically-hard FePt alloys). Also, tests of the developed models are provided through comparison (feed-back) with measurements in WP4.
Related to Task 1.1. Theory development for ultrafast, intensive light-matter interactions (partner P6, with P1 and P7).
To treat dynamical processes on ultrashort time scales (typically femtoseconds) theoretical underpinning and theory development is required. The underpinning has been provided in period I by the development of a theoretical framework capable of describing the interaction of the materials electrons with intensive, ultrashort radiation pulses (deliverable D1.1). The developed theory, which is based on the time evolution of the electron density matrix using the Liouville-Von Neumann equation, has been employed to derive a quantum theory for magnetization induced by a circularly polarized light pulse (the inverse Faraday effect).
It has been proposed by the Strasbourg group (Bigot and collaborators) that ultra-relativistic spin-photon interaction could contribute to an ultrafast laser-induced demagnetization. To examine the influence of such relativistic spin-photon interactions we have developed theory for such processes and performed ab-initio calculations of their influence on the magneto-optical response of Ni. We have derived an exact formulation of the ultra-relativistic terms on the basis of the Foldy-Wouthuysen transformation to the Dirac-Kohn-Sham Hamiltonian, and have treated the additional appearing relativistic terms within a response theory formulation. Performing an ab-initio calculation of the influence of relativistic light-induced spin-flip transitions on the magneto-optics, we find that these can give only a very small contribution (≤ 0.1%) to the laser-induced magnetization change in Ni (R. Mondal, M. Berritta, K. Carva, and P.M. Oppeneer, Phys. Rev. B 91 (2015) 174415).
Currently there does not exist a single model that incorporates all interaction channels between all quasi-particles within a non-equilibrium formulation. All theory development requires therefore validation against measurements. Within Task 1.1 a first comparison between theory and measurements of the spin (S) to orbital (L) moment ratio in a polycrystalline Fe film were undertaken. This was done with the electron magnetic circular dichroism (EMCD) which permits measurements with nanometer scale resolution. The measured ratio is in good agreement with the result from ab-initio calculations (S. Muto et al., Nat. Commun. 5 (2014) 3138).
Further comparisons with experiments were performed for the ultrafast non-equilibrium spin-dynamics of spins in different orbitals (4f, 5d) in Gd metal, and for the ultrafast demagnetization in Fe/Au and Fe/Ru films (see D1.3); these investigations are mentioned further below.
Related to Task 1.2. Theory for the inverse Faraday effect and origin of opto-magnetic field (partner P6).
In a material that is excited by an intense pulse of circularly polarized light a strong opto-magnetic field can be created through the inverse Faraday effect. This opto-magnetic field could provide a sizable contribution to generating an ultrafast magnetization reversal. A quantum theory of the light-induced magnetic polarization was developed in period I (D1.4). In period II we have coded the derived expressions and implemented these in an ab-initio electronic structure code on the basis of the density functional theory. Investigations of selected materials have been performed. Specifically, we have computed the light-imparted magnetization in the ferromagnets Fe, Co, Ni, in the hard-magnetic recording material FePt, and nonmagnetic metals such as Au. We have analysed the contributions to the opto-magnetic field as well as its dependence on the photon energy. In particular, we find large effects for materials with heavy elements (e.g. Au, Pt) (M. Berritta, R. Mondal, K. Carva, A. Aperis, P. Maldonado, and P.M. Oppeneer, to be published).
Related to Task 1.3. Energy and spin transfer channels in laser-induced demagnetization (partner P6, with P5, P7, P1).
The phenomenon of ultrafast all-optical demagnetization has been attributed previously to several different mechanisms, such as, Elliott-Yafet electron-phonon spin-flip scattering or ultrafast spin-transfer caused by laser-excited hot electrons. In this task we develop theory for these processes and perform ab-initio calculations to quantify the amount of demagnetization that can be achieved.
In the Elliott-Yafet model the spin of the electrons is transferred ultrafast to the lattice by electron-phonon spin-flip scatterings. We have developed a generalized, relativistic Eliashberg theory to describe this process and carried out ab-initio calculations to quantify the demagnetization induced by electron-phonon interaction in the transition-metal ferromagnets bcc Fe, fcc Co and fcc Ni. The developed formalism allows treating laser-created thermalized as well as non-equilibrium, non-thermal hot electron distributions. We found that in particular non-thermal distributions lead to a stronger demagnetization rate than hot, thermalized distributions, yet their demagnetizing effect is not enough to explain the experimentally observed demagnetization occurring within 300 fs. This implies that other mechanisms need to be considered (K. Carva, M. Battiato, D. Legut, and P.M. Oppeneer, Phys. Rev. B 87 (2013) 184425).
Another mechanism of ultrafast demagnetization could be direct, lateral transfer of spin-polarized laser-excited electrons. We have developed semi-classical transport theory to treat the energetics of such non-equilibrium, hot electrons. The developed theory can treat the presence of several different layers in the laser-irradiated material. The derived spin-dependent transport equation is solved numerically and the obtained results can be compared to experiments. The required input is ab-initio calculated hot electron lifetimes and velocities. For a ferromagnetic/non-magnetic metallic junction where the ferromagnetic layer is laser-excited, the computed spin dynamics shows that injection of a superdiffusive spin current in the non-magnetic layer is achieved. The injected spin current leads to a fast demagnetization of the ferromagnetic polarization in the ferromagnet. We have compared theoretical predictions of laser-induced demagnetization of Ni and Au/Ni films with measurements performed at the Helmholtz-Zentrum, Berlin (P7). Element-specific x-ray magnetic circular dichroism (XMCD) measurements reveal a clear time-delay in the demagnetization of the Au/Ni film as compared to the bare Ni film. This can be explained by the time needed for the hot electrons to traverse the Au film (30 nm) and reach the Ni film. A sizeable demagnetization of the Ni in the Au/Ni system is predicted to be caused by laser-excited hot electrons coming from the Au layer into the Ni film (A. Eschenlohr, M. Battiato, P. Maldonado, N. Pontius, T. Kachel, K. Holldack, R. Mitzner, A. Föhlisch, P.M. Oppeneer, and C. Stamm, Nat. Mater. 12 (2013) 322).
The superdiffusive spin transport model has also been used to study the terahertz radiation emission from Fe/Au and Fe/Ru heterostructures. A laser excitation of the Fe layer is used to create a spin current into the non-magnetic layer that has either low (Ru) or high (Au) electron mobility. The resulting transient spin current is detected by means of an ultrafast, contactless ampere meter based on the inverse spin Hall effect, which converts the spin flow into a terahertz electromagnetic pulse. A good agreement was achieved between theoretical predictions of the spin currents and the measured charge current (resulting from the inverse spin Hall effect). The spin current pulses and the resulting terahertz transients can be modified by tailoring the magnetic heterostructures (T. Kampfrath et al., Nat. Nanotech. 8 (2013) 256).
Related to Task 1.4. Theory for ab-initio parametrization of spin Hamiltonians.
Spin Cluster Expansion (partners P5 and P1): to obtain realistic spin-model parameters we applied the Relativistic Torque Method (RTM) and the Spin Cluster Expansion (SCE) technique to various exchange coupled composite layered systems, such as Fe/9(FePt)/Fe and MgO/Fe/MgO. We have combined the SCE technique with the Relativistic Disordered Local Moment (RDLM) scheme to compute site-resolved magnetic properties. We investigated the layer dependent effective exchange parameters and magnetic anisotropies through the systems, and found that the RTM and the SCE give very similar results for the layer resolved quantities; however, for Fe/FePt/Fe, due to the vanishing Pt magnetic moments in the paramagnetic phase, the SCE leads to reduced exchange couplings in the FePt slab. (C.J. Aas et al., Phys. Rev. B 88 (2013) 174409). For MgO/Fe/MgO, our calculations showed strong anti-ferromagnetic in-plane Fe-Fe exchange interactions near the MgO/Fe interface, but dominating ferromagnetic in-plane Fe-Fe interactions in the central Fe layers. A strong layer dependence of the on-site magnetic anisotropies was also computed, with a change of anisotropy energy from out-of-plane near the interface to in-plane in the central Fe layers. (R. Cuadrado and R. Chantrell, Phys. Rev. B 89 (2014) 94407).
The RDLM scheme combined with the RTM provides a technique that enables to calculate the spin-model parameters as a function of temperature, from the ferromagnetic to the paramagnetic state. Applications to Fe and FePt show non-monotonous temperature dependence for the nearest-neighbour exchange interactions, whereas more distant interactions can even undergo a transition from ferromagnetic to antiferromagnetic character. (A. Deák, Phys. Rev. B 89 (2014) 224401; A. Deák, PhD dissertation, BME 2015).
Ab-initio LDA+U calculations have furthermore been performed for ferrimagnetic 4f-transition metal compounds, such as DyCo5 and GdFe2, TbFe2, and Gd/Fe multilayers, for spin dynamics calculations in WP2 and WP3. (L. Oroszlány et al., arXiv:1503.08940 accepted to Phys. Rev. Lett. (2015); publication on DyCo5 is under preparation).
The influence of temperature-dependent exchange interactions has been computed for bulk Fe. The computed exchange parameters have been used in atomistic spin-dynamics simulations. The influence of the temperature-dependence is currently being investigated; its influence on the magnetization curve and Curie temperature is small. Systematic calculations of the exchange interactions up several thousands of K in both the spin- and electron temperatures have been performed. These interactions can then be directly used in atomistic simulations of ultrafast spin-dynamics induced by laser pulses. (A. Deák, PhD dissertation, BME 2015; D. Hinzke et al., to be published)
Orbital-resolved spin Hamiltonian (partners P3 and P6):
In an effort to improve the description of the ultrafast spin-dynamics in GdFeCo alloys, which contain the rare-earth element Gd, a novel spin model has been developed which treats separately the spin-dynamics of the 5d and 4f electron spins on Gd. As the 4f electrons are localized the 4f spin moment interacts only “on-site" with the 5d spin moment. Employing ab-initio calculated intra-atomic exchange in atomistic simulations provided a clear explanation of the transient ferromagnetic state and revealed conditions under which optical switching to a spin-reversed state could be achieved. The model allows the transfer of energy from the 5d to 4f electrons via the intra-atomic exchange.
This spin model - with all its parameters derived from first principles – has recently been applied to elemental Gd. It forecasts different dynamics for the spin moments of the d- and f-electrons on a time scale of several picoseconds. Such disparate dynamics of 4f and 5d spins has been confirmed by recent measurements of the group of M. Weinelt in Berlin. A joint manuscript was recently accepted for publication in Nature Communications.
Related to Task 1.5. Spin dynamics within the multi-band Hubbard model (partner P2, with P4).
We have developed a low-energy theory for the magnetic interactions occurring between electrons in the multi-band Hubbard model (MBHM) under non-equilibrium conditions, which are determined by an external time-dependent electric field, which simulates laser-induced spin dynamics [A. Secchi, S. Brener, A. I. Lichtenstein and M. I. Katsnelson, Ann. Phys. 333, 221-271 (2013)]. Using advanced many-body techniques (a path integral formulation of the Kadanoff-Baym-Schwinger-Keldysh non-equilibrium technique, combined with local time-dependent rotations of the spin quantization axes of the electrons), we have mapped the MBHM to an effective model of spin vectors coupled by exchange interaction and an additional effective interaction which we have named "twist exchange". Twist-exchange interaction depends on the vector product of the interacting spins, therefore being in competition with exchange interaction (the former favouring perpendicular alignment, the latter favouring parallel/anti-parallel alignment). Although the form is similar, it is not a Dzyaloshinskii-Moriya interaction, since it arises also when relativistic interactions (such as spin-orbit coupling) are neglected.
Our procedure gives the formulas needed to compute the coefficients of the spin-spin interaction terms from electronic non-equilibrium Green’s functions and self-energies. This is the essential distinctive trait of our theory, its power lying in the fact that we can rigorously map the dynamics of the electronic system to that of the spins: in other words, we can obtain the magnetic non-equilibrium properties from the electronic non-equilibrium properties of a given material. The needed electronic Green’s functions can be computed with the methods of Dynamical Mean-Field Theory (DMFT).
Since our theory fully includes electronic dynamics, it rigorously accounts for non-Heisenberg effects, i.e. variations of the lengths of the atomic magnetic moments, which are not captured by Landau-Lifshitz equations. It also accounts for the equilibrium temperature characterizing the initial state, and it provides the parameters of the magnetic interactions both in equilibrium and out of equilibrium. We have also obtained formulas for quantum noise. Importantly, the developed formalism allows to consider an external field varying on an arbitrary time scale, being therefore suitable for ultrafast magnetism, fully including non-adiabatic effects (which are accounted for by the electronic Green’s functions).
We have extended the theory of magnetic interactions within the MBHM to include orbital and relativistic effects, namely spin-orbit coupling, magnetic anisotropy, Zeeman coupling to external magnetic fields, which required an extension of the model to a “generalized” MBHM. Our work (A. Secchi, A. I. Lichtenstein and M. I. Katsnelson, Ann. Phys. 360, 61-97 (2015)) provides formulas for the complete exchange tensor in the relativistic regime and/or in the presence of spatial symmetry-breaking effects (such as interfaces), including Dzyaloshinskii-Moriya (anti-symmetric) exchange, the anisotropic components of exchange, as well as the effective local anisotropy parameters. We have fully included the orbital degrees of freedom of the electrons, without assuming quenching of the orbital moments; our theory allows (for the first time within the Green’s function formalism) to distinguish and compute separately the contributions to the whole exchange tensor arising from the interplay of spin-spin, spin-orbital, and orbital-orbital degrees of freedom. We have also provided the technical prescriptions for the implementation of these formulas within DMFT (A. Secchi, A. I. Lichtenstein and M. I. Katsnelson, arXiv 1506.06209 accepted for publication in J. Magn. Magn. Mater. (2015)).
We have studied the optical manipulation of the spin-spin exchange interaction in iron oxides. In this work we have showed that optical excitations indeed modify the iron-iron (super-) exchange interaction in iron oxides, which is mediated by electronic transfer via intermediate oxygen atoms. A joint publication with our experimental colleagues at the Radboud University and our collaborators in Hamburg (J. H. Mentink and M. Eckstein) is accepted for publication in Nature Communications (the preprint is available at arXiv 1412.7094).
Work Package 2: Atomistic Spin Models
Summary
This WP was on-track and met all objectives within the DOW. The resources have been used as planned.
Highlights
• Atomistic/ab-initio model of Gd – beyond the fixed spin model and successful validation by comparison with experiments. A manuscript was accepted for publication in Nature Communication.
• Studies of differential spin dynamics on FeNi. Full multi-scale modelling of the material and significant contribution to comparison with experiment. A manuscript was accepted to Phys. Rev. B.
Description of WP activities and results
The aim of WP2 was the development of new spin models for complex materials and microscopic equations of motion beyond the current state of the art, to link these spin models with ab-initio calculation in WP1 and with mesoscopic models in WP3 and to verify the approaches by comparison to experiments in WP4. In the following we summarize our achievements of the last 18 months split into tasks:
Task 2.1. Spinmodels for complex materials
In this task the focus was on spinmodels for magnets with more than one sublattice, like, e.g. the ferromagnet FeNi and the ferrimagnet FeCoGd. An important part of our multi-scale modelling procedure is to link spin model calculations with atomistic resolution - and hence large numerical effort - to mesoscopic models. The latter rest either a continuum theory or on macro-spin models with effective equations of motions that have less degrees of freedom and are capable of describing realistic sample sizes. In that context the central result that members of the consortium have obtained is the Landau-Lifshitz-Bloch (LLB) equation in a new version for complex magnetic materials with two sub-lattices. This equation has to be verified by comparison with spin model simulations. Furthermore, thermodynamic equilibrium input functions for the LLB approach have to be calculated in terms of spin model simulations.
Our work on the two-sublattice system (FeNi) used already a full multi-scale approach deriving first a spin model from ab-initio methods and then, in a second step, describing the spin-model with two macro-spins only following the LLB equation of motion. Although FeNi does not exhibit heat-driven magnetization reversal, it nonetheless exhibits distinct sublattice magnetization dynamics in form of different timescales for demagnetisation of each lattice. Our comparison of spin model and macro-spin dynamics verifies our multi-scale approach, where - in the LLB- approach - the dynamics can be successfully described with two macro-spins only. A joint manuscript on the mult-scale modelling of FeNi from groups in Uppsala, Madrid and Konstanz was recently accepted for publication in Phys. Rev. B.
Simulations of FeGd-ferrimagnetic resonance simulations revealed the complex temperature dependence of the ferrimagnetic resonance modes (ferromagnetic mode and exchange mode) in FeGd, currently the best investigated material for all-optical switching. A direct comparison of spin model simulations with analytical calculations based on the two-macrospin LLB approach shows very good agreement again underpinning the importance of the LLB approach.
This task ended in month 24. In was concluded on-time with Deliverable 2.2 “Macroscopic calculations; comparison with spin model“ which details our work which was summarized above.
Task 2.2. Models beyond fixed spin length
While many magnetic materials can be described with a simple Heisenberg exchange as leading part of the Hamiltonian, in some cases more complex models beyond the assumption of fixed spin length are needed. We extended our collaboration between the Konstanz and Uppsala groups in an effort to develop models beyond fixed spin length by a distinct treatment of different types of electrons and their role for the excitation process. The model separates the 5d and 4f electron spins of the Gd, i.e. the orbital character of the spin is introduced. The model then allows the transfer of energy from the 5d to 4f electrons via the intra-atomic exchange. This spin model - with all its parameters derived from first principles - forecasts different dynamics for the magnetization of d- and f-electron on a time scale of several picoseconds, a result that is well confirmed by recent experiments performed at the Free University in Berlin. A joint manuscript of our groups in Uppsala and Konstanz with the group of M. Weinelt in Berlin was recently accepted for publication in Nature Communications.
In another project for models beyond fixed-spin length we focused on a detailed understanding of the temperature dependence of magnetic material properties. The temperature dependence of macroscopic physical quantities is due to thermal fluctuations of the microscopic degrees of freedom, which --- for magnetic systems --- is the atomic magnetic moments. The Hamiltonian of the system is then parameterized in the form of a spin model. However, the question arises as to how far the parameters of the spin model itself are temperature dependent due to temperature dependent changes of the electronic structure. In collaboration between Budapest and Konstanz we calculated the temperature dependence of the Heisenberg exchange from first-principles in order to investigate the influence of their temperature dependence on magnetic phenomena at finite temperatures. We focus on the understanding of the interplay between these two types of temperature dependence --- coming from thermal fluctuations of the spin degrees of freedom on the one hand and changes in the electronic structure leading to temperature dependent spin model parameters on the other. As a test system Fe was modelled in the bcc phase. Finite temperature spin-fluctuations are taken into account using the Relativistic Disordered Local Moment scheme as implemented in the Korringa-Kohn-Rostoker method (see WP1). From these calculations the electronic structure is obtained as a function of the magnetization from the ferromagnetic state down to the paramagnetic state. For a given value of the magnetization, the exchange parameters are evaluated by using the relativistic torque method in as much the statistical average of the exchange coupling is performed in terms of the Coherent Potential Approximation. Then we use Langevin dynamics simulations and compare simulations where we either assume constant ground state spin model parameters (exchange interactions and atomic magnetic moments) or m-dependent spin model parameters where we use a self- consistent scheme for the calculation of the temperature dependence of m while taking into account the m-dependent spin model parameters. The equilibrium magnetization curve is clearly affected by the temperature dependence of the exchange and we continued our investigation towards the dynamic behavior under the assumption of time-varying spin model parameters. Our temperature dependent parameters went into the FEMTOSPIN database and a final publication is in preparations.
Upon femtosecond laser excitation of a metallic trilayer or bilayer system fast spin transport can occur from the excited layer to the adjacent layers, which leads to a nonthermal magnetisation redistribution in the layers. Subsequently a fast longitudinal spin evolution occurs, attempting to bring the material back to its spin equilibrium; the appearing spin evolution cannot be captured with fixed-spin length models. Therefore a theoretical formulation on the basis of the Landau-Lifshitz-Bar'yakhtar equation was developed as well. Effectively the longitudinal spin evolution is concurrent with a strong spin current owing between the layers.
This task was concluded in month 24, details are given in Deliverable 2.3 “Models beyond fixed spin length; underlying theory“ which was submitted in month 24 and Deliverable 2.4 “Advanced models beyond fixed spin length“ submitted in month 36.
Task 2.3. Beyond Langevin Dynamics
In most of our atomistic and micromagnetic simulations use a Langevin dynamics approach, where stochastic fields are introduced in the Landau-Lifshitz-Gilbert equation of motion with a strength calculated from near-equilibrium properties. The damping term is rather phenomenological and is a result of the averaging over instantaneous bath degrees of freedom. This approach may fail for the modelling of ultra fast dynamics where the phonon, electron and spin dynamics occurs at the same timescale. To go beyond the standard Langevin dynamics we explore two approaches:
First, in the classical approach we simulate the lattice degrees of freedom explicitly as energy and angular momentum reservoir for the spin system. To follow the flow of energy as well as angular momentum we derive and use coupled equations of motion for both subsystems on an atomistic level. These equations avoid the phenomenological Landau-Lishitz (or Gilbert) damping paving the way for a new type of spin-molecular dynamics simulations. As a first application the dynamics of the Einstein-deHaas-Effect was investigated, where the angular momentum flow from spin- into the lattice degrees of freedom was calculated microscopically.
Second, a quasi-classical approach where we propose a method to study the finite-temperature behaviour of small magnetic clusters based on solving the stochastic Landau-Lifshitz-Gilbert equations, where the effective magnetic field is calculated directly during the solution of the dynamical equations from first principles instead of relying on an effective spin Hamiltonian. Different numerical solvers for the dynamical equation were investigated. As an example of this new type of dynamics we performed detailed investigations for a monatomic chain of ten Co atoms on top of Au(001) surface.
This task was concluded in month 33. Details are given in Deliverable 2.5 “Beyond Langevin Dynamics”, which was submitted in month 24
Task 2.4. Heat-bath models of ultrafast processes
In the most common approaches for the study of magnetization dynamics the heat bath is added phenomenologically as damping term in the equation of motion. Physically the heat-bath for the spin system is provided by the electron system and the lattice degrees of freedom. In this task an improved model of the coupled spin and lattice dynamics has been developed to explore the effect of the lattice acting as a heat bath. An example system of bcc Fe was modelled and was tested for the energy conservation and the phonon dispersion. With thermal noise and damping incorporated on both the spin and lattice system the equilibrium magnetisation and susceptibility showed a Curie temperature of 1050 K and the calculated magnon dispersion showed typical ferromagnetic bands. The range dependent exchange interaction does not provide a suitable coupling due to the symmetry of the equations of motion and so a specific coupling term is also included based on the spin-orbit coupling. By including this term with out thermal noise for the spin system magnon modes are excited at the edge of the Brillouin zone and relax into longer wavelength modes.
This task was concluded in month 36. Details are given in Deliverable 2.6 “Heat-bath models of ultrafast processes”.
Work Package 3: Mesoscopic model development
Summary
The work within this WP was delivered on-time and met most of objectives within the DOW. Each partner as planned has used the resources outlined in the consortium agreement. The goal of this work package was to provide a platform for incorporating atomistic scale detail and providing a means for comparison with experiment. This has been broadly achieved resulting in a number of cross WP publications.
Highlight
• Creation of large-scale micromagnetic framework and programs (MARS and VAMPIRE) for modelling of high-temperature ultra fast magnetisation dynamics for ferro and ferromagnetic continuous and granular materials and multilayers.
• Articles published in Nature Scientific Reports and Physical Review Letters.
Description of WP activities and results
The aim of WP3 was the development of new types of micromagnetics, suitable for modeling of ultra-fast magnetization dynamics at large scale. For this purpose we further developed the theoretical framework based on the Landau-Lifshitz-Bloch (LLB) equation for ferro and ferrimagnetic materials. The WP3 completes the multi-scale modelling scheme since it uses the information from WP1 and WP2, it also connects with WP4 through the direct comparison with the experimental data.
Our achievements of the last 18 months split into tasks:
Task 3.1. Mesoscopic multi-scale models for ferromagnetic materials
In this task multi-scale models for one-component materials such as Ni, Co, FePt and several bilayers such as Gd/Fe have been created. The diluted magnetic semiconductors were excluded from consideration by the decision of the consortium. To incorporate miscroscopic scattering mechanism, the quantum LLB equation was derived (published recently in Phys.Rev.B) incorporating phonon and electron scattering The coloured noise was also incorporated into the LLB equation. The LLB equation has been used to model the ultra-fast dynamics (including the domain wall and bubbles) in FePt and vortices and domain walls in FeNi and multiferroics (recently accepted at Physical Review Letters).
Task 3.2. Development of novel models for ferrimagnets and antiferromagnets
In this task we derived a novel LLB equation for two-component systems in classical and quantum cases. The models were applied for RE-TM alloys such as GdFeCo, TbFe and CoFe. The ab-initio information from Budapest group was incorporated for GdFe, TbFe and FeRh large-scale modelling. The use of the ferrimagnetic LLB equation has allowed us to achieve theoretical understanding of many important characteristics of the ultra-fast dynamics in two-component systems. Namely, we predicted that (i) the switching in small dots becomes precessional (ii) the switching is defined by different demagnetisation speeds of materials, consequently in highly coupled materials such as TbFe Laves phase, deterministic switching does not take place (iii) at high temperatures the demagnetisation in Gd may become faster than that of Fe in GdFeCo, and the polarity of the transient-like state may change (iv) while Fe experiences a slowing critical down at high temperatures in GdFeCo, Gd – does not, this explains that high temperatures are not good for switching (v) the dependence on RE concentration is highly non-trivial and one can find different situations: for small intersublattice coupling, the switching is more effective when Gd concentration is larger and for large coupling the situation is the opposite. All this findings have been published in series of articles in Physical Review B between several groups (and workpackages) in the consortium.
The large-scale modelling has been also applied for modelling of ultra-fast dynamics in Gd/Fe multilayers achieving understanding of several experimental situations (collaboration between Madrid, Nijmegen and York groups), particularly a non-trivial occurrence of precession when going through the magnetisation compensation point.
Task 3.3 Development of models for granular and polycrystalline materials
The models of granular and polycrystalline materials based on the Voronoi construction were developed in the first part of the project by Madrid and York groups. In the second part, the work involved the incorporation of the models into the software MARS and VAMPIRE
Task 3.4 Development of the optimized code for advanced material and device design
Several in-house codes for LLB micromagnetics have been created in York, Konstanz and Madrid groups. These were developed in collaboration but optimised for different purposes. The optimised MPI parallel code (MARS), working on GPU, which will be suitable for public release has been created in York. The database for several materials was created and maintained in the Femtospin webpage with the input from all theoretical partners. Without these codes development steps the work carried out in this WP would not have been possible. Whilst the codes were developed as part of the FemtoSpin project for ultrafast magnetisation dynamics, the codes will have a lasting impact for the members of the consortium going forward and are already finding appropriate uses for research beyond ultrafast dynamics (e.g. vortex core dynamics in composite multiferroics).
Task 3.5 Micromagnetic and multiscale modelling of heat-assisted all-optical magnetic recording.
Both York and Madrid groups were using the large-scale models to investigate the possibility of ultra-fast all-optical magnetic recording. Particularly, we have investigated the magnitude and the duration of the field coming from the inverse Faraday effect to explain recent experimental data and to make predictions in FePt. Large-scale micromagnetic program was used for this purpose and the laser pulse intensity was varied. We have found that the inverse Faraday field either of the magnitude above 10T or duration more than several picoseconds is necessary for all-optical recording. The switching speed may be fast (below 0.5 ps) depending on the magnitude of the field and the temperature, defined by the laser pulse intensity (to be published).
Work Package 4: Experiments and link to multiscale calculations
Summary
This WP has met all objectives within the DOW. The materials preparation aspects were initially delayed but has eventually delivered the necessary samples for the optical and X-ray experiments. The resources have been used as planned.
Highlights:
• Measurements of differential demagnetisation in NiFe and comparison with theoretical predictions.
• Development of element specific optical microscopy and measurements on TbFeCo
• Demonstration of angular momentum transport between Gd and Fe sublattices with fs time and nm spatial resolution, using fs-Xray scattering
• Demonstration of AOS in Gd/Fe multilayers, as predicted by the model of AOS in antiferromagnetically coupled multilayers.
Description of WP activities and results
The aim of WP4 was to develop and apply novel experimental tools on validated nanostructured test samples to obtain fundamental input parameters for models and to test the output of the mesoscopic models with time resolved optical, THz and X-ray experiments.
Task 4.1: Fs-XMCD
For the fs-XMCD experiments we made use of two facilities: the fs-slicing facility at BESSY-II at the Helmholtz-Zentrum Berlin and the Linac Coherent Light Source (LCLS) at SLAC, Stanford. We have demonstrated that the element specific demagnetization proportional to the magnetic moment (I. Radu et al, Nature 472, 205 (2011)) is a very general phenomenon that appears in both anti-ferromagnetically and ferromagnetically coupled sublattices (I. Radu et al, SPIN, 2015). We have determined the demagnetization times for a large number of elements, both in their pure form and in various alloys. These results support the recent theoretical models of ultrafast all-optical demagnetization and switching.
The experiments at the LCLS have led to the surprising results that the FeGdCo samples that have been shown all-optical switching are inhomogeneous on the nanoscale. The time and q-dependent XMCD data demonstrate that there is angular momentum exchange between these areas, as evidenced by the time delay in the dynamics at larger q values (C. Graves et al, Nature Mat 12, 293-298(2013). These unique results directly support the theoretical models of intersublattice exchange.
Several Gd/Fe and Gd/FeCo multilayer samples grown by the Belfast group have been measured using element-specific XMCD technique as a function of temperature. All the investigated samples Ta(5nm)/[Gd(0.5nm)/Fe90Co10(2nm)]8/Ta(5nm) Ta(5nm)/[Gd(3nm)/Fe90Co10(2nm)]4/Ta(5nm) and Ta(5nm)/[Gd(1nm)/Fe(1nm)]10/Ta(5nm) are showing an in-plane anisotropy. We have observed a magnetization compensation temperature of ~250K for [Gd(3nm)/Fe90Co10(2nm)]4 sample, while for [Gd(1nm)/Fe(1nm)]10 and [Gd(0.5nm)/Fe90Co10(2nm)]8 the compensation temperature were below 10K or above Tc, respectively. The Task was successfully finished with deliverable D4.1.2 Fs X-ray spectroscopy
Task 4.2: fs X-ray microscopy
Several experiments with holographic imaging have been attempted at the LCLS, using a FeGd sample on specifically designed membranes made of SiN. Single shot switching has been observed, with smallest structures in the tens of nm regime, showing the potential of all-optical switching on the nanoscale. We have also attempted to use plasmonic antennas to focus the optical laser beam and achieve controlled switching at nanometer length scales. Unfortunately these experiments were not very successful, presumably due to the quality of the antennas. The Task was finished with deliverable D4.4: Fs Xray microscopy.
Task 4.3: fs optical spectroscopy
We have developed a new femtosecond pump-probe set-up that allows to probe the spin dynamics in magnetic thin films and heterostructures in fields up to 7Tesla and at temperatures down to 4K. With this system we have probed the d–f exchange interaction in EuTe using pump-probe experiments and the spin interactions in ferromagnetic (In,Mn)As (R. R. Subkhangulov,et al, Laser-induced spin dynamics in ferromagnetic (In,Mn)As at magnetic fields up to 7 T; Phys.Rev. B 89, 060402(R) (2014); R. R. Subkhangulov, et al, All-optical manipulation and probing of the d–f exchange interaction in EuTe, Scientific Reports 2014).
We have demonstrated element specific probing with visible lasers, using the frequency dependence of their magneto-optical response (A. R. Khorsand, et al, Phys. Rev. Lett. 110, 107205 (2013), showing a similar transient ferromagnetic state as was seen in FeGdCo before using Xrays. In particular, we demonstrated that in FeTb one can study the dynamics of the Tb- and Fe-spins individually, by choosing the wavelength of light above and below 600 nm, respectively, as presented in Fig. 4.3.1(Left). The possibility of using visible laser light also increases significantly the signal-to-noise ratio in the element-specific measurements compared with other techniques. Exploiting this feature, we were able to investigate with extremely high reproducibility and low noise the demagnetization rate as a function of the impinging pump fluence. Surprisingly we found that this rate of demagnetization presents a piecewise behavior, as presented in Fig.4.3.1(Right). A
Fig. 4.3.1. (Left) Ultrafast sublattice magnetization dynamics of TbFe at λFe = 800 nm and λTb = 500 nm, corresponding to dominantly the Fe and Tb sublattices, respectively. A long lasting ferromagnetic state is excited, with a fluence of F = 8 mJ/cm2[4]. (Right) Demagnetization rate as a function of pump laser fluence; a clear super-linear trend is measured for fluences above 4 mJ/cm2.
linear trend, typical for magnetic metals, is followed by an enhanced (super-linear) demagnetization rate. Atomistic models (York) give rise to a similar behaviour but do not as yet completely explain this phenomenon. We have also looked at the details of the Gd-Fe spin interactions in the demagnetization and clarified the role of the intersublattice exchange interaction and the compensation point in this process (A. Mekonnen, et al, Phys. Rev. B 87, 180406 (2013); R. Medapalli, et al, Phys. Rev. B 86 054442 (2012)).
As simulations have shown that AOS should be possible in FePt/Fe exchange coupled multilayers, we have started dynamic studies of highly anisotropic granular FePt films in their L1(0) phase. Experiments were done in a newly developed pump-probe set up at the Nijmegen High Field Magnet Laboratory, allowing the study of the static and dynamic properties of magnetic thin film samples in fields up to 38Tesla. Samples were provided by HGST-Hitachi. The first results have shown large inherent resonance frequencies in the THz regime and a damping parameter of 0.1 (J. Becker, et al, Laser induced spin precession in highly anisotropic granular L1(0) FePt. Appl. Phys. Lett., 104 (2014)).
We have also performed stroboscopic pump-probe measurements on Fe/Gd multilayer samples, both above and below TM (for the description of the samples, see Task4.4). We show that we are able to induce a switching event with a single optical pulse both below and above TM. In particular, all-optical switching is possible up to about TM + 100 K. At higher temperature is not possible anymore to ignite the switching event.
This Task was successfully finished and yielded the deliverables D4.6 - femtosecond optical spectroscopy (heterostructures): determination of the coupling of the dynamics in magnetic heterostructures (AFM/FM); Because of the discovery of TIMS, we did not further pursuit the determination of the dependence of pulse parameters and frequency dependence for the Inverse Faraday Effect, which was part of the original deliverable.
Task 4.4: fs optical microscopy
We have dramatically improved our optical microscopy capabilities. Single shot imaging now allows pump-probe experiments to look at the temporal development of magnetic domains in optically excited thin magnetic films with fs time and one micron spatial resolution. We have also improved the speed and stability of our magneto-optical microscope, by a combination of mechanical and software improvements. The latter allow for automatic control and corrections for drift (Y. Hashimoto, et al, Review of Scientific Instruments, 85(6). 10.1063/1.4880015 (2014). We have also demonstrated that optical interference can greatly enhance the efficiency of all-optical switching (M. Savoini et al. ,Phys. Rev. B 86, 140404, 2012).
In the past 10 years, all-optical switching has been demonstrated in GdFeCo amorphous alloys. With a deepening understanding of the underling mechanism driving the magnetization reversal process, theoretical predictions of other possible system in which the switching could occur have been made. In particular a synthetic ferrimagnetic structure (even rare-earth free) has been proposed within the FemtoSpin consortium. We have investigated the magnetic properties of an intermediate step, where the transition metal and the rare-earth elements are separate in a multilayer stack. Thus we have deposited 4 different samples through sputtering, varying the thickness of the single layers. Figure 4.4.1 shows a schematic of the magnetic layers in the different samples, where n represents the total number of layers and t the thickness of the layers (equal for Gd and Fe, unless otherwise specified). The total thickness of the magnetic sample is kept constant (tTot=20 nm).
We have investigated the magnetic properties of the 4 samples as a function of the temperature, down to liquid nitrogen temperature (T=70 K). Samples A, B, C showed in-plane anisotropy. D instead was out-of-plane magnetized. An increase of the coercivity at lower temperatures is apparent for all the samples, but only for C a clear magnetization compensation temperature is measurable at TM=175 K (sample B might present it at T=0 K). A similar value of TM has been found for sample D (out-of-plane anisotropy). All these sample were designed to have a composition percentage similar to the amorphous alloy Gd25[FexCo(1-x)]75. It is remarkable that by tuning the number of layers, thus the interaction between the elements, we are able to tune both the magnetic anisotropy and the magnetization compensation temperature. Another important point is that the amorphous alloy with the mentioned composition generally shows TM>300 K, double than the one measured for C or D.
Using a single-shot pump-probe imaging technique, a strongly spatially inhomogeneous magnetization reversal process is observed (see Fig. 1) as a function of the local excitation. At certain experimental conditions the excited domain shows a periodic change of the magnetic contrast accompanied by a gradual shrinking of the oscillating part with a linear velocity of the shrinking equal to 30 km/s. This observation, together with a high amplitude magnetization precession makes this magnetization dynamics very different from the one observed in RE-TM amorphous alloys.
Figure 1: Spatially inhomogeneous magnetization reversal process in Gd/FeCo multilayers. Insets show the magneto-optical contrasts after a single ultra-short laser pump illuminates the sample. After a certain delay the magnetization state is probed and the magneto-optical images are obtained. Evolution of the illuminated area cross-section is plotted as a function of time. Spatially inhomogeneous ultrafast magnetization reversal with the magnetization precession is accomplished by a gradual shrinking of the oscillating part. The speed of such a shrinking is indicated as 30 km/s.
The study reveals changes of the effective magnetization precession damping within the laser-illuminated area, where the temperature gradient is suggested to be responsible for this dynamics [3]. The Task was successfully finished with deliverable D4.6.
Task 4.5 Materials and Nanostructuring
The task was to provide materials customised to meet the various requirements of the consortium in pursuit of the project objectives regarding material studies. A number of systems ranging from RETM alloys and multilayers, to complex transition metal based ferrimagnetic structures were developed and fabricated. Materials were sent to P2 and P7 for the study of switching dynamics on the femtosecond scale.
Partners required the materials in most cases to be ferrimagnetic, exhibiting magnetic compensation near to or below room temperature. There was no specific requirement regarding direction of magnetic anisotropy (although a practical media is expected to be perpendicular to the film plane) and some systems exhibited in-plane magnetic anisotropy and others were out-of-plane. Method of preparation was planar magnetron sputtering in ultra high vacuum and substrates were typically silicon or glass wafers. Process temperatures were in the range 300K to 750K. Validation was carried out using Vibrating Sample Magnetometry and Magneto-optical Kerr Effect measurements.
The materials produced fell into three main categories: rare earth transition metal (RETM) materials, synthetic ferrimagnets, and ordered FePt based materials with high anisotropy. RETM materials were mainly alloys and multilayers of Gd and Fe or FeCo, where the compensation temperatures were controllable through the relative concentration of rare earth to transition metal in the films. Synthetic ferrimagnets were transition metal based multilayered systems involving ferromagnetic layers such as Fe, Co and Ni or their alloys, coupled antiferromagnetically through an appropriate spacer layer. Compensation points were achieved through the matching of the magnetic properties of the component layers.
Materials for P7 were subject to a number of constraints specific to the requirements of their femtoslicing and XMCD experiments. For this work, it was necessary to have the coupled layers made of different magnetic elements so their switching characteristics could to distinguished. In addition there were restrictions on film thickness, a preference for compensation temperatures below room temperature, and the need for films to be grown on a special aluminium foil, which was a very different type of substrate to the silicon and glass used during material development and also limited the process temperatures used. Consequently, it was not possible to fabricate a synthetic ferrimagnet with perpendicular magnetic anisotropy that was compatible with the experimental techniques of P7, and the most promising materials for P7 were RETM multilayers or transition metal based synthetic ferrimagnets with in-plane magnetic anisotropy.
Materials for the thermally induced switching scheme proposed by P1 require high anisotropy and strong coupling to be effective. Efforts were made toward producing a suitable structure based on the calculations of P1, which were for L10 FePt antiferromagnetically coupled to Fe through a suitable spacer. Much work was done on achieving the ordered L10 phase of FePt at temperatures attainable on our tools, which are lower than is typical for L10 FePt production. Antiferromagnetic coupling between L10 FePt and Fe was demonstrated using an Ir spacer and was found to be affected by the thickness of the L10 FePt and Fe layers.
A general problem for synthetic ferrimagnetic materials was the loss of properties due to elevated temperatures applied either during deposition or by post annealing. This had implications for the longevity of the materials and also imposed serious limits on the type of structures that could be grown. It was a particular issue for perpendicular materials or materials with high anisotropy, where alloys such as L10 FePt are a necessary component of the structure, and require significant temperatures during manufacture. We were able to demonstrate that a possible solution exists in the use of thinner layers in repeated multilayer structures, which could improve both ferrimagnetic properties and thermal stability. This provides a basis for further study on how heating affects certain properties such as microstructure and the integrity of the ultrathin spacer layer responsible for strong antiferromagnetic coupling essential for a ferrimagnet. The latter may also be important in the development of future theoretical models, where microstructure is often neglected and materials are assumed to be perfectly formed and orientated monolayer stacks. This task was completed with deliverable D4.10 Materials and nanostructuring.
Task 4.6: THz control
The goal of this task was to demonstrate the possibility to control the magnetic state and properties using THz pulses. We have shown the possibility to resonantly pump a lattice mode to trigger a structural phase transition (A. D. C Aviglia et al, Phys. Rev. Lett. 108,136801 (2012). Using femtosecond resonant soft X-ray diffraction at the LCLS free electron laser, we demonstrated that the resonant optical excitation of an infrared-active phonon mode in a LaAlO3 substrate induces melting of the antiferromagnetic order in a NdNiO3 thin film, epitaxially grown on top of it. The magnetization dynamics in the thin film involve a supersonic phase front propagation, triggered by the lattice distortion at the substrate-film interface (M. Först. A.D. Caviglia et al., in preparation).
In addition, experiments were carried out on the lattice control of magnetic excitations in bulk orthoferrites. Our preliminary data indicate that the resonant excitation of an optical phonon mode in ErFeO3 (at multi-THz frequencies) drives a coherent magnon, as observed via time-resolved Faraday rotation.
Potential Impact:
Potential impact
The FemtoSpin project was carried out within a rapidly evolving industrial context. In terms of magnetic information storage, the drive to higher recording densities is based on Heat Assisted Magnetic Recording (HAMR), which uses laser pulses to heat the storage medium so as to allow reversal of the magnetisation. This relies on a combination of laser heating coupled with standard technology to generate a localised magnetic field to induce the magnetisation switching. Because of materials limitations, this field is limited in magnitude: a factor which will ultimately limit areal storage densities. Technologically, the complexity of manufacture of the write transducer is already slowing down the pace of development. The use of optical switching would remove the requirement for the inductive write transducer, significantly reducing both manufacturing costs and power requirements. At the same time, the field of spin electronics (or Spintronics), in which device functionality is dependent on the spin of the electron rather than simply the charge, is developing rapidly. Spintronics is a strong candidate to replace conventional electronics as this reaches its physical limitations. Again, optical reversal is a potential candidate for switching the magnetisation in spintronic devices.
Although technical difficulties remain to be overcome, Heat Assisted Magnetic Recording (HAMR) is closing in on providing the next generation of ultrahigh density recording systems. In May 2014 Seagate announced a 1.4Tbit/in2 areal density demonstration (the first to exceed conventional recording demonstrations) having previously shown 1000 hours of continuous write (the benchmark requirement). However, HAMR densities will be limited by the available write field (around 1Tesla) using inductive technology, due to the requirement of avoiding errors due to thermally induced back switching. Due to the physical and technical understanding within the FemtoSpin project, all-optical recording must be considered a realistic candidate for progress beyond HAMR. Here it must be noted that all candidate technologies face similar problems of writing and stability at extreme densities, and the large effective fields involved in all-optical technology could give it a strong advantage. Equally important could be the removal of inductive technology from the writing process in magnetic recording, leading to very significant design and process simplifications with important implications for cost reductions and reduced environmental impacts; that latter also enhanced by significantly reduced energy cost per bit in the write process. This represents an important potential advance for European industrial potential, supporting the major production centre of Seagate in Northern Ireland which produces around 25% of the world-wide total output (around 1 billion p.a.) of recording heads; an important European industrial resource.
Scientific highlights
• Development of an ab-initio code for the calculation of the opto-magnetic field (i.e. the magnetization induced by circularly polarized laser light), on the basis of the derived quantum theory for the opto-magnetic field.
• A theoretical framework has been derived for demagnetization due to transfer of the spin of hot (laser-excited) electrons to the phonon system and the resulting demagnetization rates were ab-initio computed for 3d ferromagnets.
• Ultrafast demagnetization due to spin transport has been investigated and was shown to give rise to emission of THz radiation
• Understanding the TIMS phenomenon and its prediction in structured media
• Atomistic/ab-initio model of Gd – beyond the fixed spin model and successful validation by comparison with experiments.
• Studies of differential spin dynamics on FeNi. Full multi-scale modeling of the material and comparison with experiment.
Multiscaling and collaborative code development
In magnetic materials the problem of linking lengthscales is compounded by the complex dynamical behaviour of spin systems and the difficulty of obtaining accurate values for magnetic materials properties from ab-initio calculations since the quantities of interest (the exchange energy and magnetic anisotropy values) are very small components of the total energy of the systems and require specialized techniques as well as fully relativistic models. Femtospin has made great strides in improving multiscale magnetic calculations and developing them into an integrated formalism. In particular,
• ab-initio determination of magnetic properties and parameterization of atomistic spin Hamiltonians (Budapest, Uppsala, Konstanz, York); automatic generation of spin model parameters for the Vampire atomistic code is almost complete.
• Macrospin simulations and atomistic testing/ parameterization (ICMM, Konstanz, York). This collaboration has produced a suite of models optimized for continuous and granular media. This collaboration has also developed a ferrimagnetic LLB equation for macrospin simulation.
• (ICMM, RU, York); atomistic and macrospin approaches have been combined to produce understanding of the dynamic behavior of ferrimagnetic materials during the thermally induced magnetization switching process.
Femtospin code development: public code release
– York atomistic code (Visual Atomistic Massively Parallel IntegRation Engine; VAMPIRE). On public release, Details available from vampire.york.ac.uk. Described in invited topical review; R. F. L. Evans, et. al., J. Phys.: Condens. Matter, 26, 103202 (2014) (23pp) (selected as one of the highlights of 2014 in J. Phys.: Condens. Matter). This paper has had almost 1000 downloads and already VAMPIRE has a user base of around 50. The code is in trial use in industry to support the development of advanced media structures for HAMR.
– MAgnetic Recording Simulator; MARS. Developed for advanced simulations of all-optical recording and HAMR in collaboration with Seagate/WD.
Document Database
Throughout the project a number of documents, files and articles have been produced.
The vast majority of the material produced has been stored in the private (member) area of the project website. A significant effort has also been made to create a database of the material properties calculated during the project. This website will remain for the short to medium term, managed by the University of York. The main code developed under the remit of the project is the VAMPIRE code which is publicly available at vampire.york.ac.uk where new versions are uploaded upon new release. The visualisation code developed in Konstanz (IMAGIN) is located on the internal pages of the FemtoSpin website for use within the consortium. The database will be placed on the outward facing pages of the Femtospin website, which will be maintained for the foreseeable future.
Dissemination
A huge number of publications have been published through the efforts of the members of the consortium in prestigious journals such as Nature Communications, Nature Materials, Physical Review Letters and Scientific Reports, to name but a few.
Outputs
1. Calculations of specific materials design parameters enabling a Dutch patent (2008039). Patent process continuing in Europe (EP2795622 (A2)) and the United States (US2014368303).
2. Atomistic code (Vampire) on public release. Very good take-up by academia.
3. Preparing advanced optical and heat-assisted magnetic recording model (MARS) for public release.
Other Outputs
4. Publications; 70 papers in high impact journals including Nature journals (7) and Physical Review Letters (2) and Scientific Reports (3).
5. 68 invited papers at International conferences
6. Organisation of a summer school in Nijmegen
7. Initiation of the Ultrafast Magnetism Conference (Rasing, Chantrell with Bigot and Huebner; first edition in Strasbourg in 2013 and second in Nijmegen in 2015)
Through regular meetings or the members of the consortium various channels for circulating the key results of the project and their impact have been planned and executed to great success. Assisted by the leading role of the members of the consortium in this field a large number of prestigious invited papers have been central to disseminating results to the magnetism community within the EU and beyond.
The leading role of the members of the consortium in theoretical and experimental magnetism has provided excellent opportunities throughout the project for engaging with the community to demonstrate the cutting edge techniques used within the consortium. Through workshops and other outreach activities the progress made in theoretical and experimental techniques has been shared with other scientists. We were also instrumental in the establishment of a new conference series, the Ultrafast Magnetism Conference.
A further aim of the FemtoSpin project was to increase the profile of ultrafast magnetization dynamics for data storage applications, as well as to raise awareness of the theoretical and experimental techniques used and developed by the consortium. By engaging with industrial partners through joint workshops and by making regular visits to various members of industry the project has succeeded in part in achieving these goals.
List of Websites:
www.femtospin.eu
Prof. Roy Chantrell
Dept. of Physics
The University of York
Heslington
York
North Yorkshire
UK
Email: roy.chantrell@york.ac.uk
