Periodic Reporting for period 3 - MULTIFLEXO (Hierarchical multiscale modeling of flexoelectricity and related materials properties from first principles)
Berichtszeitraum: 2020-04-01 bis 2021-09-30
Flexoelectricity, the coupling between an inhomogeneous deformation and the electrical polarization, has emerged a “hot” topic in modern materials science due to its cross-cutting relevance to many phenomena of fundamental and technological interest. Understanding the intriguing physics that governs its behaviour at the nanoscale is crucial to harnessing the potential of strain gradients in practical applications, and such a progress requires a substantial support from theory. In spite of impressive recent advances, first-principles calculations of flexoelectricity remain technically challenging at several levels: first, the breakdown of translational lattice periodicity that a strain gradient entails is problematic to treat in the context of traditional electronic-structure methods; second, the stringent length- and time-scale constraints of direct quantum-mechanical approaches limit the applicability of these methods to real problems, which often involve complex sample shapes and morphologies. This project is aimed at overcoming these obstacles from their very root, via the development of innovative electronic-structure and multiscale methodologies, and at using these advances to address a number of pressing physical questions in the context of energy and information technologies. In particular, the objectives of this project are: (i) identifying the microscopic mechanisms that are most effective at delivering a strong flexoelectric response in a variety of materials; (ii) understanding how these bulk effects are modified by size, shape and boundary conditions, and how they interact with other material properties; (iii) supporting the experimental interpretation by critically assessing alternative physical interpretations of the observed effects (e.g. compositional gradients); (iv) exploring the functionalities enabled by strain gradients in complex materials systems, including 2D crystals, semiconductor nanowires and multiferroics.
In the early stages of this project we have primarily directed our efforts at understanding the fundamentals of flexoelectricity from the point of view of quantum mechanics, and at developing efficient and accurate methodologies for predicting the flexoelectric performance of real materials. This work has led to a number of breakthrough advances in the context of first-principles electronic-structure theory. As a matter of fact, we have successfully implemented one of the most powerful ideas of this proposal, which consists in applying the traditional long-wave approach (a workhorse of condensed-matter physics since the early years) to modern density-functional perturbation theory (DFPT). The latter is nowadays the state-of-the-art method for predicting a vast range of materials properties, including phonon frequencies, dielectric, elastic and piezoelectric coefficients. Flexoelectricity, before this project started, was not part of this list. The reasons are quite deep: the response to a strain gradient involves a breakdown of translational periodicity, which at first sight constitutes an insuperable obstacle for methods that are traditionally based on periodic boundary conditions. To attack this problem we had to rethink DFPT from its very roots, and develop an entirely new strategy. As a result, we now have at our disposition a brand new method, which we call "long-wave DFPT", that elegantly solves not just flexoelectricity, but also the whole class of problems that flexoelectricity belongs to. Examples of spatial-dispersion effects that are now, thanks to our work, within the reach of standard electronic-structure implementations include Lorentz forces in extended crystals and natural rotatory power in chiral systems. All these properties, including the full flexoelectric tensor for an arbitrary insulating system, can now computed in few minutes by using the publicly distributed ABINIT simulation package, where our methodological advances have been implemented and tested. Such a scenario, which we optimistically described in the "five years from now" box of the grant proposal, is now a reality.
This breakthrough did not happen in a day. It took a number of small, intermediate steps to arrive at where we stand now. First, we have developed and tested the calculation of the flexoelectric coefficients based on the current-density response; this allowed for the first time to perform all bulk calculations on the primitive unit cell only (C. E. Dreyer, MS and D. Vanderbilt, PRB 2018). Next, we have established a full-fledged quantum theory of deformations in curvilinear coordinates (MS and D. Vanderbilt, PRB 2018), identifying a formal relationship to orbital magnetism; we have then proceeded to its numerical implementation and test (A. Schiaffino, C. E. Dreyer, D. Vanderbilt and MS, PRB 2019). Finally, we have implemented and tested the first applications of long-wave density-functional perturbation theory to the clamped-ion bulk flexoelectric tensor and the dynamical quadrupoles (M. Royo and M. Stengel, PRX 2019). The lattice-mediated contributions to the flexoelectric tensor followed shortly after (manuscript in preparation), and we're currently attacking other spatial dispersion effects (e.g. natural optical rotation, geometric magnetization, etc.) together with representative materials applications. It will take require a lot more work to take advantage of all the opportunities that this initial work has opened, but we can say that we are now moving efficiently into the right direction.
Our work has not only been methodological. For example, we have published a highly innovative study of ferroelastic domain walls in SrTiO3. To do that, we have developed a DFT-based continuum model to describe the evolution of the order parameters across the wall, and identified the role of flexoelectricity in determining the induced electrical polarization. (A. Schiaffino, M. Stengel, PRL 2017) This can be regarded as our first implementation the "multiscale" part of the MULTIFLEXO project, where microscopic and macroscopic simulations are combined to draw the "best from both worlds". This led us to the discovery of two previously overlooked coupling mechanisms that involve antiferrodistortive tilts and their gradients. These couplings also bear important implications for the physics of SrTiO3 at low temperatures. (B. Casals et al., PRL 2018). We're currently formalizing these findings into a general theoretical framework, that allows for the systematic construction of "first-principles macroscopic theories", readily applicable to the emerging research area of topological structures in ferroics (domain walls, spirals, skyrmions, etc.) We have also generalized our methods to systems with lower dimensionality, which enabled us to calculate the flexoelectric properties of several two-dimensional materials.
This breakthrough did not happen in a day. It took a number of small, intermediate steps to arrive at where we stand now. First, we have developed and tested the calculation of the flexoelectric coefficients based on the current-density response; this allowed for the first time to perform all bulk calculations on the primitive unit cell only (C. E. Dreyer, MS and D. Vanderbilt, PRB 2018). Next, we have established a full-fledged quantum theory of deformations in curvilinear coordinates (MS and D. Vanderbilt, PRB 2018), identifying a formal relationship to orbital magnetism; we have then proceeded to its numerical implementation and test (A. Schiaffino, C. E. Dreyer, D. Vanderbilt and MS, PRB 2019). Finally, we have implemented and tested the first applications of long-wave density-functional perturbation theory to the clamped-ion bulk flexoelectric tensor and the dynamical quadrupoles (M. Royo and M. Stengel, PRX 2019). The lattice-mediated contributions to the flexoelectric tensor followed shortly after (manuscript in preparation), and we're currently attacking other spatial dispersion effects (e.g. natural optical rotation, geometric magnetization, etc.) together with representative materials applications. It will take require a lot more work to take advantage of all the opportunities that this initial work has opened, but we can say that we are now moving efficiently into the right direction.
Our work has not only been methodological. For example, we have published a highly innovative study of ferroelastic domain walls in SrTiO3. To do that, we have developed a DFT-based continuum model to describe the evolution of the order parameters across the wall, and identified the role of flexoelectricity in determining the induced electrical polarization. (A. Schiaffino, M. Stengel, PRL 2017) This can be regarded as our first implementation the "multiscale" part of the MULTIFLEXO project, where microscopic and macroscopic simulations are combined to draw the "best from both worlds". This led us to the discovery of two previously overlooked coupling mechanisms that involve antiferrodistortive tilts and their gradients. These couplings also bear important implications for the physics of SrTiO3 at low temperatures. (B. Casals et al., PRL 2018). We're currently formalizing these findings into a general theoretical framework, that allows for the systematic construction of "first-principles macroscopic theories", readily applicable to the emerging research area of topological structures in ferroics (domain walls, spirals, skyrmions, etc.) We have also generalized our methods to systems with lower dimensionality, which enabled us to calculate the flexoelectric properties of several two-dimensional materials.
The progress beyond the state of the art should be clear from the above paragraphs. In the last period of the project we plan on finalizing the remaining ongoing tasks. We expect to complete our methodological development and showcase it with applications to systems of fundamental and practical interest, including magnetic insulators and chiral crystals.