Periodic Reporting for period 1 - SCALES (Multiferroic phase field models of the coupled dynamics of bismuth ferrite)
Reporting period: 2021-02-01 to 2023-01-31
Multiferroics are an interesting class of materials. They display both electric and magnetic order. They also exhibit a non-trivial coupling between the two phenomena leading to the possibility of i.e. manipulating the magnetization with an electric field. This one example (among others) is advantageous in the context of next-generation device design because suitable properties can be obtained with low-power or with ultrafast stimulii. Therefore, multiferroics have been proposed as components in device prototypes ranging from beyond-CMOS logic gates, magnetoresistant spintronic valves, to electro-optic modulators among many others. Within the SCALES project, we developed a model of a particularly popular multiferroic BiFeO3 (BFO). This is a ferroelectric antiferromagnet with useful room temperature properties. To study these materials theoretically, atomistic methods can become prohibitive if too many atoms are in the simulation box. This leads to difficulties to predict and understand physical phenomena at the device-relevant scale (typically a few hundred nanometers). Therefore, we were motivated to develop a continuum model of this material which coarse-grains or averages the material behavior over longer distances. This involved coupling the ferroelectric phase field method to the micromagnetic simulation approach. This allows one to simulate both the electric and magnetic order in a single simulation with real-time scales. These types of simulations are important for the field because materials properties of BFO (and other multiferroics) can then be extracted from an arbitrary simulation geometry of a nanostructure. We aimed to benchmark and develop a useful model for not only the low energy ground states of the structure (which are static in time) but also understand the dynamical behavior of the order parameters (electric polarization or magnetic spin) under applied fields. Furthermore, we aimed to develop this model in an open-source framework (MOOSE) that is freely available and extendable to other physical phenomena in BFO (or other types of multiferroics) and is continuously-integrating with the underlying software libraries (thus preserving reproducibility).
Our work encompassed first developing the model of the coupled ferroelectric-antiferromagnet system which involved parameterization of materials coefficients that are useful for modeling at large length scales.
First, we focused on the ferroelectric (structural) domain walls. In BFO, there are many types that can arise each having their own distinct formation energy. For every wall, a specific profile of the electric polarization, oxygen octahedral cage antiphase tilt and spontaneous strain exists. By performing multiple simulations of the different types of walls, we were able to fit the coefficients that govern their energy against predictions from density functional theory. This yielded excellent agreement and paved the way for the next step of the project: to add magnetism. We implemented a two-sublattice micromagnetic model on top of the ferroelectric phase field model. For homogeneous polarization (no domain walls), we demonstrated great agreement with respect to the literature of this material. It is well known that BFO is a noncollinear antiferromagnet is a weak canted magnetization due to an antisymmetric Dzyaloshinskii-Moriya exchange interaction. For the next part, we relaxed the magnetization textures on top of various low-energy ferroelectric domain walls. This revealed delicate features in the angular quantities that characterize the canted magnetism. This concluded the model development and we were able to exploit the full model on two distinct applications.
The first of which, was spin wave transport across the multiferroic domain boundaries. Spintronics relies on the generation, control, and read-out of traveling packets of spin. Understanding spin transport in multiferroics is a challenging task as one needs to understand not only the spin dynamics but also the coupling to the structural order. We simulated spin wave transport across the low-energy DWs in BFO and demonstrated that they hinder the possible detected signal useful for devices. This rectification was shown to be strongly frequency-dependent due to the magnetic component of the DW absorbing the incoming energy. We postulate that this is in qualitative agreement with recent experimental observations.
The second application that we demonstrated with the model is part of the "holy grail" of multiferroics. That is, to switch the magnetization with an applied time-dependent electric field. We showed that this switching depends strongly on one of the micromagnetic simulation parameters (damping) which is a relatively unexplored topic. To isolate this effect, we performed two types of simulations with a nonzero frequency for the electric field (a slow switch) as well as a instantaneous switch to demonstrate that the time-dependence of the structural switching (that which comes from the electric polarization and the oxygen octahedral cage antiphase tilts along with strain) does not influence the final state appreciably. This sensitivity on the switching path of magnetization on the phenomenological damping constant warrants future work but we demonstrate that such a task is well suited from the model developed within SCALES.
All of these results are summarized in an article submitted to Physical Review B on April 1st. The paper is hosted on the arXiv preprint server at http://arxiv.org/abs/2304.00270(opens in new window). Thus, the results are freely and openly available to the general public in the preprint. In addition, we disseminate our results in the Ferret website located at https://mangerij.github.io/(opens in new window) . The SCALES results have a dedicated special page located in the MSCA2020 dropdown menu. The key results of the project are summarized along with representative examples to reproduce our results. These pages detail how the use, read and understand the code, and also visualize the postprocessed outputs. The SCALES-related pieces of the Ferret repository are easily extendable to other physical phenomenon in BFO as well as other related multiferroic materials.
First, we focused on the ferroelectric (structural) domain walls. In BFO, there are many types that can arise each having their own distinct formation energy. For every wall, a specific profile of the electric polarization, oxygen octahedral cage antiphase tilt and spontaneous strain exists. By performing multiple simulations of the different types of walls, we were able to fit the coefficients that govern their energy against predictions from density functional theory. This yielded excellent agreement and paved the way for the next step of the project: to add magnetism. We implemented a two-sublattice micromagnetic model on top of the ferroelectric phase field model. For homogeneous polarization (no domain walls), we demonstrated great agreement with respect to the literature of this material. It is well known that BFO is a noncollinear antiferromagnet is a weak canted magnetization due to an antisymmetric Dzyaloshinskii-Moriya exchange interaction. For the next part, we relaxed the magnetization textures on top of various low-energy ferroelectric domain walls. This revealed delicate features in the angular quantities that characterize the canted magnetism. This concluded the model development and we were able to exploit the full model on two distinct applications.
The first of which, was spin wave transport across the multiferroic domain boundaries. Spintronics relies on the generation, control, and read-out of traveling packets of spin. Understanding spin transport in multiferroics is a challenging task as one needs to understand not only the spin dynamics but also the coupling to the structural order. We simulated spin wave transport across the low-energy DWs in BFO and demonstrated that they hinder the possible detected signal useful for devices. This rectification was shown to be strongly frequency-dependent due to the magnetic component of the DW absorbing the incoming energy. We postulate that this is in qualitative agreement with recent experimental observations.
The second application that we demonstrated with the model is part of the "holy grail" of multiferroics. That is, to switch the magnetization with an applied time-dependent electric field. We showed that this switching depends strongly on one of the micromagnetic simulation parameters (damping) which is a relatively unexplored topic. To isolate this effect, we performed two types of simulations with a nonzero frequency for the electric field (a slow switch) as well as a instantaneous switch to demonstrate that the time-dependence of the structural switching (that which comes from the electric polarization and the oxygen octahedral cage antiphase tilts along with strain) does not influence the final state appreciably. This sensitivity on the switching path of magnetization on the phenomenological damping constant warrants future work but we demonstrate that such a task is well suited from the model developed within SCALES.
All of these results are summarized in an article submitted to Physical Review B on April 1st. The paper is hosted on the arXiv preprint server at http://arxiv.org/abs/2304.00270(opens in new window). Thus, the results are freely and openly available to the general public in the preprint. In addition, we disseminate our results in the Ferret website located at https://mangerij.github.io/(opens in new window) . The SCALES results have a dedicated special page located in the MSCA2020 dropdown menu. The key results of the project are summarized along with representative examples to reproduce our results. These pages detail how the use, read and understand the code, and also visualize the postprocessed outputs. The SCALES-related pieces of the Ferret repository are easily extendable to other physical phenomenon in BFO as well as other related multiferroic materials.
The continuum-scale multiferroic simulation capability developed here is fully-open source. Furthermore, the results and code are continuously integrating with the underlying software stack (as part of the MOOSE ecosystem). Thus, the results are reproducible on future operating systems or new libraries. As scientific computing becomes more complicated, preserving reproducibility of simulation and published results through open-source databases and dedicated testing services is essential. This transparent approach to science allows for greater reach and radically enhances the quality of the research.