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(odnośnik otworzy się w nowym oknie). 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/(odnośnik otworzy się w nowym oknie) . 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.
