Session M41: Theoretical and Computational Modeling of Ferroelectrics and Multiferroics

Magnetoelectric multipoles and spin textures in real-space and reciprocal space

In condensed matter systems, the multipoles provide a quantitative measure of the complex angular distribution of the charge and magnetization densities in a broken-symmetry phase of a solid. Magnetoelectric multipoles, that break both space-inversion I and time-reversal T symmetries, quantify the antisymmetric magnetization density of a solid. In my talk, I will discuss a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles [1]. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. Taking the examples of skyrmions, antiskyrmions, and bimerons of different helicities, we show that the nonzero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity, and geometry of the spin texture. We have proposed straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures. Similarly, to the description of real-space spin textures by real-space magnetoelectric multipoles, momentum-space spin textures can also be described by k-space magneto-electric multipoles [2]. These k-space magnetoelectric multipoles are reciprocal to the real-space charge dipoles associated with the broken inversion symmetry. Using the prototypical ferroelectric PbTiO₃ as an example material, I will discuss the tuning of the k-space magnetoelectric multipoles and their possible detection using designed magnetic Compton scattering techniques.   

Theory of domain structure in electron-doped ferroelectric thin films

To reduce the energy cost of strong depolarizing fields, insulating ferroelectric often films break up into nanoscale ``Kittel'' domains of opposite polarization that are separated by uncharged 180^? domain walls. Here, I report on recent self-consistent solutions of coupled Landau-Ginzburg-Devonshire and Schrödinger equations for an electron-doped ferroelectric thin film. The model is based on LaAlO3/SrTiO3 interfaces in which the SrTiO3 substrate is made ferroelectric by cation substitution or strain. Electron doping destabilizes the Kittel domains. As the two-dimensional electron density increases, there is a smooth crossover to a zigzag domain wall configuration. The domain wall is positively charged, but is compensated by the electron gas, which attaches itself to the domain wall and screens depolarizing fields. The domain wall approaches a flat head-to-head configuration in the limit of perfect screening. The polarization profile may be manipulated by an external bias voltage and the electron gas may be switched between surfaces of the ferroelectric film.

    

Modeling Local Distortions in Zn1-xMgxO Ferroelectrics

Non-von Neumann computing architectures offer opportunities to maximize the energy efficiency and floating-point-computation performance of microprocessors, beyond the von Neumann computing model in which the data-storage and data-processing functions of the computer are physically separated. One example of such architectures is three-dimensional ferroelectric microelectronics (3DFeMs) that take advantage of third-dimensional interconnects, enabling low-power computation. The integration of ferroelectric memory capabilities into field-effect transistors requires the development of ferroelectric materials that would be scalable and compatible with current microelectronic technologies. In this work, we study the mechanisms of polarization switching in recently proposed Zn_1−xMg_xO (ZMO) ferroelectric materials. To understand cation ordering in ZMO at finite temperature, we validated and applied large-scale Monte Carlo simulations in the canonical ensemble using Metropolis and Wang-Landau samplings. Finite-temperature Monte Carlo simulations strongly suggest that short-range cation ordering critically influence the stability and ferroelectric response of ZMO compounds. Analyzing local distortions associated with temperature-dependent cation ordering may ultimately provide insight into the mechanisms facilitating polarization switching in ZMO.   

Spin-polarized Flexoelectricity

Flexoelectricity describes the coupling between electric polarization and a strain gradient. First-principles methods for calculating flexoelectric tensor components have been previously developed that involve calculating electronic and lattice contributions using various charge-moment and force tensors. In magnetic materials, these charge moments can be spin-polarized – that is, the densities of spin up and down electrons can respond differently to atomic displacement. Based on this principle, we developed a method for calculating spin-polarized flexoelectric tensor components. We apply our method to a ferromagnetic oxide finding a sizeable spin-polarization of the flexoelectric tensor. Furthermore, we calculate its three independent flexoelectric tensor components and use these to predict an effective spin-polarized beam-bending flexoelectric constant along the (100) direction. The potential applications to spintronics through a metal-oxide interface is discussed.

    

Understanding Dynamics of Heterogeneous Ferroelectric Oxides at the Nanoscale using Graph Neural Networks on Reactive Force-Field Simulations

Ferroelectrics are a technologically important class of materials for next generation microelectronics platforms, such as ferroelectric memristors, which show spontaneous long-range ordering of electric polarization. Recent advances have even shown formation of novel nanoscale chiral polar structures, such as polar skyrmions in heterogeneous oxides, that open new possibilities for storing and manipulating information at the nanoscale. While formation of long-range polar order as well as polar skyrmions is understood to be a delicate balance between coupling between microscopic degrees of freedom, there is a critical need to understand dynamics of polarization switching in such heterogeneous materials under high fields. In this talk, we will present insights into the dynamics of polarization switching in defective BaTiO₃, obtained from combining large-scale atomistic reactive simulations with dynamical graph neural network approaches. Specifically, we will focus on how polar-structure and dynamics changes around point-defects, and how this interaction influences domain-wall dynamics.

    

Dynamic Atomic Off-centering and Its Selective Coupling with Phonons in KTa(1-x)NbxO3

The mechanism of ferroelectric phase transitions (e.g. displacive or order-disorder) in simple compounds like BaTiO₃ and KNbO₃ has remained debated for decades. Finally solving this question requires simultaneously resolving atomic dynamics, local crystal distortions and complex correlated disorder. To address this challenge, we map the energy and momentum resolved dynamic structure factor S(Q, E) with neutron scattering and we perform DFT-accuracy machine-learning MD (MLMD) simulations, to rationalize the spatial and temporal correlations of atomic disorder and the coupling with phonons. Here, we focus on correlated atomic off-centering in KTaO₃ and KTa_(1−x)Nb_xO₃ (KTN) and find an intermediate picture between displacive and order-disorder scenarios. Our experiments show two-dimensional diffuse sheets from correlated local disorder in KTN, contrasting with displacive KTaO₃. Our first-principles and MLMD simulations reveal that correlated 1D chains of off-centered B-site atoms in KTN are energetically favorable, and show how the correlated disorder selectively couples with the ferroelectric instability as well as transverse acoustic modes. These results provide insights into these model systems and offer general guidance for related systems whose atomistic behavior remain debated.   

Theory of Electro-Optic Response in Tetragonal BaTiO3

The linear electro-optic (EO), or Pockels effect offers a promising path to fabrication of ultra-low power ultra-compact electro-optic modulators in silicon photonics bridging the optical technology with conventional silicon. Barium titanate, BaTiO₃ (BTO), has emerged as a promising electro-optic material that can be integrated with silicon photonics. In this talk, we report the first principles calculations of the EO or Pockels tensor in tetragonal BTO. Due to the lattice anharmonicity, predicting the Pockels response using functional theory (DFT) has been a challenge. However, our results indicate that the problem may be deeper. We show that the conventional P4mm structure of BTO is most likely a dynamic average of lower symmetry structures in agreement with recent experiments [1]. Using this argument as a starting point, we calculate both the ionic and piezo contributions of the EO tensor in good agreement with available experimental values.

 

[1] M. S.  Senn et al. PRL 116, 207602 (2016)

    

FerroX : A GPU-accelerated, 3D Phase-Field Simulation Framework for Modeling Ferroelectric Devices

Fundamental understanding and design of ferroelectric/multiferroic materials and devices for logic-in-memory and transistor enhancement is essential to enable low switching energies and thereby revolutionary power reductions in computing. Efficient modeling and simulations can provide in-depth insights into the underlying physics, as well as pave the road to facilitate researchers with reliable design tools for new microelectronic devices. In this talk, we will present a performance-portable, 3D phase-field simulation framework, FerroX, for modeling and design of ferroelectric-based microelectronic devices. FerroX is open-source (https://github.com/AMReX-Microelectronics/FerroX) and demonstrates a significant (15x) speedup on GPU architectures compared to the CPU counterparts. We will demonstrate the application of the code with simulations of multi-domain negative capacitance effects in Metal-Ferroelectric-Insulator-Metal (MFIM) and Metal-Ferroelectric-Insulator-Semiconductor-Metal (MFISM) devices. Additionally, we will report the latest upgrades, including the addition of strain in total free energy of ferroelectrics and the development of a micromagnetic module for modeling multiferroics.   

Manipulation of spin orientation in iron-doped ferroelectric oxides from first principles

Atomic-scale control of isolated spins by electric fields is highly desirable for future technological applications. Ferroelectric oxides containing dilute concentrations of magnetic dopants provide a possible platform for achieving this functionality. Within a ferroelectric, electric field-based polarization switching changes the local crystallographic environment of a magnetic dopant atom, which via a magnetoelastic interaction impacts its spin directionality. In this work, we explore this concept using the example of Aurivillius-phase oxide Bi₂WO₆ with a tungsten-site Fe³⁺ dopant. By combining group theoretic analysis with density functional theory calculations, we show that ferroelectric switching in Bi₂WO₆  proceeds via a two-step pathway. Magnetocrystalline anisotropy energy calculations reveal that the Fe³⁺ dopant spin substituted into the low-symmetry Bi₂WO₆ crystal structure aligns along an easy axis. By tracking changes to the spin directionality during ferroelectric switching, we show that a 90? switch in the polarization direction leads to a 112? reorientation of the spin-easy axis. We comment on the generalization of our findings to other families of ferroelectric oxides and magnetic dopant species.

    

Ferroelectric switching pathways, domain structure, and domain wall vortex in SrBi2(Ta,Nb)2O9

Aurivillius-phase oxides SrBi₂B₂O₉ (B=Ta, Nb) are room temperature ferroelectrics which are well known for their fatigue resistance, low coercive fields, and potential application in ferroelectric random-access memory. Previous work has shown that the trilinear coupling between the electrical polarization and two octahedral rotation distortions of different symmetries plays a key role in the structural phase transition sequence and stabilization of the ferroelectric phase in SrBi₂Ta₂O₉. However, the implications of the trilinear coupling on the ferroelectric switching mechanism in these materials remain to be understood. In this work, we use the group theoretic analysis and density functional theory calculations to enumerate and explore the energetics of ferroelectric switching paths in SrBi₂B₂O₉ and identify several low-energy one- and two-step ferroelectric switching pathways. Moreover, we show how the relative energy barriers of these switching paths can provide the insight into the domain structure of these oxides. In particular, our findings indicate that three-fold domain wall vortices are energetically favorable in SrBi₂B₂O₉ which corroborates experimental reports of the domain structure in SrBi₂Ta₂O₉.  This work advances our fundamental understanding of the technologically important family Aurivillius oxides.     

Exploring Electrically Controlled Magnons for Post-Moore Microelectronics with Exascale Modeling

The post-Moore's law era has seen unprecedented growth of electronic microdevices harnessing novel physical couplings beyond conventional single-phase materials. To gain an in-depth understanding of the interaction between the physical mechanisms, we are exploring the validation, design and optimization of magnetoelectric spin-orbit logics. Using the GPU-accelerated software package we have developed (https://github.com/AMReX-Microelectronics), we are studying the manipulation of chiral-spin transport with ferroelectric polarization, which allows control of magnons by external electric fields. With the capability to explore full physical interactions, this new approach provides a pathway to understand and develop new fully integrated electronic systems beyond the capability of traditional semiconductor technologies.

    

First-principles theory of phonon magnetic moment

Chiral phonons have recently been shown to possess finite magnetic moment that consists of both nuclei and electron contributions. Classical (using Born effective charge) and quantum theories for the electron’s contribution have both been developed. However, the two theories carry essential differences in handling the geometric effects, and quantitative comparisons between the two theories are missing in realistic materials. Here, we developed a first-principles scheme to calculate phonon magnetic moment from quantum theory. We found observable magnetic moments of chiral phonon modes in a gated two-dimensional material. In contrast, the magnetic moments vanish according to classical theory. This contrast highlights the central role of geometric effects in phonon magnetic moments. In addition, the magnetic moments have significant electric-field tunability and mode selectivity. Our numerical methods and predictions open a new route to finding dynamical multiferroicity in realist material systems.

    

Local symmetry breaking in different phases of BaTiO3

Macroscopically, the different phases of BaTiO₃ have been generally understood by considering an averaged structure with the ordered local dipole or without the local dipole. However, microscopically, the local dipole configurations (LDC) in different phases remain poorly understood except for the ground state BaTiO₃. Experimental local probes, e.g., pair distribution function (PDF), and frequency-dependent structure factor S(q,w), as well as density functional theory (DFT) calculations[1] reveal that the LDC in their averaged crystal structures, especially in cubic, does not describe well the system. Here, using DFT including in finite T Molecular Dynamics and minimizing the energy (E=U-TS) in supercells, we find the existence of LDC in all the phases of BaTiO₃ before & after temperature sets in. Except for ground state BaTiO₃, the calculated and measured LDC in different phases differentiates from the ordered LDC or no LDC from their averaged structures. Further direct comparisons between the calculated PDF and S(q,w) based on the DFT minimized structures and the experimental measured PDF and S(q, w) confirm that local symmetry breaking due to LDC in different phases of BaTiO₃. Our work bridges the theoretical simulation to the experimentally local measurement.