Modeling and predicting responses of magnetoelectric materials
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Introduction The magnetoelectric (ME) effect in materials includes the direct ME effect (the appearance of electric polarization upon applying a magnetic field) and the converse ME effect (the appearance of magnetization upon applying an electric field). Such ME effects make the ME materials promising for applications as sensors, transducers, filters, oscillators, phase shifters, and memory and logic devices.1–4 Practical applications of ME devices require strong enough ME coupling effects, which can be promoted either through new ME materials or by the optimal design of ME composites, or heterostructures integrating ferroelectric and magnetic materials. However, these approaches are somewhat tedious from an experimental standpoint, and thus effective multiscale simulation methods are highly desired. Density functional theory (DFT), the effective Hamiltonian method, continuummedium methods (such as phase-field and effective-medium methods), as well as finite element methods have demonstrated great success in understanding ME coupling mechanisms as well as for the prediction of new materials4–8 (see Figure 1). Nevertheless, great challenges still exist in understanding the ME response on multiple time and length scales, especially when dealing with strong electronic correlations, realistic microstructures, the dynamics of topological features, and the prediction of new ME mechanisms or materials. In this article, we present a review of several computational techniques, from the mesoscopic scale down to atomistic and electronic
scales, for exploring ME materials and mechanisms, and a brief outlook for the future for this class of materials.
Mesoscopic scale Early works on modeling and predicting the response of ME materials were carried out using continuum-medium methods at the mesoscale, which not only provided quantitative understanding of the direct ME responses in bulk ME composites, but also predicted new composites with a giant ME effect.2 In recent years, mesoscale modeling of ME materials has focused on nanocomposites, especially heterostructures integrating ferroelectric and magnetic materials. Magnetization switching or domain structure in ME heterostructures can be directly controlled by applying an electric field, offering attractive possibilities for novel potential ME devices such as memories, spintronic devices, and electrically tunable microwave devices. On the mesoscale, the phase-field method is powerful for understanding electric-field control of magnetism by investigating complex magnetic/ferroelectric domain evolution processes, and thereby designing novel ME devices.7,8 For example, based on phase-field simulations of electric-field-induced magnetization switching via strain-mediated ME coupling, the combination of a spin-valve or magnetic tunnel junction (a key component in most spintronic devices) with a ferroelectric layer has been designed to construct an electric-field actuated magnetic random-access memory.9
Ben Xu, School of Materials Science and Engineering, Tsinghua University, China
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