Anomalous Hall effect from nonlinear magnetoelectric coupling

TL;DR

This paper develops a phenomenological theory and identifies material candidates for the anomalous Hall effect driven by nonlinear magnetoelectric coupling, expanding understanding beyond linear effects in spintronics.

Contribution

It introduces a symmetry-based phenomenological framework for nonlinear magnetoelectric coupling-induced AHE and proposes specific materials as candidates for experimental observation.

Findings

Nonlinear magnetoelectric coupling can induce AHE in various magnetic point groups.

Electric-field driven AHE is reversible with magnetic order reversal.

Cr₂O₃ and CoF₂ are identified as candidate materials for this effect.

Abstract

The anomalous Hall effect (AHE) is a topology-related transport phenomenon being of potential interest in spintronics, because this effect enables the efficient probe of magnetic orders (i.e., data readout in memory devices). It is well known that AHE spontaneously occurs in ferromagnets or antiferromagnets with magnetization. While recent studies reveal electric-field induced AHE (via linear magnetoelectric coupling), an AHE originating from {\it nonlinear} magnetoelectric coupling remains largely unexplored. Here, by symmetry analysis, we establish the phenomenological theory regarding the spontaneous and electric-field driven AHE in magnets. We show that a large variety of magnetic point groups host an AHE that is driven by uni-axial, bi-axial, or tri-axial electric field and that comes from nonlinear magnetoelectric coupling. Such electric-field driven anomalous Hall conductivities are reversible by reversing the magnetic orders. Furthermore, our first-principles calculations suggest Cr$_2$O$_3$ and CoF$_2$ as candidates hosting the aforementioned AHE. Our work emphasizes the important role of nonlinear magnetoelectric coupling in creating exotic transport phenomena, and offers alternative avenues for the probe of magnetic orders.