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Anomalous Hall effect from nonlinear magnetoelectric coupling

Longju Yu, Hong Jian Zhao, Yurong Yang, Laurent Bellaiche, Yanming Ma

TL;DR

This work develops a symmetry-based phenomenological framework for the anomalous Hall effect (AHE) arising from nonlinear magnetoelectric coupling, showing that spontaneous and electric-field–driven AHE can occur across many magnetic point groups and are reversible by reversing the magnetic order. The authors derive an effective-field description for AHE, linking uni-, bi-, and tri-axial electric fields to specific Hall-conductivity components via nonlinear MEC, and validate the theory with first-principles calculations on Cr$_2$O$_3$ and CoF$_2$, where substantial AHE signals appear under applied fields. They demonstrate that reversing the magnetic order flips the AHE sign and propose practical measurement strategies (gate/polarization schemes and dc+ac techniques) to detect E-field–driven AHE. Overall, the work highlights nonlinear MEC as a fertile mechanism to realize and probe exotic transport in magnetic materials with potential spintronic applications.

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.

Anomalous Hall effect from nonlinear magnetoelectric coupling

TL;DR

This work develops a symmetry-based phenomenological framework for the anomalous Hall effect (AHE) arising from nonlinear magnetoelectric coupling, showing that spontaneous and electric-field–driven AHE can occur across many magnetic point groups and are reversible by reversing the magnetic order. The authors derive an effective-field description for AHE, linking uni-, bi-, and tri-axial electric fields to specific Hall-conductivity components via nonlinear MEC, and validate the theory with first-principles calculations on CrO and CoF, where substantial AHE signals appear under applied fields. They demonstrate that reversing the magnetic order flips the AHE sign and propose practical measurement strategies (gate/polarization schemes and dc+ac techniques) to detect E-field–driven AHE. Overall, the work highlights nonlinear MEC as a fertile mechanism to realize and probe exotic transport in magnetic materials with potential spintronic applications.

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 CrO and CoF 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.
Paper Structure (10 sections, 9 equations, 2 figures, 2 tables)

This paper contains 10 sections, 9 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Results and discussion
  4. Anomalous Hall effect and Hall vector
  5. Anomalous Hall effect in magnets
  6. Phenomenological theory
  7. Electric-field driven AHE in Cr$_2$O$_3$ and CoF$_2$
  8. Possible measurement strategies
  9. Summary and outlook
  10. Derivations of effective magnetic fields

Figures (2)

  • Figure 1: The crystal and magnetic structures for two compounds. The Cr, Co, O and F ions are denoted by cyan, orange, yellow and grey spheres, respectively. The magnetic moments are shown by red arrows. (a): Cr$_2$O$_3$ with $+L$ magnetic order parameter. (b): CoF$_2$ with $+L$ magnetic order parameter. The $x$, $y$, and $z$ directions in each panel are orthogonal to each other.
  • Figure 2: The electric-field driven anomalous Hall conductivity components in Cr$_2$O$_3$ and CoF$_2$ as functions of chemical potential (defined with respect to the Fermi level). Panels (a)-(c) depict the anomalous Hall conductivity components in Cr$_2$O$_3$: $\sigma_{zy}$ induced by a uni-axial $E_x$ field, $\sigma_{yx}$ induced by a uni-axial $E_y$ field, and $\sigma_{yx}$ induced by a uni-axial $E_z$ field. Panels (d) and (e) show the anomalous Hall conductivity components in CoF$_2$: $\sigma_{zy}$ induced by a bi-axial $[E_x,E_z]$ field, and $\sigma_{yx}$ induced by a uni-axial $E_x$ field.