The anomalous Hall effect (AHE) is a topology-related transport phenomenon 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 have revealed electric-field induced AHE (via linear magnetoelectric coupling), an AHE originating from 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 uniaxial, biaxial, or triaxial 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 ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and ${\mathrm{CoF}}_2$ 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.

Close

PrevNext

View figure in article

• Anomalous Hall effect
• Hall effect
• Magnetoelectric effect
• Transport phenomena