Observation of the In-plane Anomalous Hall Effect induced by Octupole in Magnetization Space

TL;DR

This paper reports the discovery of an in-plane anomalous Hall effect in common ferromagnets, caused by an octupole in the anomalous Hall conductivity, challenging existing theories and opening new avenues for magnetic device design.

Contribution

It introduces the concept of an octupole in anomalous Hall conductivity as the origin of in-plane AHE in cubic ferromagnets, contradicting previous understanding.

Findings

In-plane AHE observed in iron and nickel.

Octupole of anomalous Hall conductivity identified as the mechanism.

Potential for new magnetic device applications.

Abstract

The Anomalous Hall Effect (AHE) manifests as a transverse voltage proportional to magnetization in ferromagnetic materials under the application of a charge current, being an indispensable tool for probing magnetism, especially in nanoscale devices. However, the AHE primarily sensitizes to out-of-plane magnetization, thereby hindering its capacity to discern the in-plane magnetization, a characteristic prevalent in ferromagnetic films. Here we challenge this conventional understanding by demonstrating the in-plane magnetization-induced AHE in iron and nickel, two ubiquitous ferromagnets. This observation of the in-plane AHE is remarkable as it contradicts existing theories that forbid such phenomena in cubic crystal systems. We trace the origin of this unanticipated phenomenon to a hitherto unconsidered octupole of the anomalous Hall conductivity in the magnetization space, a mechanism we propose could enable the detection of in-plane AHE in a wide range of ferromagnetic materials. This work realizes the in-plane AHE in common ferromagnets by exploiting the anomalous Hall conductivity octupole, revealing a new physical origin of the AHE and promising to revolutionize the design of magnetic devices and sensors.