Theory of Harmonic Hall Responses of Spin-Torque Driven Antiferromagnets

TL;DR

This paper develops a comprehensive theoretical framework for analyzing harmonic Hall responses in antiferromagnets driven by spin-torque, enabling the separation of different torque contributions through magnetic field scans.

Contribution

It introduces a general theory for harmonic Hall responses in collinear antiferromagnets, including analytical expressions and validation through numerical simulations.

Findings

Analytical formulas for harmonic Hall signals as functions of magnetic field

Successful distinction of field-like and damping-like torque contributions

Experimental guidance demonstrated with $ ext{Fe}_2 ext{O}_3$ and NiO

Abstract

Harmonic analysis is a powerful tool to characterize and quantify current-induced torques acting on magnetic materials, but so far it remains an open question in studying antiferromagnets. Here we formulate a general theory of harmonic Hall responses of collinear antiferromagnets driven by current-induced torques including both field-like and damping-like components. By scanning a magnetic field of variable strength in three orthogonal planes, we are able to distinguish the contributions from field-like torque, damping-like torque, and concomitant thermal effects by analyzing the second harmonic signals in the Hall voltage. The analytical expressions of the first and second harmonics as functions of the magnetic field direction and strength are confirmed by numerical simulations with good agreement. We demonstrate our predictions in two prototype antiferromagnets, $\alpha-$Fe$_{2}$O$_{3}$ and NiO, providing direct and general guidance to current and future experiments.