Rigid-Body Anisotropy in Noncollinear Antiferromagnets

TL;DR

This paper develops a microscopic theory linking spin-orbit coupling and rigid-body spin order rotation to characterize anisotropy effects in noncollinear antiferromagnets, surpassing traditional symmetry methods.

Contribution

It introduces a group representation approach using tensor basis functions to systematically describe anisotropy effects in complex magnetic systems.

Findings

Successfully applied to Mn3Sn and Mn3Ir

Accurately captures anisotropy energy and Hall conductivity dependencies

Provides a generalized framework for broader magnetic anisotropy phenomena

Abstract

Characterizing the anisotropic structure in noncollinear antiferromagnets is essential for antiferromagnetic spintronics. In this work, we provide a microscopic theory linking the anisotropy effects induced by the rigid-body rotation of spin order to spin-orbit coupling. Our method goes beyond the conventional magnetic group theory, offering a concise yet powerful tool to characterize diverse anisotropy effects in complex magnetic systems. Using the group representation theory of the spin group, we obtain a set of basis functions formed from tensor elements of spin-orbit vector--which originates from spin-orbit coupling and is tied to the rigid-body rotation of the spin order--to systematically describe the structure of anisotropy effects. As a concrete example, we apply our framework to coplanar antiferromagnets Mn$_3$Sn and Mn$_3$Ir, demonstrating that the corresponding basis functions can well capture both the geometric and magnitude dependencies of the magnetic anisotropy energy and anomalous Hall conductivity. Finally, we discuss the generalization of our framework to broader classes of anisotropy phenomena in magnetic systems.