A tensorial approach to 'altermagnetism'

TL;DR

This paper introduces a tensorial framework to describe altermagnetism, a non-relativistic magnetic band splitting phenomenon, classifying altermagnets and linking them to other magnetic properties for better material identification.

Contribution

It develops a tensor-based classification of altermagnets within magnetic point groups, connecting altermagnetism to known bulk properties and aiding in material discovery.

Findings

Most altermagnets are also piezomagnetic and MOKE-active.

Provides a classification scheme for altermagnetic point groups.

Establishes criteria for identifying potential altermagnets.

Abstract

I present a tensorial approach to the description of $\vec{k}/-\vec{k}$-symmetric, time-reversal-odd splitting of electronic bands in magnetic materials, which can be of non-relativistic origin and was recently given the name of `altermagnetism'. I demonstrate that tensors provide a general framework to discuss magnetic symmetry using both spin groups and magnetic point groups, which have often been contrasted in recent literature. I also provide a natural classification of altermagnets in terms of the lowest-order tensorial forms that are permitted in each of the 69 altermagnetic point groups. This approach clarifies the connection between altermagnetism and well-known bulk properties, establishing that the vast majority of altermagnetic materials must also be piezomagnetic and MOKE-active, and provides a rational criterion to search for potential altermagnets among known materials and to test them when the magnetic structure is unknown or ambiguous.