Spin Group Symmetry Criteria For Unconventional Magnetism

TL;DR

This paper introduces a comprehensive symmetry-based framework for classifying and understanding unconventional magnetism, unifying even- and odd-parity magnets and revealing new mechanisms and candidate materials.

Contribution

It provides a unified spin space group classification for unconventional magnets, uncovering new mechanisms and enabling prediction of novel magnetic materials.

Findings

Classifies magnets into three spin texture types: collinear, coplanar, noncoplanar.

Identifies eight mechanisms for odd-parity and seven for even-parity magnets.

Predicts new candidate materials exhibiting these mechanisms.

Abstract

Unconventional magnetism has typically been classified into two fundamental classes: even-parity magnets (EPMs) and odd-parity magnets (OPMs). These two classes exhibit identical and opposite spin splittings, respectively, under momentum inversion, while both maintain symmetry-compensated magnetization. In this Letter, we present a unified spin space group-based framework that establishes comprehensive symmetry criteria for both classes. Our framework not only yields a complete classification of EPMs and OPMs but also uncovers a wealth of new symmetry-driven mechanisms for them. Specifically, we classify both classes into three types based on their spin textures: collinear (type-I), coplanar (type-II), and noncoplanar (type-III), and we demonstrate that both classes can be realized across collinear, coplanar, and noncoplanar magnetic orders. We identify eight distinct symmetry-driven mechanisms for OPMs and seven for EPMs, among which some paradigms of unconventional magnetism, for instance, altermagnets naturally emerge as one specific mechanism of EPMs. Using these established criteria, we identify numerous candidate materials from the Magndata database, realizing some new symmetry mechanisms for OPMs and EPMs. Our work establishes a foundational symmetry framework for understanding, predicting, and designing unconventional magnetic materials.