Geometric Spin Degeneracy in Spin-Orbit-Free Compensated Magnets

TL;DR

This paper introduces a geometric framework explaining spin degeneracies in spin-orbit-free compensated magnets, highlighting how zero net magnetization can lead to protected band nodes without traditional symmetry.

Contribution

It develops a theoretical model showing spin degeneracies can be protected by geometric constraints rather than symmetry in compensated magnetic systems.

Findings

Zero net magnetization leads to spin-degenerate nodes.

The mechanism applies to weak-interaction regimes.

Provides a unified description of degeneracies in various magnetic phases.

Abstract

Compensated magnets with vanishing net magnetization can exhibit both pronounced spin splitting and unconventional band degeneracies. In altermagnets, such degeneracies are enforced by crystal and magnetic symmetries. In compensated ferrimagnets, however, they may arise even in the absence of the corresponding symmetry protection, raising a fundamental question about the origin of spin degeneracy in spin-orbit-free magnetic systems. Here, we develop a theoretical framework for spin-orbit-free compensated magnets in which spin degeneracies are protected by geometric constraints rather than by spin symmetry. We show that zero net magnetization imposes a strong condition for the emergence of nodes formed by formally spin-degenerate bands, even when no conventional spin symmetry is present. Our analysis, applicable in the weak-interaction regime, identifies a general mechanism for spin degeneracy beyond group-theoretical protection. The framework accounts for the unconventional spin degeneracies recently reported in compensated ferrimagnets and provides a unified description of band degeneracies across a broad class of magnetic phases with negligible spin-orbit coupling.