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Prototypes of Nonrelativistic Spin Splitting and Polarization in Symmetry Broken Antiferromagnets

Xiuwen Zhang1,*,†, Jia-Xin Xiong1,*, Lin-Ding Yuan2, and Alex Zunger1,‡

  • *These authors contributed equally to this work.
  • †Contact author: xiuwen.zhang@colorado.edu
  • ‡Contact author: alex.zunger@colorado.edu
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Phys. Rev. X 15, 031076 – Published 25 September, 2025

DOI: https://doi.org/10.1103/mrzv-wmcf

Abstract

Antiferromagnets that break both space-time reversal and translation-spin-rotation symmetries were recently predicted [L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Phys. Rev. B 102, 014422 (2020)] to possess splitting between the otherwise spin-degenerate energy bands even without the relativistic spin-orbit coupling (SOC). Here, we point out that such nonrelativistic spin splitting (NRSS)—in particular, “spin splitting type 4” (SST-4) symmetry-broken antiferromagnets—can be divided into subgroups having distinct patterns of spin splitting and spin textures, depending on additional auxiliary symmetries of spin interconversion and polarity. These SST-4 subgroups include the α-type (no spin-interconverting symmetry) having spin splitting at the Brillouin zone center, as well as the β subgroup in which a rotation symmetry is applied and determines the alternating spin texture and the γ subgroup having exclusively reflection spin-interconverting symmetry. Unlike ferrimagnets, the α-type compounds are shown to have tiny net magnetization at finite temperature and thus avoid the adverse effect of the stray field. The α and β subgroups can be either polar or nonpolar, whereas the γ subgroup is polar only, providing a basis for possible switching by external fields. The combination of NRSS-enabling and auxiliary symmetries is used here as a filter for identifying previously synthesized compounds as specific prototypes. Their characteristic splitting and spin polarization are calculated by density functional theory to the benefit of potential future experimental testing. Interesting results are as follows: (i) SOC-independent NRSS can exceed the magnitude of the SOC-induced Rashba and Dresselhaus spin splitting in semiconductors. (ii) Examples of predicted α-type insulating compounds include BiCrO3 (nonpolar) and Mn2ScSbO6 (polar), the latter having spin splitting of 158 meV and 160 meV in the valence and conduction bands, respectively. (iii) The β-type (Cu2Y2O5 and FeF2) and γ-type compounds (Mn4Nb2O9 and FeScO3) are distinguished both by their auxiliary symmetries and polarity. The spin textures of γ-type compounds are mirror reflected with spin degeneracy of the wave vectors on that mirror. These observations will likely broaden the experimental playing field of NRSS physics significantly.

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Antiferromagnets are materials where neighboring atomic magnetic moments point in opposite directions, canceling out overall magnetization. In conventional Néel antiferromagnets, electrons with different spins occupy different energy levels (spin bands); these bands are degenerate in the absence of spin-orbit coupling, a relativistic effect. Previously, we designed collinear antiferromagnets where spin splitting can occur without spin-orbit coupling by breaking two key symmetries: space-time reversal and translation-spin rotation. These special cases form a class we call nonrelativistic spin splitting. Here, we uncover additional “auxiliary symmetries,” such as the ability to interchange opposite-moment sublattices and the presence of polarity, and use them to classify different patterns of spin splitting and polarization.

We classify symmetry-broken collinear antiferromagnets into three subgroups: α type, which lacks spin-interconverting symmetry; β type, which has rotational symmetry; and γ type, which has exclusive mirror symmetry. Using density functional theory calculations, we identify example materials for each subgroup and analyze their spin-polarization patterns. In β-type materials (altermagnets), the spin polarization alternates, while in γ-type materials it is mirror reflected. α-type materials show an unexpected remarkable spin splitting in the center of the Brillouin zone, a fundamental region of the material’s momentum space. We further distinguish α-type antiferromagnets from compensated ferrimagnets by calculating how their total magnetization responds to changes in perturbed electronic occupation. We also find that polarity plays a role in enabling electric switching, with α and β types being either polar or nonpolar, and γ type always being polar.

These results show that auxiliary symmetry is a powerful tool for predicting and controlling spin behavior in antiferromagnets. By revealing how different symmetry patterns produce distinct electronic properties, our work provides a road map for discovering new materials for spintronics.

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Phys. Rev. X 15, 031076– Published 25 September, 2025
  • Received 4 October 2024
  • Revised 1 May 2025
  • Accepted 21 July 2025
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