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arXiv:2609.10930

Hyperspin Altermagnets

Hai-Yang Ma, Yuanchang Li, Hu Xu, Shengbai Zhang, Jin-Feng Jia

cond-mat.mtrl-scicond-mat.otherquant-phSubmitted Sep 10, 2026• Announced Sep 11, 2026
arXivHTMLPDF

Abstract

The behavior of spin quantum in k-space is key to identifying altermagnets (AMs) as the third kind of fundamental collinear magnetism. In contrast, non-collinear 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 non-collinear magnets, we reveal it is a hyperspin, rather than the usual spin, that commutes with Hamiltonian. Unexpectedly, these non-collinear magnets should also show collinear spin-split bands in k-space like collinear AMs. We therefore classify such non-collinear 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 non-collinear magnets that may possess other kinds of conserved quantities.

Journal reference
Phys. Rev. Lett. 137, 116704 (2026)
DOI
10.1103/dnr2-gv31
Comments
6 pages, 2 figures, 1 table

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The behavior of spin quantum in k-space is key to identifying altermagnets (AMs) as the third kind of fundamental collinear magnetism. In contrast, non-collinear 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 non-collinear magnets, we reveal it is a hyperspin, rather than the usual spin, that commutes with Hamiltonian. Unexpectedly, these non-collinear magnets should also show collinear spin-split bands in k-space like collinear AMs. We therefore classify such non-collinear 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 non-collinear magnets that may possess other kinds of conserved quantities.
Recent years have seen a proliferation in investigations on Altermagnetism due to its exciting prospects both from an applications perspective and theoretical standpoint. Traditionally, altermagnets are distinguished from collinear antiferromagnets using the central concept of halving subgroups within the spin space group formalism. In this work, we propose the Fundamental Lemma of Altermagnetism (FLAM) deriving the exact conditions required for the existence of altermagnetic phase in a magnetic material on the basis of site-symmetry groups and halving subgroups for a given crystallographic space group. The spin group formalism further clubs ferrimagnetism with ferromagnetism since the same-spin and opposite-spin sublattices lose their meaning in the presence of multiple magnetic species. As a consequence of FLAM, we further propose a class of fully compensated ferrimagnets, termed as Alterferrimagnets (AFiMs), which can show alternating momentum-dependent spin-polarized non-relativistic electronic bands within the first Brillouin zone. We show that alterferrimagnetism is a generalization of traditional collinear altermagnetism where multiple magnetic species are allowed to coexist forming fully compensated magnetic-sublattices, each with individual up-spin and down-spin sublattices.
Magnetic order with vanishing net magnetization can produce non-relativistic spin-split bands, broadly categorized into even-parity altermagnets and odd-parity ppp-wave magnets. Here, we introduce a spin-bond theory that unifies these seemingly distinct phenomena into a single algebraic framework. We demonstrate that non-relativistic spin textures are fundamentally governed by two components of the electronic bond: unitary spin phases and Hermitian spin amplitudes. The unitary sector generates odd-parity p-wave and emergent spin-orbit-like textures, while the Hermitian sector generates even-parity spin fields, including the uniform ΓΓΓ-split and bond-structured altermagnetic limits. Beyond unifying known phases, our theory uncovers a mixed non-commuting regime that emerges when the unitary and Hermitian sectors fail to commute, revealing an underlying non-commuting spin-bond structure. This regime generates a non-coplanar spin texture characterized by an even-in-momentum transverse spin polarization, providing a direct spectroscopic fingerprint for spin- and angle-resolved photoemission spectroscopy. Furthermore, we establish that this synthetic spin-orbit coupling can be dynamically tuned by geometrically controlling the non-commutation of the bond sectors. By providing a microscopic foundation for such tuning, our theory paves the way for advanced applications, including field-free spin qubits.
Altermagnets, a newly classified type of collinear magnet, exhibit zero magnetization, akin to antiferromagnets, but have spin-split electronic bands, akin to ferromagnets. Their low-energy excitations are predicted to be magnons, but with linear energy-momentum dispersion, typical of antiferromagnets, and additional chiral splitting analogous to those of electronic bands. However, such predictions are made using linear spin wave theory, which considers infinitely long-lived noninteracting magnons. This study employs nonperturbative quantum many-body calculations, via tensor network algorithms, to find how a chiral magnon will acquire finite lifetime and how the bands will shift due to magnon-magnon interaction. Such corrections to noninteracting magnon bands could be detected by Raman scattering experiments, for which the recipe is provided. Although the same interaction effects are often described in magnetism by nonlinearity of the Landau-Lifshitz-Gilbert equation, direct comparison using altermagnetic magnons as the testbed, shows how such classical methods cannot fully reproduce the results of quantum many-body calculations.
Altermagnetism has recently emerged as a third fundamental branch of magnetism, combining the vanishing net magnetization of antiferromagnets with the high-momentum-dependent spin splitting of ferromagnets. This study provides a comprehensive real- and momentum-space analysis of topological phases in two-dimensional d-wave altermagnets. By employing a tight-binding Hamiltonian, we characterize the topological phase transition occurring at a critical intra-sublattice hopping strength (taCt_a^CtaC​). We examine the emergence of Dirac nodal points and the resulting Berry curvature singularities, supported by a visual analysis of pseudospin texture winding. Crucially, we analize spin splitting, effective altermagnetic strength, and investigate the transport implications of these phases, uncovering giant conductivity anisotropy and spin-dependent ``steering'' effects driven by group velocity distribution across the Fermi surface. Beyond bulk properties, we analyze the edge state topology in ribbon geometries through the lens of information-theoretic markers like fidelity-susceptibility and inverse participation ratio, offering a robust alternative to traditional Chern number calculations, without relying on translational symmetry. Our results demonstrate that the hybridization of edge states in ultra-narrow nanoribbons opens a controllable energy gap, a feature we exploit to propose a novel topological altermagnetic field-effect transistor design where ballistic and spatially spin-polarized transport can be electrostatically gated. This work establishes a theoretical and information-theoretic framework for ``edgetronics'' in altermagnetic materials, paving the way for next-generation, high-speed spintronic and ``spin-splitter'' logic devices and architectures.
Altermagnetism represents a type of collinear magnetism, that is in some aspects distinct from ferromagnetism and from conventional antiferromagnetism. In contrast to the latter, sublattices of opposite spin are related by spatial rotations and not only by translations and inversions. As a result, altermagnets have spin-split bands leading to unique experimental signatures. Here, we show theoretically how a d-wave altermagnetic phase can be realized with ultracold fermionic atoms in optical lattices. We propose an altermagnetic Hubbard model with anisotropic next-nearest neighbor hopping and obtain the Hartree-Fock phase diagram. The altermagnetic phase separates in a metallic and an insulating phase and is robust over a large parameter regime. We show that one of the defining characteristics of altermagnetism, the anisotropic spin transport, can be probed with trap-expansion experiments.
Altermagnets are a new class of symmetry-compensated magnets with large spin splittings. Here, we show that the notion of altermagnetism extends beyond the realm of Landau-type order: we study exactly solvable Z_{2} quantum spin(-orbital) liquids (QSLs), which simultaneously support magnetic long-range order as well as fractionalization and Z_{2} topological order. Our symmetry analysis reveals that in this model three distinct types of "fractionalized altermagnets (AM^{*})" emerge, which can be distinguished by their residual symmetries. Importantly, the fractionalized excitations of these states carry an emergent Z_{2} gauge charge, which implies that they transform projectively under symmetry operations. Consequently, we show that "altermagnetic spin splittings" are now encoded in a momentum-dependent particle-hole asymmetry of the fermionic parton bands. We discuss consequences for experimental observables such as dynamical spin structure factors and (nonlinear) thermal and spin transport.