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Inherent altermagnetism in minimal tight-binding models of regular hyperbolic lattices

Eric Petermann*, Kristian Mæland, Haye Hinrichsen, and Björn Trauzettel

  • *Contact author: eric.petermann@uni-wuerzburg.de
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Phys. Rev. Research 8, 033359 – Published 24 September, 2026

DOI: https://doi.org/10.1103/h2ys-c3rz

Abstract

Altermagnets are a novel class of magnetic systems characterized by their momentum-dependent spin splitting without net magnetization. In this work, we extend established Euclidean tight-binding models of altermagnets to regular hyperbolic lattices in two spatial dimensions defined on a discretized Poincaré disk. Using hyperbolic crystallography and Abelian hyperbolic band theory, we show that the inclusion of next-nearest-neighbor hopping is sufficient to induce spin splitting in minimal tight-binding models of bipartite hyperbolic lattices. While certain families and special cases of hyperbolic lattices remain antiferromagnetic, we identify an entire family and a special case that generically permit spin splitting in this framework. Hence, altermagnetism is inherent to certain hyperbolic lattices. Since Abelian hyperbolic band theory yields a momentum space that is at least four dimensional, we classify the leading spin-splitting harmonics using four-dimensional atomic orbitals. As an outlook, we apply non-Abelian hyperbolic band theory to the {10,5} lattice. Although its Abelian spectrum is spin degenerate, two selected higher-genus supercells exhibit spin splitting. This finding suggests that spin degeneracy does not necessarily persist within all translation representation sectors.

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Phys. Rev. Research 8, 033359– Published 24 September, 2026
  • Received 11 May 2026
  • Accepted 1 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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