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arXiv · 2605.10602

Inherent Altermagnetism on regular hyperbolic lattices

Eric Petermann·Kristian Mæland·Haye Hinrichsen·Björn Trauzettel
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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 Poincar\'e disk. Using hyperbolic crystallography and hyperbolic band theory, we show that the inclusion of next-nearest neighbor hopping is sufficient to induce spin splitting in bipartite hyperbolic lattices. While certain families and special cases of hyperbolic lattices remain antiferromagnetic, we identify an entire family and a special case that show spin splitting in this framework. Hence, altermagnetism is inherent to certain hyperbolic lattices. Since 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.

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Eric Petermann, Kristian Mæland, Haye Hinrichsen, Björn Trauzettel. 2026-05-11. Inherent Altermagnetism on regular hyperbolic lattices. https://arxiv.org/abs/2605.10602

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