Inherent Altermagnetism on regular hyperbolic lattices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911671684956160 |
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| author | Petermann, Eric Mæland, Kristian Hinrichsen, Haye Trauzettel, Björn |
| author_facet | Petermann, Eric Mæland, Kristian Hinrichsen, Haye Trauzettel, Björn |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10602 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inherent Altermagnetism on regular hyperbolic lattices Petermann, Eric Mæland, Kristian Hinrichsen, Haye Trauzettel, Björn Mesoscale and Nanoscale Physics Strongly Correlated Electrons High Energy Physics - Theory 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 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. |
| title | Inherent Altermagnetism on regular hyperbolic lattices |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.10602 |