Inherent Altermagnetism on regular hyperbolic lattices

TL;DR

This paper demonstrates that altermagnetism, characterized by momentum-dependent spin splitting without net magnetization, naturally occurs in certain hyperbolic lattices using extended tight-binding models.

Contribution

It extends Euclidean altermagnet models to hyperbolic lattices and shows that spin splitting can be inherently present in these non-Euclidean structures.

Findings

Next-nearest neighbor hopping induces spin splitting in bipartite hyperbolic lattices.

Certain hyperbolic lattice families exhibit spin splitting, indicating inherent altermagnetism.

Hyperbolic band theory requires four-dimensional momentum space for classification.

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.