Orbital piezomagnetic polarizability of pure insulating altermagnets in two dimensions

The distinctive symmetry properties of pure altermagnets make them natural candidates for piezomagnetism. Previous work motivated by the piezomagnetic properties of altermagnets has primarily focused on the spin magnetization response to applied strain. In this paper we study orbital piezomagnetic effects–the orbital magnetization response to applied strain–in minimal lattice models of pure insulating altermagnets in two dimensions. We obtain general microscopic expressions for the orbital magnetization in the presence of strain, as well as the orbital piezomagnetic polarizability, i.e., the defining response characteristic of pure altermagnets. We apply these expressions to three specific tetragonal lattice models, two corresponding to $d$-wave altermagnets and one describing a $g$-wave altermagnet. Whereas the $d$-wave altermagnets are associated with a linear piezomagnetic polarizability, the $g$-wave altermagnet exhibits a nonlinear piezomagnetic effect. Our analysis reveals how the polarizabilities are related to and determined by the Berry curvature of the occupied bands. Connections to materials of current interest are discussed.

💡 Research Summary

In this work the authors develop a comprehensive theory of orbital piezomagnetism in two‑dimensional pure insulating altermagnets. Altermagnets are collinear magnets with fully compensated sublattice moments; unlike ordinary antiferromagnets they display a non‑uniform, non‑relativistic Zeeman‑like spin splitting that is dictated by crystal symmetry. “Pure” altermagnets are defined by magnetic space groups that forbid any net magnetization and any anomalous Hall response, yet they can host non‑trivial Berry‑curvature structures such as mirror Chern bands or topological nodal crossings. The central question addressed is whether external strain can unlock these hidden topological features and generate an orbital magnetization, i.e., a piezomagnetic response that is purely orbital in origin (the spin contribution vanishes in the insulating regime).

The paper begins by constructing a minimal tight‑binding description on a bipartite lattice with two magnetic sublattices (A and B). The electron operators (c_{k\alpha\sigma}) are grouped into a four‑component spinor, and the Bloch Hamiltonian is written as
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