Orbital piezomagnetic polarizability of pure insulating altermagnets

The distinctive symmetry properties 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.