Zeeman-type spin splittings in strained d-wave altermagnets

Recently, altermagnetic materials have become rather attractive because such materials showcase combined advantages of ferromagnets (e.g., spin current) and antiferromagnets (e.g., low stray field and ultrafast spin dynamics). Symmetry arguments imply that $d$-wave altermagnets may host strain-induced nonrelativistic Zeeman-type spin splittings (ZSSs), and a theoretical, numerical, and experimental justification of such phenomena are of high necessity. In the present work, we work with collinear spin point groups (SPGs) and use symmetry analysis to identify 15 SPGs that host strain-induced nonrelativistic ZSSs. These 15 SPGs coincide with the cases associated with $d$-wave alternating spin splittings reported in literature. We further corroborate our analysis by first-principles numerical simulations, which indicate that a shear strain of $2\%$ creates sizable nonrelativistic ZSSs of up to 177, 100, and 102 meV in CoF$_2$, LiFe$_2$F$_6$ and La$_2$O$_3$Mn$_2$Se$_2$ $d$-wave altermagnetic semiconductors, respectively. Our work suggests an alternative route toward creating spin current in altermagnets, which may be used to design altermagnetic-based spintronic devices.