Zeeman-type spin splittings in strained d -wave altermagnets

Recently, altermagnetic materials have become rather attractive because such materials showcase the combined advantages of ferromagnets (e.g., spin current) and antiferromagnets (e.g., a 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 paper, we work with collinear spin point groups (SPGs) and use a 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 the 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 ${\mathrm{CoF}}₂, {\mathrm{LiFe}}₂{\mathrm{F}}₆$, and ${\mathrm{La}}₂{\mathrm{O}}₃{\mathrm{Mn}}₂{\mathrm{Se}}₂ d$-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.