Optical Response Beyond Magnetic Symmetries
The optical response of magnetic materials is conventionally classified through magnetic space groups (MSGs), where spin and lattice are locked by the relativistic spin-orbit interaction. However, most optical observables are governed primarily by nonrelativistic physics, and thus a purely MSG-based description can overlook important insights. Here we systematically show that spin-space groups (SSGs), which operate at the nonrelativistic level, provide a broader and more predictive framework for analyzing a variety of optical responses of magnets. Focusing on linear optical absorption, we derive the transformation rules imposed by SSGs and show that they generate effective real-space point groups, which can enforce relations among charge response coefficients that are absent from conventional MSG analysis. We illustrate the basic principle in a Lieb-lattice altermagnet model with tunable spin-orbit coupling, where SSG predictions on the linear dichroism remain remarkably accurate even when relativistic band splittings become sizable. We further establish the predictive power of this framework through first-principles calculations on two altermagnetic candidates: the actinide UCr2Si2C, where the optical absorption remains nearly isotropic despite its strong spin-orbit coupling and the pronounced anisotropy apparent from magnetic symmetries, and the transition-metal fluoride RbMnF4, where birefringence is confined to a single plane by symmetries emerging exclusively from SSGs. Finally, we extend the concept to the spin Hall response of the coplanar noncollinear antiferromagnet ScMnO3, where SSGs explain the hierarchy of calculated spin Hall coefficients, demonstrating their direct relevance to spintronics as well.