Optical signatures of spin symmetries in unconventional magnets

Abstract: The concept of spin symmetries has gained renewed interest as a valuable tool for classifying unconventional magnetic phases, including altermagnets and recently identified p-wave magnets. In this work, we show that in compounds with weak spin-orbit coupling, the dominant spin and charge photoresponse is determined by spin group rather than the conventional magnetic group symmetry. As a concrete realization we consider the nonlinear shift photocurrent in Mn$_5$Si$_3$, a material that features the two possible classes of unconventional p-wave magnetism in the form of two competing spin structures, a coplanar and non-coplanar one. While both are predicted to generate shift currents based on magnetic symmetry considerations, only the non-coplanar configuration survives the spin symmetry requirements. This is numerically confirmed by our $\textit{ab-initio}$ calculations, providing a protocol to experimentally identify the spin configuration of this promising material in photogalvanic or transport measurements.