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Magnetic materials show rich optical responses related to the magnetic order.These phenomena reflect the nature of their excitations, providing a powerfulprobe for the magnetic states and a way to control them. In recent years, suchstudies were extended to the optical control of spin current using nonlinearoptical response similar to the photogalvanic effect. However, neither acandidate material nor a general formula for calculating the photogalvanic spincurrent is known so far. In this work, we develop a general theory for thephotogalvanic spin current through a magnetic resonance process. Using thenonlinear response formalism, we find the nonlinear conductivity consists oftwo contributions that involve one and two magnon bands; the latter is acontribution unknown to date. We argue that the two-band process produces alarge photogalvanic spin current in the antiferromagnetic phase of bilayerCrI$_3$ and CrBr$_3$, whose resonance frequency can be tuned between GHz-THzrange by an external magnetic field. Our findings open a route to the studieson the photogalvanic effect of spin angular momentum in realistic setups.

Large photogalvanic spin current by magnetic resonance in bilayer Cr trihalides