Large photogalvanic spin current by magnetic resonance in bilayer Cr trihalides

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