Large photogalvanic spin current by magnetic resonance in bilayer Cr trihalides

Abstract: 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.