Electrical control of spin photocurrent in a magnetoelectric oxide Cr$_2$O$_3$

Controlling magnetism by electric field or current is a central topic in spintronics. In this work, we argue that the magnon spin photocurrent can also be controlled by the electric field in magnetoelectrics. Taking Cr$_2$O$_3$ as an example, we demonstrate how the spin current is modified by the electric field, using nonlinear response theory. We find that the Dzyaloshinsky--Moriya interaction induced by the applied field plays a key role in modifying spin-current conductivity, which exhibits pronounced anisotropy with respect to the light polarization. In particular, both the resonance frequency and the peak intensity show distinct dependences on the external electric field $E$, demonstrating electrical control of the spin photocurrent. In addition, we show that the two-magnon processes give rise to a continuum spectrum, a consequence of the field-induced spin canting. These results show that Cr$_2$O$_3$ is a promising platform for realizing electrically tunable spin photovoltaic effect.