Controlling magnons in magnetic insulators is key to their application in spintronics. In this work, we study the magnon spin photocurrent in effective spin models for ${\mathrm{Cr}}_2{\mathrm{O}}_3$, a material known for its magnetoelectric (ME) effect. Using the nonlinear response theory, we show that the magnon spin current can be generated by both linearly and circularly polarized electromagnetic waves via one-magnon processes. For linearly polarized waves, the spin current arises even in the absence of a static magnetic field. In contrast, circularly polarized waves induce a spin current only when a static magnetic field is present, and the current reverses its direction upon inversion of the field. The sensitivity to the external magnetic field and the contrasting behaviors under linearly and circularly polarized electromagnetic waves delineate the spin photocurrent from other competing contributions, such as spin pumping and inhomogeneous heating, facilitating experimental verification. Our results show that ${\mathrm{Cr}}_2{\mathrm{O}}_3$ is an interesting candidate for the experimental investigation of the magnon photocurrent.

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• Magnonics
• Spin current
• Spin optoelectronics
• Holstein-Primakoff method