Nonlinear Photocurrent as a Hallmark of Altermagnet

The recent rise in interest in altermagnetism─a magnetic state distinct from ferromagnetism and antiferromagnetism─nessitates the development of a reliable probing method to distinguish it from other types of compensated magnetism. Here, we investigate nonrelativistic spin groups and relativistic magnetic groups to identify and categorize the permissible spin and charge photocurrents of compensated collinear magnets. Our results indicate that, in altermagnets, the charge and spin photocurrents exhibit a similar temperature profile due to their shared dependence on carrier relaxation effects, whereas in antiferromagnets, these currents behave in stark contrast. As a real-material example, we performed first-principles calculations of the altermagnetic phase of MnO and analyzed it using a simplified four-band model. We demonstrate that the normal injection current directly reflects the magnetic band geometry of altermagnets: the direction and magnitude of the injection current are delicately correlated with the interband Berry curvature and the alternating spin splitting of energy bands. We suggest that nonlinear photocurrent could serve as a promising probing tool to reveal the particular magnetic phase and band geometry of altermagnets.