Nonlinear photocurrent as a hallmark of altermagnet

The recent rise of interest in altermagnetism – a novel magnetic state distinct from ferromagnetism and antiferromagnetism – necessitates 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 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 the first-principles calculations of the altermagnetic phase of MnO and analyzed it using a simplified four-band model. We demonstrate the normal injection current directly reflects the unique magnetic band geometry of altermagnets: the direction and magnitude of the injection current are delicately correlated with the inter-band Berry curvature and the alternating spin splitting of energy bands.