Quantum metric induced magneto-optical effects in $\mathcal{PT}$-symmetric antiferromagnets

The magneto-optical effects (MOEs), as a fundamental physical phenomenon, can reveal the electronic structures of materials. The related probing methods are widely used in the study of magnetic materials. However, space-time inversion ($\mathcal{PT}$) symmetric antiferromagnets were previously believed to be magneto-optically inactive. Here, we point out that this traditional understanding is incorrect. Based on our generic formulas and symmetry analysis, we find that in $\mathcal{PT}$-symmetric antiferromagnets, it is the quantum metric, i.e., the real part of the quantum geometry, that induces MOEs. Combining a tight-binding model and first-principles calculations, we confirm this observation by showing MOEs in the $\mathcal{PT}$-symmetric antiferromagnet. Our work demonstrates that $\mathcal{PT}$-symmetric antiferromagnets previously thought to lack MOEs can indeed exhibit MOEs and greatly broaden the research on MOEs.