Orbital-Selective Mott Transition and Correlation-Amplified Charge Ordering in the Altermagnet CsCr$_2$S$_2$O

Altermagnet CsCr$_2$S$_2$O undergoes a Verwey-type metal-to-insulator transition (MIT) driven by lattice distortion and a stripe charge order on the Cr sublattice, reminiscent of the physics in Fe$_3$O$_4$. However, atomic distortions occur exclusively at the ligand sites rather than the Cr sites. What drives such a pronounced charge imbalance between Cr sites thus remains a mystery. Utilizing DFT+DMFT calculations, we identify an orbital-selective Mott transition, which leaves the correlated metallic $d_{yz}$ orbital governing the low-energy physics. We demonstrate that S-site distortions trigger an initial, tiny charge asymmetry between Cr sites via Cr-$d_{yz}$ and S-$p$ orbital hybridization. Crucially, this asymmetry is significantly amplified by dynamical electronic correlations, resulting in a large discrepancy in both the charge and electron correlations of the Cr-$d_{yz}$ orbital between distinct Cr sites. This further induces a substantial differentiation in local spin polarizations in the altermagnetic state, ultimately driving the MIT. In contrast, we predict that replacing S with Te weakens this correlation-amplification effect and fails to induce an MIT due to weaker electron correlations. Our findings demonstrate that many-body effects can drastically amplify ligand instabilities to reshape the electronic structure of altermagnets, highlighting that ligand engineering is of paramount importance for realizing robust metallic altermagnetism.