Anomalous crystal-field splitting in layered perovskites

Layered perovskites exhibit a variety of novel physical phenomena, many of which are closely related to the crystal-field (CF) splitting of the transition-metaldorbitals. However, several compounds (e.g. Sr₂IrO₄and Sr₂CrO₄) show an unexpectedly different sign of the crystal field splitting from the one inferred by the conventional CF theory. Whether this sign inversion is common for layered perovskites is not clear yet. In this work, we study the anomalous CF splitting in the A₂BL₄family by combining density functional theory calculations with low-energy tight-binding modeling based on Wannier functions. We show that in the compounds with such a sign inversion (explicit anomaly) the layered structure together with the compression of A-cubes triumphs over the local elongation of BL₆octahedra in determining the CF splitting. The results reveal that the anomalous CF splitting is a common feature for layered perovskites. This work sets an important caution mark about the application of the conventional CF theory to these materials.