A Universal Framework for Controlling Non-Relativistic Spin Splitting

Abstract: Non-relativistic spin splitting in antiferromagnets has recently attracted considerable attention. Here we present a universal framework for controlling such spin splitting by identifying and manipulating the key atomic distortions that govern it through external perturbations. We demonstrate this concept by tuning the spin-splitting energy in three representative materials with diverse symmetries, inversion-symmetric MnF$_2$, ferroelectric BaCuF$_4$, and LaMnO$_3$/RMnO$_3$ superlattices. Our results emphasize the essential role of higher-order magnetic multipoles and the intrinsic structure-spin correlations in these systems, thereby advancing current efforts to control spin splitting in real materials and motivating future experimental studies.