A Universal Crystal-Field Design Principle for Orbital-Order-Driven Altermagnetism

Altermagnets combine collinear antiferromagnetic order with nonrelativistic spin splitting, enabling spintronic functionalities without relying on spin–orbit coupling. While staggered orbital ordering has recently emerged as an alternative route to altermagnetism, its generality has remained unexplored. Here, we establish a universal crystal-field design principle for orbital-order-driven altermagnetism. We show that structural relaxation consistently reconstructs the crystal-field landscape, activating a common $d_{xz}\mathrm{/}{d}_{yz}$ orbital manifold that drives spontaneous staggered orbital ordering and robust $d$-wave nonrelativistic spin splitting across transition-metal compounds spanning electron fillings from $d^1$ to $d^7$. By introducing a unified symmetry framework based on layer-dependent magnetic and orbital order parameters, we demonstrate how interlayer stacking determines whether the system realizes a bulk altermagnetic state or a globally compensated antialtermagnetic phase. Furthermore, we reveal that this symmetry-protected spin-split texture gives rise to highly anisotropic spin-polarized conductivities. Our results establish crystal-field engineering as a predictive design strategy for discovering and engineering orbital-order-driven altermagnets.