Orbital Altermagnetism

Abstract: We introduce the concept of \emph{orbital altermagnetism}, a symmetry-protected magnetic order of pure orbital degrees of freedom. It is characterized with ordered anti-parallel orbital magnetic moments in real space but momentum-dependent orbital band splittings, analogous to spin altermagnetism. Using a minimal tight-binding model with complex hoppings in a square-kagome lattice, we show that such order inherently arises from staggered loop currents, producing a $d$-wave-like orbital-momentum locking. First-principles calculations show that orbital altermagnetism emerges independent of spin ordering in in-plane ferromagnets of CuBr$_2$ and VS$_2$, so that it can be unambiguously identified experimentally. On the other hand, it may also coexist with spin altermagnetism, such as in monolayer MoO and CrO. The orbital altermagnetism offers an alternative platform for symmetry-driven magnetotransport and orbital-based spintronics, as exemplified by large nonlinear current-induced orbital magnetization.