Orbital magnetic field effect on spin waves in a triangular lattice tetrahedral antiferromagnetic insulator

We theoretically study the effect of a uniform orbital magnetic field on spin waves in a triangular lattice tetrahedral antiferromagnetic insulator without spin–orbit coupling. Through symmetry analysis and microscopic calculation, we show that the optical spin wave mode at the Brillouin zone center can acquire a small orbital magnetic moment, although it exhibits no magnetic moment from the Zeeman coupling. Our results are potentially applicable to intercalated van der Waals materials and twisted double-bilayer graphene.