Orbital Zeeman effect: Signature of charge in the carriers of ferromagnetism

By deriving the quantum hydrodynamic equations for an isotropic single-band ferromagnet in an arbitrary magnetic field, we find that a massive mode recently predicted splits under the action of the field. The splitting is a peculiarity of charged fermions and is linear in the field to leading order in $q$ bearing resemblance to the Zeeman effect in this limit, and providing a clear signature for the experimental observation of this mode.