  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.
