  We present a dynamical mean-field study of antiferromagnetic magnons in one-,
two- and three-orbital Hubbard model of square and bcc cubic lattice at
intermediate coupling strength. Weinvestigate the effect of anisotropy
introduced by an external magnetic field or single-ion anisotropy.For the
latter we tune continuously between the easy-axis and easy-plane models. We
also analyzea model with spin-orbit coupling in cubic site-symmetry setting.
The ordered states as well as themagnetic excitations are sensitive to even a
small breaking ofSU(2)symmetry of the model andfollow the expectations of
spin-wave theory as well as general symmetry considerations.
