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.
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