  Effect of rotationally-invariant Hund's rule coupling on a magnetism of
multiorbital Hubbard models is studied within a dynamical mean field theory
framework. Comparison of static magnetic susceptibilities and local densities
of states of two- and three-orbital models of a complete rotationally invariant
Coulomb interaction and a "density-density" Hartree type interaction shows the
different role of spin-flip interactions for different band fillings. In the
particle-hole symmetric case the Mott-Hubbard physics dominates due to the
strong effective Coulomb interaction, while for the multiple electronic
configurations away from half-filling (two electrons in the three band model)
the formation of local magnetic moments due to Hund's exchange interaction
becomes the most significant effect for itinerant magnetic systems. A shift of
the temperature of magnetic ordering due to the rotationally-invariant Hund's
rule coupling is found to be the largest in a three-orbital model with a
two-electron occupancy where the single particle spectrum is metallic and is
not sensitive to different forms of the Coulomb vertex. A larger enhancement of
the effective mass in a model with a rotationally-invariant interaction is
discussed. In the half-filled case we find a drastic change in the density of
states close to the Mott transition which is related to the spin-flip Kondo
fluctuations in a degenerate orbital case, while the corresponding shift of the
magnetic transition temperature is relatively small. It is shown that a change
in the ground state degeneracy due to a different symmetry of the Coulomb
interaction in the density-density model leads to a breakdown of the
quasiparticle peak at the Fermi level in the proximity of a Mott transition on
the metallic side. We discuss the relevance of rotationally-invariant Hund's
interaction in the transition metal magnetism.
