  Spin-only approaches to anisotropic effects in strongly interacting materials
are often insufficient for systems close to the Mott regime. Within a model
context, here the consequences of the low-symmetry relevant
Dzyaloshinskii-Moriya (DM) interaction are studied for strongly correlated, but
overall itinerant, systems. Namely, we investigate the Hubbard bilayer model
supplemented by a DM term at half filling and in the hole-doped regime. As an
add-on, further results for the two- impurity Anderson model with DM
interaction are also provided. The model Hamiltonians are treated by means of
the rotational invariant slave boson technique at saddle point within a
(cellular) cluster approach. Already small values of the anisotropic
interaction prove to have a strong influence on the phases and correlation
functions with increasing U. An intriguing metallic spin-flop phase is found in
the doped bilayer model and a reduction of the RKKY exchange in the
two-impurity model.
