  We study the influence of ferromagnetic nonlocal exchange on correlated
electrons in terms of a $SU(2)$-Hubbard-Heisenberg model and address the
interplay of on-site interaction induced local moment formation and the
competition of ferromagnetic direct and antiferromagnetic kinetic exchange
interactions. In order to simulate thermodynamic properties of the system in a
way that largely accounts for the on-site interaction driven correlations in
the system, we advance the correlated variational scheme introduced in [M.
Sch\"uler et al., Phys. Rev. Lett. 111, 036601 (2013)] to account for
explicitily symmetry broken electronic phases by introducing an auxiliary
magnetic field. After benchmarking the method against exact solutions of a
finite system, we study the $SU(2)$-Hubbard-Heisenberg model on a square
lattice. We obtain the $U$-$J$ finite temperature phase diagram of a
$SU(2)$-Hubbard-Heisenberg model within the correlated variational approach and
compare to static mean field theory. While the generalized variational
principle and static mean field theory yield transitions from dominant
ferromagnetic to antiferromagnetic correlations in similar regions of the phase
diagram, we find that the nature of the associated phase tranistions differs
between the two approaches. The fluctuations accounted for in the generalized
variational approach render the transitions continuous, while static mean field
theory predicts discontinuous transitions between ferro- and
antiferromagnetically ordered states.
