  We present our preliminary studies of an effective model of a superconductor
with short coherence length involving magnetic interactions. The Hamiltonian
considered consists of (i) the effective on-site interaction U, (ii) the
intersite magnetic exchange interactions (Jz, Jxy) between nearest-neighbors
and (iii) the intersite charge exchange term I, determining the hopping of
electron pairs between nearest-neighbor sites. In the analysis of the phase
diagrams and thermodynamic properties of this model for half-filling (n=1) we
have adopted the variational approach, which treats the on-site interaction
term exactly and the intersite interactions within the mean-field
approximation. One finds that the system considered can exhibit very
interesting multicritical behaviors (including tricritical, critical-end and
bicritical points) caused by the competition between magnetism and
superconductivity, even for n=1. Our investigations show that, depending on the
values of interaction parameters, the system at half-filling can exhibit three
homogeneous phases: superconducting (SS), (anti-)ferromagnetic (F) and
nonordered (NO). The transitions between ordered phases (SS, F) and the NO
phase can be first order as well as second order ones, whereas SS-F transition
is first order one. Temperature dependencies of the order parameters and
thermodynamic properties of the system at the sequence of transitions: SS-F-NO
with increasing temperature for J/I=0.3, U/I0 = 0.69 and n=1 are also
presented.
