  The Half-Metallic Ferromagnetic behavior of some double perovskites attracts
much interest. In this work, we studied the magnetic behavior of the double
perovskite Pb2FeReO6. The magnetic atoms are Fe and Re and have the spins S=5/2
and {\sigma}=1, respectively. In a first step, we provide a theoretical study
of the ground state phase diagrams .In fact, we present and discuss the stable
configurations from the all 6x3=18 possible configurations. Secondly, the
magnetic properties of this compound when varying different physical parameters
is carried out. Besides, we used Monte Carlo simulations (MCS), under the
Metropolis algorithm to provide the magnetic behavior of the studied system as
a function of the temperature, the crystal field, the exchange coupling
interactions and the external magnetic field. In addition, we studied and
discussed the critical temperature of the double perovskite Pb2FeReO6. To
complete our study, we presented and analyzed the hysteresis loops for specific
values of physical parameters.
