  In this work, we study the equiatomic quaternary Heusler Alloy CoFeCrP using
two methods: DFT and Monte Carlo simulations. The DFT method allowed us to
illustrate the structural, electronic and magnetic properties of this alloy.
The ground state phase diagrams have been presented to show the stable
configurations in different physical parameter planes. On the other hand, the
Monte Carlo simulations, performed under the Metropolis algorithm, permitted to
deduce the critical the behavior of the equiatomic quaternary Heusler alloy
CoFeCrP. The structural properties results show that the phase of type I, of
this alloy is the most stable configuration. In addition, the band structures,
and density of states calculations results show that this compound exhibits a
half-metallic character with a 100 % of spin polarization (SP) at the
Fermi-level. The total magnetic moment of the Heusler compound is found to be
4.00 mu_B. Moreover, it is found that the Slater-Pauling is well described for
this alloy. Our results show that this material is a potential candidate for
the spintronic applications. This is due to its half-metallicity, its high spin
moments, its complete SP polarization and its high Curie temperature.
