  In this work, we used the density functional calculation (DFT) implemented in
the Quantum Espresso software, using the approximations (GGA, GGA+U) to
illustrate the electronic and magnetic properties of the perovskite CaMnO$_3$.
It has been found that the CaMnO$_3$ perovskite is stable in the G-AFM phase.
When expecting the total and partial DOSs, a strong contribution of the d-Mn
states has been outlined. The Coulomb correction U and the site exchange
interaction J have been implemented and then we compared the two approximations
GGA and GGA+U. It is found that the GGA+U method leads to more accurate results
since this correction takes into account the bonding effects between different
atoms. To complete this study we performed the simulations under Monte Carlo
code based on the Metropolis algorithm. In fact, we have simulated the physical
quantities: magnetization, susceptibility, and specific heat of the studied
CaMnO$_3$ material as a function of temperature.
