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Based on the density functional theory and the Monte Carlo Simulation (MCS), the structural, the electronic and the magnetic properties of Sr 2 TiMoO 6 double perovskite have been studied with (GGA), (GGA + U) and (GGA + U + SOC) approaches. The lattice parameter, the band structure and the electronic densities of states have been analyzed. Furthermore, the results show a half-metallic behavior of the compound with (GGA + U) . By the energy calculation, Sr 2 TiMoO 6 oxide shows an antiferromagnetic ordering. The exchange coupling of Sr 2 TiMoO 6 has been also computed in order to investigate the magnetic properties by using MCS in the framework of the Ising model. Interesting phenomena have been obtained such as the first-order transitions and multiple hysteresis loops. These results make Sr 2 TiMoO 6 a promising candidate for spintronic applications. [ABSTRACT FROM AUTHOR]