  In This work, we apply the Monte Carlo simulations to study the magnetic
properties and compensation behavior of a core/shell double fullerene structure
X_60 where the symbol X can be assigned to any magnetic atom. We focus our
study on a system formed by a double sphere forming a core-shell. The two
spheres are containing the spins: S=1/2 in the core; and {\sigma}=1 in the
shell, respectively. In a first step, we investigate and discuss the
corresponding ground state phase diagrams in different planes. Also, we
illustrated the behavior of the magnetizations and the effect of the coupling
exchange interactions as well as the crystal field. The effect of the external
magnetic field, and the exchange coupling interactions on the hysteresis loops
have been inspected. To complete this study, we showed the existence of the
compensation temperature for the studied system.
