The behavior of the compensation temperature of a mixed Ising ferrimagneticsystem on a square lattice in which the two interpenetrating square sublatticeshave spins $\sigma$ ($\pm 1/2$) and spins $S$ ($\pm 1,0$) has been studied withMonte Carlo methods. Our model includes nearest and next-nearest neighborinteractions, a crystal field and an external magnetic field. This model isrelevant for understanding bimetallic molecular ferrimagnetic materials. Wefound that there is a narrow range of parameters of the Hamiltonian for whichthe model has compensation temperatures and that the compensation point existsonly for small values of the external field.
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