The behavior of the compensation of a mixed spin-1 and spin-1/2 Heisenberg ferrimagnetic system on a square lattice is investigated theoretically by a two-time Green-function technique which takes into account the quantum nature of Heisenberg spins. The model includes the nearest and next-nearest neighbor interactions between spins, a crystal field and an external magnetic field. This model can be relevant for understanding the magnetic behavior of bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We study the spin-wave spectra of the ground state and investigate the effects of the next-nearest neighbor interactions, a crystal field and an external magnetic field on the compensation temperature. It is found that a compensation point appears and it is basically unchanged when the next-nearest-neighbor interaction between spin-1/2 is taken into account and exceeds a minimum value for other values in Hamiltonian fixed. The compensation temperature is influenced by the next-nearest-neighbor interaction between spin-1 and the external magnetic field and it is disappearing as these parameters exceed the trivial values.
