The magnetic properties (phase diagram and magnetization) of a ferrimagnetic system, consisting of two magnetic sublattices (A and B ) with different spins (S_A = ½ and S_B = ½ ) and different inter-actions coupling together, are investigated within the framework of the effective -field theory with correlations. Furthermore, each considered sublattice has in-plane triangular symmetry requiring a coordination number of magnetic atoms z = 6 which may affect the general magnetic behavior of the system.

The effects of crystal-field interaction D_B in the sublattice B (with S_B i  1/₂) on the magnetic properties are examined in detail. Because of the higher coordination number and different kinds of interactions acting on the system of spins, we find a number of interesting phenomena: (i) the temperature dependence of the total magnetization shows many characteristic behaviors depending on D_B and S_B, (ii) the presence of compensation points is conditioned by the given values of different parameters while the second order transition temperatures are studied according to each specific circumstance. The aspects of interest in this study is mainly the higher coordination number of magnetic species and the realistic interactions which are taken into account. This model can be relevant for understanding the magnetic behaviors of the new class of lamellar oxides AMO₂ (A = Li, Na, Na,..; M = Ni, Fe, Co,..).