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The thermodynamics properties of a ferromagnetic Heisenberg model with the exchange anisotropy of a spin-1 system in presence of single-ion anisotropy (D) and external magnetic field (h) are studied here using the pair approximation approach. We treat the model in three-dimensional lattice with coordination number z=6. Other coordination numbers have been also examined. Within this approximation based on Gibbs free energy, we investigate the effect of both single-ion and exchange coupling anisotropies on the thermodynamic quantities such as magnetization, entropy, heat capacity, susceptibility and entropy change as in-process measures. The objective is to describe magnetocaloric effect (MCE) and relative cooling power aiming to optimize them. We find some interesting phenomena in these quantities due to external magnetic field, exchange anisotropy and single-ion anisotropy. For conflicting interactions, re-entrance behavior can occur. Interestingly, high spin size as well as strong exchange or single-ion anisotropy can improve the MCE performances. PA method [8,9]. It is clear from the above matrix elements that the matrix representation of H ij in this base is symmetric. Therefore, we need to determine the eigenvalues by diagonalizing the matrix of H . ij After performing calculations, we find the following eigenvalues: E J D D J J 2.4. Critical temperature The Curie temperature T C can be found by linearization of self-consistent equation (20) when 0 l  and external magnetic field h=0, leading to: z z J J w 1 2 e 2e cosh e 2e 4 cosh 2e cosh , 2 7 D J D J D J D J

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We use the Pair Approximation method to analyze the magnetic and magnetocaloric behaviors of diluted mixed spin SA = 1 and spin SB = 1/2 with the anisotropic Heisenberg model, on a cubic lattice with coordination number z=6. Our system is described in presence of an external magnetic field; the phase diagram and thermodynamic properties related to the concentration of magnetic atom (A or B) and the single ion anisotropy are constructed and discussed. Special attention is paid to magnetocaloric properties provided by isothermal entropy change as well as the cooling capacity. These cooling power keys are plotted and discussed as a function of interaction anisotropy and magnetic component concentration of two sublattices ions A and B. Numerical results show a double peak structure in the entropy change curve and the inverse magnetocaloric effect related to the presence of the negative single-ion anisotropy.

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