Green's function approach of an anisotropic Heisenberg ferrimagnetic system

We have investigated the influence of the exchange anisotropy parameter on the magnetization, critical and compensation temperatures and susceptibility of the anisotropic Heisenberg ferrimagnetic system with the single-ion anisotropy under an external magnetic field using the double-time temperature-dependent Green's function theory. In order to decouple the higher order Green's functions, Anderson-Callen's decoupling and random phase approximations have been used. This model is useful for understanding the temperature dependence of total magnetization of Lithium-chromium ferrites Li0.5Fe1.25Cr1.25O4 for which negative magnetization is characteristic. We observe that the critical temperature increases when the exchange anisotropy increases. When the system is under an external magnetic field, one obtains the first-order phase transition where the magnetization jumps for all the values of the exchange anisotropy parameters.