Magnetic Properties of Mg x Cu1−x Cr2O4 Spinels are Studied by Different Theoretical Methods

Abstract

The external magnetic field induced the reorientation of magnetization of a ferromagnetic (or antiferromagnetic) treated within the framework of many-body Green’s function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green’s functions. Magnetization and magnetic susceptibility are investigated when an external magnetic field is applied in (x-z)-plane. The mean field theory is applied to calculate the nearest neighbour and the next-neighbour super-exchange J 1(Cr−Cr) and J 2(Cr−(Mg(Cu)−O)−Cr), respectively, for the Mg x Cu1−x Cr2O4 in the range of 0 ≤ x ≤ 1. The intra-planar and the inter-planar interactions are deduced. The high-temperature series expansions (HTSEs) are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random-phase approximation (RPA). The magnetic-phase diagram is deduced. A spin-glass phase is predicted for intermediate range of concentration. The spin glass is obtained. The obtained results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The obtained values are comparable to those of 3D Heisenberg model.