Magnetic phase diagram of diluted spinel Zn1-xCuxCr2Se4 system

By using mean field theory, we have evaluated the nearest-neighbour and the next-neighbour super-exchange J1(x) and J2(x), respectively, for Zn1-xCuxCr2Se4 in the range 0≤x≤1. The intraplanar and the interplanar interactions are deduced. High-temperature series expansions 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. The magnetic phase diagram is deduced. A spin glass phase is predicted for intermediate range of concentration. The 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 values are comparable to those of the 3D Heisenberg model, and are insensitive to the dilution x