Magnetic properties of the spinel systems ACr2X4 (A = Zn, Cd, Hg; X = S, Se)

The magnetic properties of the spinels systems Zn1−xCdxCr2Se4 and Hg1−xCdxCr2S4 have been studied by mean-field theory and high-temperature series expansions in the range 0 ≤ x ≤ 1. The nearest neighbour and the next-nearest-neighbour super-exchange interaction J1(x) and J2(x) respectively, are calculated for the two systems, using the first theory in the range 0 ≤ x ≤ 1. The intra-planar and the inter-planar interactions are deduced. The corresponding classical exchange energy for the magnetic structures is obtained.The second theory has been applied to the spinel systems Zn1−xCdxCr2Se4 and Hg1−xCdxCr2S4, combined with the Padé approximants method, to determine the magnetic phase diagrams (TC versus dilution x) in the range 0 ≤ x ≤ 1. The obtained theoretical results are in agreement with the experimental ones obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ  ) and with the correlation lengths (vv) are deduced for the two systems in the ordered phase.