Magnetic phase diagrams of the spinels AB2xGa2−2xO4 (A = Zn, Co; B = Al, Cr) systems

The magnetic properties of the spinels CoAl2xGa2−2xO4 and ZnCr2xGa2−2xO4 systems in the range 0 ≤ x ≤ 1 have been studied by mean field theory and high-temperature series expansions. By using the first theory, we have evaluated the nearest neighbour and the next-neighbour super-exchange interaction J1(x) and J2(x), respectively, for the first systems in the range 0 ≤ x ≤ 1 and J1(x = 1), J2(x = 1) for the second system. The intra-planar and the inter-planar interactions are deduced. The corresponding classical exchange energy for magnetic structure is obtained for the first system.The second theory have been applied in the spinels CoAl2xGa2−2xO4 and ZnCr2xGa2−2xO4 systems, combined with the Padé approximants method, we have obtained the magnetic phase diagrams (TN versus dilution x) in the range 0 ≤ x ≤ 1. The obtained theoretical results are in agreement with experimental ones obtained by magnetic measurements and Mössbauer spectroscopy. The threshold percolation in the second system is xp ≈ 0.4. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) are deduced in the range 0 ≤ x ≤ 1.