Critical properties and exchange interactions of antiferromagnetic A-spinel lattice: a study through high-temperature series expansions

We derive high-temperature series expansions for the spin correlation functions of the A-spinel lattice. The development is extended to the order 6 in β=1/kBT with nearest-neighbour and next-nearest-neighbour interactions. The results are given for various neighbour correlation functions (up to the third). The behaviour with the temperature is presented. It is found that the variation of critical temperature is well represented by T(α)=T(0)[1-3.0725α] for values of α (α=J2/J1) in the range -1≤α≤0. T(0) is the critical temperature of the nearest-neighbour model. The critical region is studied by applying the Pade approximants method to the corresponding high-temperature series expansion of the magnetic susceptibility and the correlation length. The approach is applied to the experimental results of the particular system A-spinel CoCo2O4. The following estimates are obtained for the familiar critical exponents: γ=1.382±0.010 and ν=0.701±0.012