On the Curie points and high temperature susceptibilities of Heisenberg model ferromagnetics

The first six coefficients in the expansion of the susceptibility χ, and its inverse, χ −1, in ascending powers of the reciprocal temperature, have been determined for the Heisenberg model of a ferromagnetic, for any spin value, S, and any lattice. The first five coefficients appropriate to the magnetic specific heat, C, have also been found. For the body-centred and face-centred cubic lattices, the χ and C coefficients are tabulated for half-integral S from 1/2 to 3. From these coefficients estimates have been made of the reduced Curie temperatures, θs c= k T c/J. It is found that for the simple, body-centred and face-centred cubic lattices the formula reproduces the estimated Curie temperatures fairly accurately. Here X=S(S+1) and z is the lattice coordination-number. It is found that, suitably scaled, the theoretical curves for inverse susceptibility against temperature above the Curie point are rather insensitive to the spin value and to the precise lattice structure. The ratio of their initial to their final gradients is approximately 0·3. A comparison is made with the experimental values of χ −1 for both iron and nickel. If iron is represented by the Heisenberg model with S=1, then the observed Curie temperature corresponds to a J value of 1·19×10−2 ev. Brief consideration is given to the use of the tabulated coefficients for antiferromagnetic problems.