Heisenberg Ferromagnet with Biquadratic Exchange

The usual Heisenberg Hamiltonian with bilinear exchange $-2J{\overrightarrow{\mathrm{S}}}_1·{\overrightarrow{\mathrm{S}}}_2$ has been extended to include a biquadratic term $-2\mathrm{}\alpha J{\left({\overrightarrow{\mathrm{S}}}_1·{\overrightarrow{\mathrm{S}}}_2\right)}^2$, with an adjustable parameter $\alpha$. A method equivalent to constant coupling was employed to calculate the effect of the biquadratic exchange term on the Curie temperature, magnetization, susceptibility, specific heat, and entropy for lattices with spin-1 atoms. As $\alpha$ goes from 0 to 1, the Curie temperature falls by a factor 2 to 3, while the asymptotic Curie temperature is reduced by the factor 2. The magnetization rises much more rapidly below $T_C$, and the specific heat has a peak and discontinuity several times higher for $\alpha =1\mathrm{}$. The curvature of the inverse susceptibility increases with $\alpha$, as does the entropy change taking place above $T_C$.