Heisenberg Ferromagnet with Biquadratic Exchange

The usual Heisenberg Hamiltonian with bilinear exchange $\ensuremath{-}2J{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{2}$ has been extended to include a biquadratic term $\ensuremath{-}2\ensuremath{\alpha}J{({\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{2})}^{2}$, with an adjustable parameter $\ensuremath{\alpha}$. 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 $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}=1$. The curvature of the inverse susceptibility increases with $\ensuremath{\alpha}$, as does the entropy change taking place above ${T}_{C}$.

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