Biquadratic exchange and first-order ferromagnetic phase transitions

Abstract

We have calculated some properties of a ferromagnet using a Heisenberg Hamiltonian with a biquadratic exchange term added. The constant-coupling approximation was employed. If the strength of the biquadratic exchange relative to the bilinear is given by a dimensionless parameter $\ensuremath{\alpha}$, there is a critical value ${\ensuremath{\alpha}}_{c}$ at which the phase transition changes character from second order for $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$ to first order for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$. The spontaneous magnetization, the exchange energy, and the spin-correlation function show discontinuous jumps at $\ensuremath{\alpha}={\ensuremath{\alpha}}_{c}$ and unstable behavior for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$.