Magnetic Disorder as a First-Order Phase Transformation

The exchange interaction that gives rise to ordered magnetic states depends upon interatomic spacing. If the lattice is deformable, then a spontaneous distortion of the lattice will occur in the ordered state. We have calculated, in the molecular field approximation, the properties of a system in which the exchange energy dependence is given by ${T}_{c}={T}_{0}[1+\frac{\ensuremath{\beta}(v\ensuremath{-}{v}_{0})}{{v}_{0}}]$. ${T}_{c}$ is the Curie temperature appropriate to a lattice volume $v$ while ${v}_{0}$ is the equilibrium volume in the absence of magnetic interactions. The course of the magnetization with temperature of such a system depends upon the steepness $\ensuremath{\beta}$ of the exchange interaction dependence on interatomic distance, the compressibility $K$, and ${T}_{0}$. The behavior may be the usual second-order transition to paramagnetism, but it can in fact become a first-order transition with the properties usually associated thereto, e.g., latent heat and discontinuous density change. In the absence of an externally applied pressure, the transition will be of the first order if $\ensuremath{\eta}\ensuremath{\equiv}\frac{40NkK{T}_{0}{\ensuremath{\beta}}^{2}{[j(j+1)]}^{2}}{[{(2j+1)}^{4}\ensuremath{-}1]}g1$. In this inequality, $N$ is the number per unit volume of magnetic ions of angular momentum $j\ensuremath{\hbar}$ while $k$ is the Boltzmann constant.