Magnetic Disorder as a First-Order Phase Transformation

TLDR

The exchange interaction that drives magnetic ordering depends on interatomic spacing, so a deformable lattice undergoes spontaneous distortion in the ordered state, and the temperature dependence of magnetization is governed by the steepness β of this dependence, the compressibility K, and the zero‑field Curie temperature T0, as illustrated by experimental studies of the first‑order transition in MnAs. Using a molecular‑field approximation, the authors express the Curie temperature T_c as a function of lattice volume v relative to the equilibrium volume v0, and derive an inequality involving the parameter η, the ion density N, Boltzmann constant k, and the exchange‑distance steepness β that predicts whether.

Abstract

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 $\ensuremath{\eta}\ensuremath{\equiv}\frac{40NkK{T}_{0}{\ensuremath{\beta}}^{2}{[j(j+1)]}^{2}}{[{(2j+1)}^{4}\ensuremath{-}1]}>1$. 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.We have reviewed the experimental evidence on the nature of the first-order magnetic transition in MnAs. We find that this evidence indicates the transition to be one from ferromagnetism to paramagnetism rather than ferromagnetism to antiferromagnetism as has been generally assumed. Application of the theory noted above gives $\ensuremath{\eta}=2$ for this transition. In addition, we derive a value for the volume strain sensitivity, $\ensuremath{\beta}=19$ and infer the compressibility to be 2.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{2}$/d.