Theory of spin-fluctuation resistivity near the critical point of binary alloys and antiferromagnets

Abstract

We present a simple theory of electrical resistivity $\ensuremath{\rho}(T)$ due to critical fluctuations in the vicinity of the N\'eel point of antiferromagnets and the order-disorder transition temperature of binary alloys. In the disordered phase, it is shown that the singular part of $\frac{\ensuremath{\partial}\ensuremath{\rho}}{\ensuremath{\partial}T}$ varies as either plus or minus the singular part of the specific heat for $T\ensuremath{\rightarrow}{T}_{N}^{+}$. The sign is determined by Fermi-surface geometry and the superlattice vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{Q}}$ of the ordered state. The temperature range, somewhat above ${T}_{N}$, where short-range ($R\ensuremath{\ll}\ensuremath{\xi}$) correlations are no longer dominant is also considered. Numerical results are given for both the short-range and long-range temperature regimes. In the ordered state, it is concluded that the long-range order does not enter $\ensuremath{\rho}(T)$ directly for $T\ensuremath{\rightarrow}{T}_{N}^{\ensuremath{-}}$ and that $\frac{\ensuremath{\partial}\ensuremath{\rho}}{\ensuremath{\partial}T}$ continues to reflect more closely the specific heat. The results are compared with experiment in the representative cases of $\ensuremath{\beta}$-brass, ${\mathrm{Fe}}_{3}$Al, dysprosium, and holmium. Some previously unsettled questions are answered and there is good agreement with experiment.