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

We present a simple theory of electrical resistivity $\rho \mathrm{}\left(T\right)\mathrm{}$ due to critical fluctuations in the vicinity of the Néel point of antiferromagnets and the order-disorder transition temperature of binary alloys. In the disordered phase, it is shown that the singular part of $\frac{\partial \rho }{\partial T}$ varies as either plus or minus the singular part of the specific heat for $T\to T_N^{+}$. The sign is determined by Fermi-surface geometry and the superlattice vector $\overrightarrow{\mathrm{Q}}$ of the ordered state. The temperature range, somewhat above $T_N$, where short-range ($R\ll \xi$) 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 $\rho \mathrm{}\left(T\right)\mathrm{}$ directly for $T\to T_N^{-}$ and that $\frac{\partial \rho }{\partial T}$ continues to reflect more closely the specific heat. The results are compared with experiment in the representative cases of $\beta$-brass, ${\mathrm{Fe}}_3$Al, dysprosium, and holmium. Some previously unsettled questions are answered and there is good agreement with experiment.