Effect of inelastic scattering on resistive anomalies at magnetic critical points

Theoretical treatments of resistive anomalies at magnetic critical points have been based on the quasielastic approximation according to which the scattering system of localized spins is essentially static on the relevant time scale. This approximation is justified by thermodynamic slowing down of spin fluctuations near the critical point. In the case of ferromagnets, for example, this view is most obviously valid for long-wavelength spin fluctuations. These, however, are irrelevant for the resistivity. In this paper, we give an exact evaluation of the lowest-order corrections to the resistivity due to inelastic scattering for both ferromagnets and antiferromagnets. These corrections are numerically significant only for very low spin (e.g., ∼ 30% for $S=\frac{1}{2}$) and vary as $\frac{1}{S(S+1\mathrm{})\mathrm{}}$. Their temperature dependence reflects directly that of the internal energy of the spin system so that static critical properties will continue to be a useful guide in interpreting resistive anomalies.