Critical behavior of the electrical resistivity in magnetic systems: Comments and theory

Following recent theoretical advances on the critical behavior of the electrical resistivity $\rho$ in magnetic systems, this paper points out that features of the critical region are not yet quantitatively explained. The need for a theory away from but close to the transition region is emphasized in view of extracting several parameters from the experimental data. A simple generalization of the Ornstein-Zernike correlation function, on both sides of $T_c$, based on Landau theory and previous work is proposed. This implies a magnetization-dependent amplitude of the correlation length below $T_c$. Different types of singularities are found as observed experimentally. Various features of $\frac{d\rho }{\mathrm{dT}}$ away from the transition temperature can also be reproduced: In particular, an unexplained bump and dip in $\frac{d\rho }{\mathrm{dT}}$ vs $T$ (below $T_c$) usually obtained from data of $\rho$ in localized spin systems can be found in our simple approach. Also, the existence of unequal magnitudes of $\frac{d\rho }{\mathrm{dT}}$ above and below $T_c$ now has a theoretical explanation.