Theory of spin-fluctuation resistivity near the critical point of ferromagnets

Abstract

A simple theory of electrical resistivity due to critical spin fluctuations ${R}_{s}(T)$ is presented in a form which is valid for ferromagnets with anisotropic Fermi surfaces. Subject to reasonable restrictions on the electronic band structure, it is shown that $\frac{d{R}_{s}(T)}{\mathrm{dT}}$ is positive and proportional to the magnetic specific heat, in the $T\ensuremath{\rightarrow}{T}_{c}^{+}$ limit, for all ferromagnets which can be described by a spin Hamiltonian with only short-range forces. A detailed treatment is given of the temperature range above ${T}_{c}$ where short-range ($R\ensuremath{\ll}\ensuremath{\xi}$) correlations no longer describe the spin fluctuations relevant to the resistivity problem. The gradual cross over to a regime dominated by longer-range correlations and the corresponding possibility of a change in sign of $\frac{d{R}_{s}(T)}{\mathrm{dT}}$ at $T>{T}_{c}$ are studied and numerical results are given. The results are interpreted in terms of the structure of the spin correlation function $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}, T)$ and the Fermi-surface geometry and provide a unified interpretation of available experimental results.