Resistance maximum in spin glasses

Abstract

The temperature ${T}_{m}$ of the resistance maximum in spin-glass magnetic alloys is calculated as a function of the Kondo temperature ${T}_{K}$ for the single impurities and the average Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction strength ${\ensuremath{\Delta}}_{c}$ between different impurities. In addition ${T}_{m}$ is shown to be independent of several other less relevant system parameters. The temperature dependence of the resistivity is obtained in the parquet approximation in the "noise model," where, besides the usual exchange scattering between conduction electrons and impurity spins, there is a transition rate ${\ensuremath{\Delta}}_{c}$ for spin-flip processes due to the RKKY interactions. The result is shown to be valid when ${\ensuremath{\Delta}}_{c}\ensuremath{\gg}{T}_{K}$, and applies to the low-${T}_{K}$ spin-glass systems like $\mathrm{Au}\mathrm{Mn}$, $\mathrm{Ag}\mathrm{Mn}$, $\mathrm{Cu}\mathrm{Mn}$, $\mathrm{Au}\mathrm{Cr}$, and $\mathrm{Au}\mathrm{Fe}$. For example, it permits the recently observed pressure variations of ${T}_{m}$ to be understood in terms of simpler behaviors of the more fundamental system parameters ${\ensuremath{\Delta}}_{c}$ and ${T}_{K}$. Asymptotically for ${\ensuremath{\Delta}}_{c}\ensuremath{\gg}{T}_{K}$ one has ${T}_{m}\ensuremath{\sim}{\ensuremath{\Delta}}_{c}\mathrm{ln}(\frac{{\ensuremath{\Delta}}_{c}}{{T}_{K}})$, which is bigger than the spin-glass freezing temperature ${T}_{0}\ensuremath{\sim}{\ensuremath{\Delta}}_{c}$ identified by the cusp in the magnetic susceptibility.