PdV: A System with a High Spin-Fluctuation or Kondo Temperature?

Abstract

The temperature dependence of the incremental resistivity $\ensuremath{\Delta}\ensuremath{\rho}(T)$ of five dilute $\mathrm{Pd}\mathrm{V}$ alloys, ranging in concentration from 0.15- to 1.0-at.% V, has been measured from 1.4 to 300 K. $\ensuremath{\Delta}\ensuremath{\rho} (T=0)$ increases linearly with V content at a rate of 3.26\ifmmode\pm\else\textpm\fi{}0.13 \ensuremath{\mu}\ensuremath{\Omega} cm/at.% V. Between 10 and 80 K, $\ensuremath{\Delta}\ensuremath{\rho}(T)$ increases rapidly with increasing temperature, in a manner characteristic of Matthiessen's-rule breakdown resulting from phonon and impurity scattering with differing anisotropies. Above 80 K, however, $\ensuremath{\Delta}\ensuremath{\rho}(T)$ decreases smoothly with increasing temperature; various attempts have been made to fit this high-temperature variation: (i) In terms of a localized-spin-fluctuation (lsf) model, these data are well fitted by $\ensuremath{\Delta}\ensuremath{\rho}(T)=C+D \mathrm{ln}[{({T}^{2}+{\ensuremath{\theta}}^{2})}^{\frac{1}{2}}]$, with lsf temperature $\ensuremath{\theta}$ estimated at about 160 K for isolated impurities. $D$, however, does not scale linearly with the V concentration $c$, and it is necessary to postulate that interimpurity interactions significantly raise $\ensuremath{\theta}$ for the interaction pair, then $D\ensuremath{\propto}c{(1\ensuremath{-}c)}^{n}$. The observed variation of $D$ can be approximately reproduced for $n=150$. (ii) These high-temperature data are also equally well fitted by the Appelbaum-Kondo expression: $\ensuremath{\Delta}\ensuremath{\rho}(T)=E{1\ensuremath{-}(\frac{16cos2{\ensuremath{\delta}}_{\ensuremath{\nu}}}{3{cos}^{2}{\ensuremath{\delta}}_{\ensuremath{\nu}}}){[(\frac{T}{{T}_{K}})\mathrm{ln}(\frac{T}{{T}_{K}})]}^{2}}$. The scaling parameter $E$ increases linearly with $c$ and the Kondo temperature ${T}_{K}$ is estimated at about 2300 K. Possible variations in the potential phase shift ${\ensuremath{\delta}}_{\ensuremath{\nu}}$ indicate that the amount of $s$-band screening may increase as $c$ increases. Further experiments are necessary, however, to determine the eventual applicability of either model. Finally, estimates are made of the Matthiessen's-rule deviations $\ensuremath{\Delta}(T)$, which are then fitted within the framework of a "parallel conduction" model, in which $\frac{1}{\ensuremath{\Delta}}(T)=\frac{1}{\ensuremath{\alpha}{\ensuremath{\rho}}_{h}}(T)+\frac{1}{\ensuremath{\beta}{\ensuremath{\rho}}_{i}}(T)$. ${\ensuremath{\rho}}_{h}(T)$ is the host and ${\ensuremath{\rho}}_{i}(T)$ the impurity resistivity. A concentration independent value for $\ensuremath{\alpha}$ of 0.31\ifmmode\pm\else\textpm\fi{}0.04 is obtained, but $\ensuremath{\beta}$ is found to vary with concentration around a value of 0.06.