Study of the Effect of High Pressure on the Kondo Resistivity of Cu(Fe) at Low Temperatures

The electrical resistance of a Cu(Fe) alloy with a concentration of about 112-ppm Fe has been measured in the temperature range $6<T<\mathrm{}40\mathrm{}$ K and in the pressure range $0<p<\mathrm{}94\mathrm{}$ kbar. The Appelbaum-Kondo resistivity formula ${\rho }_K\left(\frac{T}{T_K^{}{}_{}{}^{\prime }}\right)=A-B{\left[\right(\frac{T}{T_K^{}{}_{}{}^{\prime }}\left)\ln \right(\frac{T}{T_K^{}{}_{}{}^{\prime }}\left)\right]}^2$ was found to fit the data closely in the range $6\le T\le 16$ K and was used as an empirical scaling function of $\frac{T}{T_K^{}{}_{}{}^{\prime }\mathrm{}\left(p\right)\mathrm{}}$ in order to obtain the pressure dependence of a characteristic temperature $T_K^{}{}_{}{}^{\prime }\mathrm{}\left(p\right)\mathrm{}$. It is a result of many theoretical model calculations that ${\Theta }_K=T_F\exp {[-\omega |J_m\left|N\right(k_F\left)\right]}^{-1\mathrm{}}$. Here ${\Theta }_K$ is a Kondo temperature of the system, $T_F$ is the Fermi temperature of the host metal, $N\left(k_F\right)$ is the density of conduction-electron states at the Fermi energy of the host, and $J_m$ is an exchange energy between a conduction electron and an electron localized on the Fe impurity. $\omega$ is a constant of order unity. The free-electron Fermi energy ${\epsilon }_F\mathrm{}\left(p\right)\mathrm{}$ of Cu is also a function of pressure, and by relating $T_K^{}{}_{}{}^{\prime }\mathrm{}\left(p\right)\mathrm{}$ and ${\Theta }_K\mathrm{}\left(p\right)\mathrm{}$, we use this equation to present our results as a vibration of $\omega \left|J_m\right|$ with ${\epsilon }_F$. Schrieffer has derived the equation $\frac{1}{\left(\omega \right|J_m\mathrm{}\left|\right)\mathrm{}}=-\frac{\left|\right({\epsilon }_F-{\epsilon }_m)\times ({\epsilon }_F-{\epsilon }_m-U\left)\right|S}{\omega {\left|V_{\mathrm{kFm}}\right|}^{2}U}$ through a canonical transformation relating the Anderson and Kondo Hamiltonians. Here $U$ is a repulsive energy between two electrons located in orbitals of the Fe impurity, $S$ is the spin, and $V_{\mathrm{kFm}}$ is a mixing matrix element. ${\epsilon }_m$ and ${\epsilon }_m+U$ are energies of localized states which are associated with Fe in the Cu host. If it is assumed that the effect of applying pressure to Cu(Fe) is to raise the Fermi energy by an amount which is relatively large compared to any change in the energies ${\epsilon }_m$ and $U$, and the widths of the localized levels, Schrieffer's equation may be fitted to our measurement of $\omega \left|J_m\right({\epsilon }_F\left)\right|$. It is found using this model that for Cu(Fe) under zero applied pressure, $({\epsilon }_F-{\epsilon }_m)=0.84\mathrm{}\pm 0.20$ eV, $({\epsilon }_m+U-{\epsilon }_F)=0.82\mathrm{}\pm 0.17$ eV, and $\frac{\omega {\left|V_{\mathrm{kFm}}\right|}^2}{S}=0.27\mathrm{}\pm 0.10$ ${\mathrm{}\left(\mathrm{eV}\right)\mathrm{}}^2$.