Experimental Study of the Host NMR Linewidth and Spin-Lattice Relaxation Rate in DiluteCuFeAlloys below the Kondo Temperature

In order to determine the properties of single magnetic impurities in the Kondo state and the effects of these single magnetic impurities on the host-conduction-electron spin system, the Fe-impurity contributions to the ${\mathrm{Cu}}^{63}$-host nuclear-magnetic-resonance (NMR) linewidth $\Delta H_i$, and spin-lattice relaxation time $T_{\mathrm{li}}$, have been studied over a wide Fe-concentration range ($0<c<\mathrm{}1260\mathrm{}$ ppm) in $\mathrm{Cu}\mathrm{Fe}$. The NMR-linewidth measurements made from 1.65 to 77°K and in magnetic fields from 2 to 16 kOe and in some cases up to 60 kOe, show the anomalous behavior of the slope $S=\frac{d\Delta H_i}{\mathrm{dH}}$ originally observed by Heeger et al. and studied for a 480-ppm $\mathrm{Cu}\mathrm{Fe}$ alloy by Golibersuch and Heeger exists over a wide Fe-concentration range. This anomalous behavior, which consists of the transition from a constant slope at low fields, $S_L$, to a smaller magnitude slope at high fields, $S_H$, occurs in a relatively narrow range of fields about some critical field $H_c$. This behavior clearly results from the single-impurity contribution to the NMR linewidth as evidenced by the linear concentration dependence of both $S_L$ and $S_H$ and also by the concentration independence of $\frac{S_L}{S_H}$. $S_H$ has the same ${\mathrm{}(T+29\mathrm{})\mathrm{}}^{-1\mathrm{}}$ temperature dependence as the bulk susceptibility, while $S_L$ is enhanced for $H<\mathrm{}{H}_c$ and $T<\mathrm{}{T}_c\approx 6$ °K. At 1. 65 °K, $S_H=(1.50\mathrm{}\pm 0.10)\times {10}^{-6\mathrm{}}c$, $S_L=(2.83\mathrm{}\pm 0.10)\times {10}^{-6\mathrm{}}c$ ($c$ in ppm), and $\frac{S_L}{S_H}=1.9\mathrm{}$. These results show that the Ruderman-Kittel-Kasuya-Yosida-like oscillatory conduction-electron spin polarization existing about an impurity for $T\gg T_K$ is either enhanced for $T<\mathrm{}{T}_c$ and $H<\mathrm{}{H}_c$, or else an additional long-range oscillatory spin polarization is formed in the Kondo state. From the inverse concentration dependence of $H_c$ we conclude that long-range interactions of sufficient strength exist between Fe spins via the $d-d$ double-resonance mechanism to effectively saturate the extra oscillatory spin polarization in successively smaller applied fields as the Fe concentration increases. The impurity-induced host relaxation rate is linear in Fe concentration up to at least 300 ppm, decreasing from $T_{\mathrm{li}}^{-1\mathrm{}}=2.3\mathrm{}\times {10}^{-3\mathrm{}}c$ ($c$ in ppm) for 2.65 kOe to $T_{\mathrm{li}}^{-1\mathrm{}}=2.5\mathrm{}\times {10}^{-4\mathrm{}}c$ for 15 kOe at 1. 65 °K. The low-concentration data follow a single curve when plotted as $T{\left(c{T}_{\mathrm{li}}\right)}^{-1\mathrm{}}$ vs $\frac{T}{H} (0.1\mathrm{}\frac{{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}}{\mathrm{kOe}}<\frac{T}{H}<1.0\mathrm{}\frac{{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}}{\mathrm{kOe}})$. Comparison of this curve with the existing high-temperature ($T\gg T_K$) theories would imply that the spin-lattice relaxation in the liquid-helium temperature range is dominated by a dipolar coupling of the nuclei to longitudinal dipolar fluctuations of the impurity spin. These results are discussed in the light of the $T_{\mathrm{li}}$ data for $T>\mathrm{}{T}_K$ which does not appear to be consistent with this mechanism suggesting that none of the $T\gg T_K$ relaxation mechanisms may be simply extended to the region $T<\mathrm{}{T}_K$.