Knight-shift anomalies in heavy-electron materials

Abstract

We have studied the Knight shift $K(\stackrel{\ensuremath{\rightarrow}}{r},T)$ and magnetic susceptibility $\ensuremath{\chi}(T)$ of heavy-electron materials, modeled by the infinite-$U$ Anderson model with the noncrossing approximation method. A systematic study of $K(\stackrel{\ensuremath{\rightarrow}}{r},T)$ and $\ensuremath{\chi}(T)$ for different Kondo temperatures ${T}_{0}$ (which depends on the hybridization width $\ensuremath{\Gamma})$ shows a low-temperature anomaly (nonlinear relation between $K$ and $\ensuremath{\chi})$ which increases as the Kondo temperature ${T}_{0}$ and distance $r$ increase. We carried out an incoherent lattice sum by adding the $K(\stackrel{\ensuremath{\rightarrow}}{r})$ of a few hundred shells of rare-earth atoms around a nucleus and compare the numerically calculated results with the experimental results. For ${\mathrm{CeSn}}_{3},$ which is a concentrated heavy-electron material, both the ${}^{119}\mathrm{Sn}$ NMR Knight shift and positive muon Knight shift are studied. Also, lattice coherence effects by conduction-electron scattering at every rare-earth site are included using the average-$T$-matrix approximation. The calculated magnetic susceptibility and ${}^{119}\mathrm{Sn}$ NMR Knight shift show excellent agreement with experimental results for both incoherent and coherent calculations. The positive muon Knight shifts are calculated for both possible positions of muon (center of the cubic unit cell and middle of Ce-Ce bond axis). Our numerical results show a low-temperature anomaly for the muons of the correct magnitude but we can only find agreement with experiment if we take a weighted average of the two sites in a calculation with lattice coherence present. For YbCuAl, the measured ${}^{27}\mathrm{Al}$ NMR Knight shift shows an anomaly with opposite sign to the ${\mathrm{CeSn}}_{3}$ compound. Our calculations agree very well with the experiments. For the proposed quadrupolar Kondo alloy ${\mathrm{Y}}_{0.8}{\mathrm{U}}_{0.2}{\mathrm{Pd}}_{3}$, our ${}^{89}\mathrm{Y}$ NMR Knight-shift calculation do not show the observed Knight-shift anomaly.