Calculations of the Knight Shift Anomalies in Heavy Electron Materials

We have studied the Knight shift $K(\vec r, T)$ and magnetic susceptibility $\chi(T)$ of heavy electron materials, modeled by the infinite U Anderson model with the NCA method. A systematic study of $K(\vec r, T)$ and $\chi(T)$ for different Kondo temperatures $T_0$ (which depends on the hybridization width $\Gamma$) shows a low temperature anomaly (nonlinear relation between $K$ and $\chi$) which increases as the Kondo temperature $T_0$ and distance $r$ increase. We carried out an incoherent lattice sum by adding the $K(\vec r)$ of a few hundred shells of rare earth atoms around a nucleus and compare the numerically calculated results with the experimental results. For CeSn_3, which is a concentrated heavy electron material, both the ^{119}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. Also NMR Knight shifts for YbCuAl and the proposed quadrupolar Kondo alloy Y_{0.8}U_{0.2}Pd_{3} are studied.