Knight Shifts and Pauli Susceptibilities in Alkali Metals and Alloys

Abstract

An expression for the contact density, or Fermi-surface electron probability density at the nucleus, is developed to first order in the pseudopotential for a metal with a spherical Fermi surface, and applied to solid alkali metals and liquid binary alkali alloys at all concentrations. The explicit orthogonalization of the pseudo-wave-functions to the ionic core states permits the use of a local empirical pseudopotential. The contact density samples the Fourier transform of the pseudopotential primarily in the region just above $2k_F$; consequently the large changes in $k_F$ which occur upon alloying in the alkali metals are dominant over the details of the ionic environment in determining the behavior of the contact density. The calculated contact densities, when combined with measured alloy Knight shifts, imply a unique and roughly free-electron-like dependence of the Pauli electron-spin susceptibility upon the interelectron spacing $r_s$ in the range $4.0<\mathrm{}{r}_s<5.8\mathrm{}$. The polarizability of the ions may introduce an effective value of $r_s$ in the range $3.8<\mathrm{}r_{}^{*}{}_s{}^{}<4.6\mathrm{}$. The deduced susceptibilities are consistent with a simple picture in which the electron-ion effective masses of Na, K, Rb, and Cs are close to unity; the susceptibilities agree in this picture with a recent analysis of the observed enhancement of the Korringa constant. The calculation is in some important respects insensitive to the choice of pseudopotentials, structure factors, and core-state wave functions. The temperature dependence and change upon melting of the Knight shift are also estimated, and the extension of the calculation to other metals is briefly discussed.