Knight-Shift Anisotropy in Cubic Crystals

A general calculation of the Knight shift in metals with spin-orbit interaction is presented. For terms involving the electron-nuclear contact interaction the spin-orbit interaction was included to second order and is shown to result in anisotropy of the Knight shift even in cubic metals. Our formalism for electron-nuclear dipole interaction with spin-orbit coupling also yields anisotropy in cubic metals and reduces in the tight-binding limit to the result previously obtained by Boon. Nuclear-magnetic-resonance measurements on single crystals of the cubic metals lead and platinum have shown the anisotropy in our samples to be less than, respectively, 3.4 and 1.5 × ${10}^{-4\mathrm{}}$ of the isotropic shifts. The upper limit for lead is half the anisotropy in lead reported by Schratter and Williams.