Knight Shift in Multivalley Semiconductors. I. Theory of Contact, Orbital, and Dipolar Shift and Relativistic Effects

A theory of the Knight shift in degenerate multivalley semiconductors is presented which takes into account the spin-orbit interaction and the relativistic effects on the hyperfine coupling. This theory treats rigorously the spinor character of the wave function and the nontensorial nature of the $g$ matrix. We give a formula for the shift created by an arbitrary ellipsoidal valley. This formula involves a simple linear combination of $g$ factors and matrix elements of the hyperfine field. In most cases (except that of a spherical valley) the Knight shift is not proportional to the Pauli paramagnetic susceptibility.