Knight Shift in Multivalley Semiconductors. II. Determination of the Hyperfine Coupling Constants inN-andP-Type PbSe and PbTe

Abstract

We report a detailed experimental and theoretical investigation of the large Knight shifts of ${\mathrm{Pb}}^{207}$ in $N$- and $P$-type PbSe and PbTe at low temperature. The nuclear-resonance experiments are performed on bulk single crystals using the technique of helicon-spin interaction. We give the first quantitative account of the Knight shift of ${\mathrm{Pb}}^{207}$ due to $s$-like holes, and we determine a value of the hyperfine coupling constant that confirms the validity of augmented-plane-wave calculations for the lead salts. The large shift created by the $p$-like conduction electrons is shown to be due to the large orbital and dipolar hyperfine fields arising from $p_{\frac{1}{2}}$ states. In presence of spin-orbit interaction, the dipolar field (which previous studies, invoking cubic symmetry, ignored) cannot be neglected: It is in fact responsible for half of the shift. This study shows that a large Knight shift must not be interpreted as an experimental evidence of an $s$-like symmetry of the wave function.