Nuclear-Magnetic-Resonance Studies in PbTe and Pb1−xSnxTe: An Experimental Determination of k→·p→ Band Parameters and Magnetic Hyperfine Constants

Abstract

Measurements are reported of the Knight shifts of ${\mathrm{Pb}}^{207}$ and ${\mathrm{Sn}}^{119}$ in 61 samples of PbTe and ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$ as functions of carrier concentration, alloy composition, and temperature. The results are interpreted in terms of a quantitative six-band $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ band model for the magnetic energy levels of the valence and conduction bands. All available experimental data pertaining to effective masses and $g$ factors are examined using this model, including the results of magneto-oscillatory, magneto-optical, and other Fermi-surface studies. Remarkable agreement with published data and with the NMR data is obtained with principal matrix elements of momentum which are independent of composition. The temperature dependence of the Knight shift up to 100 K is understood in terms of the changing carrier degeneracy, but above 100 K an additional temperature dependence is observed. Unexplained structure is reported in the temperature dependence of the Knight shifts in alloy samples near their band inversions. Contact interaction and orbital hyperfine constants are reported. The orbital hyperfine constants are surprisingly large in these materials. In addition, the magnitude of the hyperfine coupling depends on alloy composition.