Measurements of the Knight shift in $n$-type InSb at low temperatures (0.4-4.2 K) are presented as a function of magnetic field $H_0$ near the quantum limit for several conduction-electron concentrations (2 × ${10}^{14}$-1.2 × ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$). The observed shift is separated into the chemical shift and the hyperfine shift ($\Delta H$). The hyperfine shift exhibits quantum oscillations (QO) as the field is varied. As with the de Haas-van Alphen effect and the QO of the nuclear spin-lattice relaxation rate ($\frac{1}{T_1}$), they are caused by oscillations in the conduction-electron density of states at the Fermi energy which occur as the magnetic field is changed. These experiments indicate that the density of states is broadened. This broadening is caused by either or both of two mechanisms: electron collisions with charged impurities (Dingle broadening) and the random spatial fluctuations in the impurity density (band tailing). Theoretical calculation of $\Delta H$ vs $H_0$ are presented and the numerical solutions are given. In these calculations, Dingle broadening is approximated as an added increment of temperature (the Dingle temperature $T_D$). The theory of Dyakonov, Efros, and Mitchell is used to calculate the effects of band tailing. The differences between $\Delta H-\mathrm{vs}-H_0$ curves calculated on the basis of each mechanism are small and are not observable in InSb. No variations in $\Delta -H$ were observed at fields which correspond to the type-$A$ and type-$B$ peaks observed in $\frac{1}{T_1}$ by Bridges and Clark.

• Received 21 May 1973

DOI:https://doi.org/10.1103/PhysRevB.9.495