Quadrupolar Nuclear Spin-Lattice Relaxation in InSb at Low and Medium Temperatures

Abstract

Measurements of the nuclear spin-lattice relaxation rate of ${\mathrm{In}}^{115}$, ${\mathrm{Sb}}^{121}$, and ${\mathrm{Sb}}^{123}$ in InSb over the temperature range 3.8 to 300°K are reported. At temperatures exceeding 7°K, the dominant relaxation process is via quadrupolar coupling to the lattice vibrations. Below 7°K, the total relaxation rate is resolved into a sum of quadrupolar ($\frac{1}{T_1^{}{}_{}{}^Q}$) and background impurity rates. For ${\mathrm{Sb}}^{121}$, $\frac{1}{T_1^{}{}_{}{}^Q}$ is proportional to $T^{9.5\pm 0.5}$ ($T=\mathrm{temperature}$). A similar result is obtained for the other nuclei, but with reduced accuracy. This result disagrees with predictions based on the Debye model, but agrees with calculations based on a more accurate density-of-states function. Over the entire temperature range 4.2 to 300°K, the ratio $\frac{T_1^{}{}_{}{}^Q\left({\mathrm{Sb}}^{123}\right)}{T_1^{}{}_{}{}^Q\left({\mathrm{Sb}}^{121}\right)}$ is 1.45±0.05, in agreement with theoretical predictions. The behavior of the ratio $\frac{T_1^{}{}_{}{}^Q\left({\mathrm{In}}^{115}\right)}{T_1^{}{}_{}{}^Q\left({\mathrm{Sb}}^{121}\right)}$ is quite different; it varies from 3.2 below 25°K to 1.4 at high temperatures. This change with increasing temperatures is attributed to the thermal excitation of optical phonons, which are more strongly coupled to In than to Sb nuclei.