Quantum Mobility and Nuclear-Spin-Echo Damping in Impure Crystals

Abstract

Dash has attributed the low-temperature loss of configurational entropy in impure crystals to the quantum mobility of the impurities. The resulting specific-heat peaks at $T=\frac{\Delta }{k_B}$ have not yet been observed, probably owing to the extremely small values of the mobility bandwidths $\Delta$. In this paper it is shown that if $\Delta \gg \hslash {\left(\frac{D^{2}g}{a^3}\right)}^{\frac{1}{3}}$, then the mobility bandwidth can be measured via nuclear-spin-echo-damping experiments carried out at temperatures much larger than $\frac{\Delta }{k_B}$. $D$ is the diffusion coefficient, $a$ is the lattice spacing, and $\overrightarrow{\mathrm{g}}$ is the magnetic-field gradient (measured in frequency units). The damping factor is shown to have an oscillatory character in this limit as opposed to the usual classical $e^{-\frac{D{g}^2{t}^3}{12}}$ form. Practical limits to the method yield $\frac{\Delta }{k_B}\gtrsim {10}^{-5\mathrm{}}$ °K as an approximate lower bound on detectable widths.