NMR in quadrupole glasses and the spectral density of orientation fluctuations

Previous NMR experiments on ${\mathrm{H}}_2$ at low temperatures ($T\lesssim 0.3$ K) and intermediate orthohydrogen concentrations ($0.1<x<\mathrm{}0.55\mathrm{}$) indicate that ${\mathrm{H}}_2$ forms a quadrupole glass state. The interpretation of the NMR data in terms of molecular orientations and/or reorientations has not been clear. We propose a unified explanation of the many NMR measurements ($T_1$, line shape, spin echoes, and stimulated echoes) in terms of the spectral density of the molecular orientations. All the data are compatible with the development of a dc component in the spectral density as the temperature is decreased while the ac parts are not greatly changed. Strictly dynamic theories are shown not to agree with the experiments. The NMR behaviors of ordinary glasses and quadrupole glasses are compared and found to reflect fundamental symmetry differences between the two states. The spin-lattice relaxation data in ${\mathrm{H}}_2$ appear to indicate a broad distribution of fluctuation frequencies. Interpretation of the observed minimum in $T_1$ as a motional minimum may be incorrect. Finally, an experimental test of the ergodicity of quadrupole glasses is proposed.