Low-frequency excitations in sodium β-alumina: An NMR study

The temperature and frequency dependence of ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$ and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ nuclear-spin relaxation (NSR) has been studied in Na β-alumina between about 1.5 and 100 K. Below 50 K the NSR is shown to be caused by low-frequency excitations of disorder modes, which are intrinsic to the glasslike state of β aluminas. The data can be interpreted consistently in the framework of thermally activated excitations of modes that are represented by asymmetric double-well-potential configurations with suitably chosen densities of states. Further, the observed NSR rates are shown to be related to corresponding ac-conductivity data via the fluctuation-dissipation theorem.