Rotational Tunneling States and the Non-Debye Specific Heat of Dipolar Glasses

Specific heat of dipolar glasses does not obey Debye law. It is of interest to know if the non-Debye specific heat can be accounted for in terms of Schottky-type specific heat arising from rotational tunneling states of the dipoles. This paper deals with rotational tunneling spectra of NH$_{4}^{+}$ ions and the non-Debye specific heat of mixed salts (e.g. (NH$_{4})_{x}$Rb$_{1-x}$Br) of ammonium and alkali halides which are known to exhibit dipolar glass phase. We have measured specific heat of above mixed salts at low temperatures (1.5 K $< T <$ 15 K). It is seen that while the specific heat of pure salts obeys Debye law, the specific heat of mixed salts does not obey Debye law. We have studied the effect of the NH$_{4}^{+}$ ion concentration, first neighbor environment of NH$_{4}^{+}$ ion and the lattice strain field on the non-Debye specific heat by carrying out measurements on suitably chosen mixed salts. Independent of above, we have measured the rotational tunneling spectra, $f(omega $), of the NH$_{4}^{+}$ ions in above salts using technique of neutron incoherent inelastic scattering. The above studies show that both the non-Debye specific heat and the tunneling spectra of the NH$_{4}^{+}$ ions depend on the NH$_{4}^{+}$ ion concentration, first neighbor environment of NH$_{4}^{+}$ ions and the lattice strain field. We have further shown that the temperature dependence of the measured specific heat can be explained for all the samples in terms of a model that takes account of contributions to the specific heat from the Debye phonons and the rotational tunneling states of the NH$_{4}^{+}$ ions. To the best of our knowledge, this is a first study where it is shown that measured specific heat of (NH$_{4})_{x}$Rb$_{1-x}$Br can be quantitatively explained in terms of an experimentally measured rotational tunneling spectra $f(omega $) of the NH$_{4}^{+}$ ions.