Damping constant and the relaxation time calculated for the lowest-frequency soft mode in the ferroelectric phase of Cd2Nb2O7

Abstract

The temperature dependence of the phonon frequency ωph and of the damping constant Γsp due to pseudospin-phonon coupling of the lowest-frequency soft mode is calculated in the ferroelectric phase near the transition temperature (TC=196K) in Cd2Nb2O7. Raman frequency of the soft mode is used as an order parameter which is calculated from the molecular field theory. On that basis, the damping constant is calculated by fitting the expressions from the pseudospin-phonon coupled model and the energy fluctuation model to the observed linewidth from the literature below TC in Cd2Nb2O7. From our analysis, we find that the molecular field theory is adequate for the soft mode behaviour and that both models are also satisfactory for the divergence behaviour of the damping constant as TC is approached from the ferroelectric phase in Cd2Nb2O7.Values of the activation energy U are extracted from the temperature dependence of the damping constant (HWHM) of the soft mode in the ferroelectric phase of this crystal. Also, the inverse relaxation time is predicted using the Raman frequency and damping constant close to the TC in the ferroelectric phase of Cd2Nb2O7, which increases considerably as TC is approached from the ferroelectric phase, as observed experimentally.