Strain-dependent pseudo-spin coupling mechanism for longitudinal sound attenuation in KDP

Abstract

The single-particle phonon propagator is calculated for a longitudinal acoustic mode in an extended Kobayashi model of KH2PO4, for temperature just above Tc. The equations of motion for the Green function are decoupled by expressing the four-spin correlation in terms of pair correlations. A second approximation involves use of a previous result for the two-spin Green function which invoked random phase decoupling, so that the results are valid only outside the critical region. With these approximations, we calculate the phonon self-energy to O(Hd2) where Hd, the anharmonic term in the Hamiltonian which gives rise to three-phonon damping, stems from the strain-dependence of proton pseudo-spin coupling. Both real and imaginary parts of the phonon self-energy are obtained, yielding an absorption coefficient for longitudinal sound which is proportional to ((T-T0)/(T-Tc))52/, where T0 is the temperature at which the soft polar mode frequency extrapolates to zero. The sound velocity should increase as T to Tc+, although rough numerical estimates suggest the increase may not be large outside the critical region.