Low-frequency response of KDP-like crystals in the spin-phonon model

The pseudo-spin model of ferroelectric crystals like KDP is extended to include coupling between the soft spin-wave mode and fluctuations in the phonon numbers via spin-two phonon terms in the hamiltonian. It is shown that this provides an explanation of the temperature dependence of the width of the Raman scattering response and predicts a central peak in some circumstances. The magnitude of the coupling may be shown to be related to the splitting of the E modes below the transition temperature since this arises from the same terms. The frequency dependence of the elastic constants is also discussed.