Coupled tunneling-lattice modes in partially deuterated hydrogen-bonded ferroelectrics

Abstract

We present a theoretical analysis of the role played by lattice optic vibrations in hydrogen-bonded ferroelectrics of K${\mathrm{H}}_2$P${\mathrm{O}}_4$ type in which a fraction of protons is randomly substituted by deuterons. The dynamics of the model system is studied by means of the equation-of-motion method applied to the Green's functions for proton (or deuteron) pseudospin and lattice coordinates. We suggest a new decoupling scheme for these functions which is more general than the usual random-phase approximation but simpler than usual second-order decouplings. Explicit expressions are derived for phonon corrections to the local single-bond response and for the dynamic interbond coupling which excludes self-interaction terms. Isotopic disorder is treated within the virtual-crystal approximation; the concentration dependence of the collective-mode eigenfrequencies is discussed for the simple case of coupling between tunneling excitations and a narrow optical band. The results are also relevant to pure (undeuterated) systems.