Effect of short-range interactions on the transverse dynamics of KD2PO4

The dynamics of K${\mathrm{D}}_2$P${\mathrm{O}}_4$ along the transverse $x$ direction is investigated using a pseudospin model which takes into account the transverse dipole moments of the hydrogen bonds and incorporates both short-range and long-range interaction effects. A four-cluster approximation to the Glauber equations of motion for the $E$-mode pseudospin fluctuations is employed. It is found that these fluctuations have three different relaxation times below $T_c$ and two above $T_c$ However, in the low-frequency region the dynamical susceptibility has a Debye-type frequency dependence with one relaxation time ${\tau }_x$. The temperature dependence of ${\tau }_x$ is calculated within the present model and is compared to that derived from the randomphase approximation (RPA). It is found that the relation between ${\tau }_x$ and the static transverse susceptibility ${\chi }_x$ is markedly different from the RPA result ${\tau }_x\propto T{\chi }_x$. The present theory explains in a consistent way the available experimental data on the dynamical properties of K${\mathrm{D}}_2$P${\mathrm{O}}_4$ in both the longitudinal and transverse directions.