Paraelectric-ferroelectric phase transitions of ${\mathrm{KH}}_2$${\mathrm{PO}}_4$, ${\mathrm{RbH}}_2$${\mathrm{PO}}_4$, and ${\mathrm{KH}}_2$${\mathrm{AsO}}_4$ studied by infrared reflectivity

The infrared-reflectivity spectra of ${\mathrm{KH}}_2$ ${\mathrm{PO}}_4$ (KDP) and its isomorphs ${\mathrm{RbH}}_2$ ${\mathrm{PO}}_4$ (RDP) and ${\mathrm{KH}}_2$ ${\mathrm{AsO}}_4$ (KDA) are reported in a wide spectral range (from 20 to 4000 ${\mathrm{cm}}^{\mathrm{-}1}$), in the paraelectric and ferroelectric phases. The phonon responses are obtained by fitting the factorized form of the dielectric function to the experimental spectra. The comparison of the data obtained in the three compounds allows the assignment of all vibrational modes. In RDP, the internal ${\nu }_{4c}$ polar mode polarized along the ferroelectric axis is found to soften upon approaching $T_C$ from below or above, although to a lesser extent. The eigenvector pattern of this mode shows that it interacts strongly via electrostatic coupling with the intersite tunneling proton motions perpendicular to the ferroelectric axis. This phenomenon is thought to be the origin of the ${\nu }_{4c}$ mode softening. This mode also couples with other polar modes of the same symmetry via a mechanism intermediate between Fano-type interference and classical mode-mode coupling. The coupled excitation evolves to yield the overdamped ferroelectric mode that triggers the paraelectric-ferroelectric phase transition. The temperature dependence of its oscillator strength agrees with that of the dielectric constant measured above piezoelectric resonances or in single domain samples. The temperature dependence of the effective charges carried by the ions, deduced from TO-LO splittings, is also consistent with a displacive mechanism.