Abstract
Soft modes in crystals are lattice vibrations with frequencies that decrease and eventually vanish as the temperature approaches a critical point, e.g., a structural change due to a phase transition. In ionic para- or ferroelectric materials, the frequency decrease is connected with a diverging electric susceptibility and, for infrared active modes, a strong increase in oscillator strength. The traditional picture describes soft modes as overdamped transverse optical phonons of a hybrid vibrational-electronic character. In this context, potassium dihydrogen phosphate (KH2PO4, KDP) has been studied for decades as a prototypical material with, however, inconclusive results regarding the soft modes in its para- and ferroelectric phase. There are conflicting assignments of soft-mode frequencies and damping parameters. We report the first observation of a longitudinal underdamped soft mode in paraelectric KDP. Upon impulsive femtosecond Raman excitation of coherent low-frequency phonons in the electronic ground state of KDP crystallites, transient powder diffraction patterns are recorded with femtosecond hard x-ray pulses. Electron density maps derived from the x-ray data reveal oscillatory charge relocations over interatomic distances, much larger than the sub-picometer nuclear displacements, a direct hallmark of soft-mode behavior. The strongly underdamped character of the soft mode manifests in charge oscillations persisting for more than 10 ps. The soft-mode frequency decreases from 0.55 THz at T = 295 K to 0.39 THz at T = 175 K. An analysis of the Raman excitation conditions in crystallites and the weak damping demonstrate a longitudinal character. Our results extend soft-mode physics well beyond the traditional picture and pave the way for an atomic-level characterization of soft modes.
Highlights
Soft modes are particular optical phonons occurring at low frequencies in polar and/or ionic crystals
The coupled nuclear and electronic motions account for basic dielectric properties of ferroelectrics and, in particular, allow for including local-field effects according to the Clausius–Mossotti relation.[7]
The results presented here reveal a highly underdamped longitudinal soft mode in paraelectric KDP crystallites
Summary
Soft modes are particular optical phonons occurring at low frequencies in polar and/or ionic crystals. The soft-mode frequency approaches zero when the crystal structure becomes unstable,[1,2] frequently connected with a divergence of the dielectric function,[3,4] and, in the case of infrared-active optical phonons, a strong increase in optical oscillator strength Such behavior has been observed in materials undergoing a transition between a para- and a ferroelectric phase at a critical temperature TC. The classical core-shell model introduced by Cochran[5,6] treats this scenario by solving the mechanical equations of motion of two coupled ions, one of them having a polarizable electron cloud In this picture, the soft mode is a transverse optical phonon with a frequency approaching zero at T 1⁄4 TC, in parallel to the divergence of the static dielectric function. It has been shown for prototypical ferroelectrics such as perovskites that the electric polarization is strongly dominated by electronic motions.[8]
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