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Lattice quantum effects in KH2PO4

Protons in ferroelectric KH2PO4 crystal (KDP) participate in hydrogen bonds and they are strongly coupled to dipoles of the heavy-ion sublattice (lattice). The KDP system is usually considered in the following way: a double-well potential acts on protons which localize below the critical temperature, Tc, into one of the wells, while the harmonic lattice system produces spontaneous electric polarization below Tc due to the proton-lattice coupling. In the coupled tunneling proton-phonon model [1], protons are represented by interacting two level systems, where the splitting energy, D, is energy of proton tunneling between two wells, while harmonic lattice only produces additional interaction between protons. The tunneling opposes the localization, so that increase of D leads to decrease of Tc and vice versa. Since deuteron has smaller value of D than proton, this model can explain the isotopic effect, i.e. higher value of Tc in KD2PO4 than in KDP. Additionally, increase of D with decrease of hydrogen-bond length, R, can explain experimental fact that Tc decreases with pressure and vanishes at the critical pressure, pc. However, several experimental results contradict to this model [1] and dielectric measurements of KDP near pc suggest that the energy responsible for vanishing of Tc is too small and does not correspond to D [2]. In the strong dipole-proton coupling model [3] and its modified version [4], it was assumed that protons, which do not interact among themselves, has excitation energies higher than kTc and hv, where v is characteristic lattice frequency. Therefore, protons in adiabatic ground state only produce ferroelectric interaction in the lattice, while the difference in ground-state energies between proton and deuteron causes the isotopic effect. Some of experimental results that contradict to the coupled tunneling proton-phonon model were explained by applying classical approximation for the lattice motion within the modified model [4]. In order to estimate lattice quantum effects in the KDP system, the path-integral Monte Carlo method is applied to this model. Calculated quantum effects are weak near Tc for the atmospheric-pressure value of R. By decreasing the value of R below the critical value, the phase transition is suppressed by lattice quantum fluctuations, which zero-point energy has similar value as the energy responsible for vanishing of Tc in KDP at pc [2]. [1] M. Tokunaga, T. Matsubara, Ferroelectrics 72 (1987) 175. [2] S. Endo, K. Deguchi, M. Tokunaga, Phys. Rev. Lett. 88 (2002) 35503. [3] H. Sugimoto, S. Ikeda, Phys. Rev. Lett. 67 (1991) 1306. [4] D. Merunka, B. Rakvin, Phys. Rev. B 66 (2002) 174101.

Quantum effects; KH2PO4 ferroelectric; Path-integral Monte Carlo method

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