Emergence of a quantum coherent state at the border of ferroelectricity

Quantum melting of magnetism or ferroelectricity can lead to novel forms of order characterized by exotic excitations and unconventional superconductivity. Here we show by means of high precision measurements of the temperature and pressure dependence of the dielectric susceptibility that quantum melting of a displacive ferroelectric leads to an unconventional quantum paraelectric state exhibiting the phenomenon of 'order by disorder', namely a fluctuation induced enhancement of electric polarization extending up to a characteristic coherence temperature T*. T* vanishes at the ferroelectric quantum critical point and the square of T* increases with a characteristic linear dependence on the applied pressure. We show that in the vicinity of T* this thermal activation phenomenon can be understood quantitatively, without the use of adjustable parameters, in terms of the hybridization of the critical electric polarization field and the volume strain field of the lattice. At still lower temperatures, well below T*, we observe a breakdown of this unconventional form of quantum paraelectricity and the emergence of a still more exotic state characterized by slowly fluctuating micro-domains of the lattice structure. We suggest that this low temperature state may be viewed as a type of instanton liquid arising from anisotropic strain induced long-range correlations of the electric polarization field.