Quantum ferroelectricity inK1−xNaxTaO3andKTa1−yNbyO3

Abstract

The effect known as ferroelectricity arises when forces between polarizable ions in a solid produce a spontaneous displacement of these ions which results in a lattice polarization below some characteristic (Curie) temperature. Fluctuations in this polarization may be thermally induced as in the case of classical ferroelectrics, or if the Curie temperature is near O K, the fluctuations can be due to quantum-mechanical zero-point motion. The term "quantum ferroelectric" is applied to those systems where fluctuations in the polarization result from the zero-point motion. Experimental determinations of variations in the dielectric constant, spontaneous polarization, and elastic compliance as a function of temperature and impurity concentration are reported for ${\mathrm{K}}_{1\ensuremath{-}x}{\mathrm{Na}}_{x}\mathrm{Ta}{\mathrm{O}}_{3}$ and $\mathrm{K}{\mathrm{Ta}}_{1\ensuremath{-}y}{\mathrm{Nb}}_{y}{\mathrm{O}}_{3}$, and these results show that the physical properties of quantum ferroelectrics differ from those of classical ferroelectrics in the following ways: First, for a quantum ferroelectric, the transition temperature depends on impurity concentration (i.e., on an effective order parameter) as ${T}_{c}\ensuremath{\propto}{(x\ensuremath{-}{x}_{c})}^{\frac{1}{2}}$, as opposed to ${T}_{c}\ensuremath{\propto}(x\ensuremath{-}{x}_{c})$ for the classical case. Second, the inverse dielectric constant varies with temperature as ${\ensuremath{\epsilon}}^{\ensuremath{-}1}\ensuremath{\propto}{T}^{2}$ for the quantum-mechanical case, instead of ${\ensuremath{\epsilon}}^{\ensuremath{-}1}\ensuremath{\propto}T$. Finally, the distribution of transition temperatures in a given macroscopic sample with a Gaussian impurity concentration distribution is $p({T}_{c})\ensuremath{\propto}{T}_{c}\mathrm{exp}(\ensuremath{-}\ensuremath{\alpha}{T}_{c}^{4})$ for the quantum ferroelectric, as opposed to a Gaussian for the classical situation. These results are in agreement with previous theoretical predictions of some of the distinguishing characteristics of quantum ferroelectricity.