Dielectric spectroscopy of SrTiO3
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Ferroelectricity was induced in $\mathrm{SrTiO}{}_{3}$ by the isotope exchange of ${}^{18}\mathrm{O}$ for ${}^{16}\mathrm{O}$. Dielectric measurements confirmed the ferroelectricity of $\mathrm{SrTi}{}^{18}\mathrm{O}{}_{3}$, showing a peak at 23 K. A hysteresis loop in the $D$ vs $E$ measurement and TO phonon observed in the Raman spectra supported the evolution of ferroelectricity in $\mathrm{SrTi}{}^{18}\mathrm{O}{}_{3}$. This is the first demonstration of $\mathrm{SrTi}\mathrm{O}{}_{3}$ becoming ferroelectric without the application of external fields or the introduction of a random field through cation substitution.
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By means of dielectric measurements and a Raman-scattering experiment, the uniaxial stress dependence of the ferroelectric and structural phonon modes in SrTi${\mathrm{O}}_{3}$ crystal has been studied at liquid-helium temperature. The ferroelectric phase transitions were induced by a stress normal to the (100) or (110) face. The inverse dielectric susceptibilities were found to change linearly with applied stress, and the phonon frequencies of corresponding ferroelectric modes were found to vary following the Lyddane-Sachs-Teller relation. These characteristics were analyzed by using the phenomenological free energy which contains as interaction terms ${Q}_{\ensuremath{\lambda}\ensuremath{\mu}}{X}_{\ensuremath{\lambda}}{(\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}})}_{\ensuremath{\mu}}+{R}_{\ensuremath{\lambda}\ensuremath{\mu}}{X}_{\ensuremath{\lambda}}{(\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\Phi}}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\Phi}}})}_{\ensuremath{\mu}}+{t}_{\ensuremath{\lambda}\ensuremath{\mu}}{(\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}})}_{\ensuremath{\lambda}}{(\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\Phi}}}\stackrel{\ensuremath{\rightarrow}}{\mathrm{\ensuremath{\Phi}}})}_{\ensuremath{\mu}}$. From the behavior of the dielectric constants below the critical stress and that of the soft-phonon-mode frequencies above the critical stress, the coupling coefficients ${Q}_{\ensuremath{\lambda}\ensuremath{\mu}}$, ${R}_{\ensuremath{\lambda}\ensuremath{\mu}}$, ${t}_{\ensuremath{\lambda}\ensuremath{\mu}}$ and other parameters in the free energy have been determined consistently. Anticrossing between the ferroelectric and structural modes was observed for an oblique-wave-vector phonon. Anomalous increase of the damping of the total symmetric ferroelectric mode near the transition stress has been found and discussed.
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Measurements of the complex dielectric permittivity in nominally pure ${\mathrm{SrTiO}}_{3}$ are reported for frequencies ${10}^{\mathrm{\ensuremath{-}}3}$ Hz\ensuremath{\le}\ensuremath{\nu}\ensuremath{\le}${10}^{8}$ Hz and temperatures 0.1 K\ensuremath{\le}T\ensuremath{\le}300 K. The experiments reveal relaxation phenomena similar to those reported from elastic measurements. The onset of constant loss below 50 K and a low-temperature relaxation reveals characteristic features of a tunneling motion. These phenomena can be interpreted to be characteristic of a quantum phase transition into a coherent quantum state.
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The lattice-dynamical characteristic of the 110\ifmmode^\circ\else\textdegree\fi{}K transition in SrTi${\mathrm{O}}_{3}$ has been elucidated by inelastic neutron scattering measurements. The transition is caused by a ${\mathrm{T}}_{25}$ soft-phonon mode at the [111] zone boundary, confirming the model recently proposed by Fleury, Scott, and Worlock. The square of the frequency of this soft mode is proportional to $T\ensuremath{-}{T}_{0}$ above the transition temperature ${T}_{0}$. At the transition, this zone boundary becomes a superlattice point, enlarging the unit cell. The results of elastic intensity measurements at the superlattice points at 78\ifmmode^\circ\else\textdegree\fi{}K are consistent with the structure given by Unoki and Sakudo in its space group $\frac{I4}{mcm({{D}_{4h}}^{18})}$ as well as in the oxygen parameter. This structure is shown to be a logical consequence of the condensed soft mode.
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Slater's theory of the dielectric constant in BaTi${\mathrm{O}}_{3}$ has been extended by treating the ionic polarizability quantum mechanically instead of classically. This leads to an expression for the dielectric constant which is good at all temperatures and shows a deviation from the Curie-Weiss law at low temperatures. The theory is applied to SrTi${\mathrm{O}}_{3}$ and to KTa${\mathrm{O}}_{3}$ above its transition at 13.2\ifmmode^\circ\else\textdegree\fi{}K.
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A series of twenty homogeneous ${\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x}\mathrm{Ti}{\mathrm{O}}_{3}$ mixed crystals has been measured dielectrically between 4.2 and 300 K. In the tetragonal phase, the dielectric constant perpendicular to the $c$ axis becomes peaked above ${x}_{c}=0.0018$, the quantum mechanical onset for displacive ferroelectricity. The polarization $\ensuremath{\perp}c$ can be switched between the two equivalent $a$ axes, i.e., the system is an $\mathrm{XY}$, $n=2$, quantum ferroelectric. Above ${x}_{r}=0.016\ifmmode\pm\else\textpm\fi{}0.002$, the $\ensuremath{\epsilon}(T)$ peaks round in a distinct manner which we attribute to the onset of a random-field-induced domain state.
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We report a low-temperature loss anomaly in several oxidic perovskites such as ${\mathrm{KTaO}}_{3}$, ${\mathrm{KTaO}}_{3}$:Nb, ${\mathrm{SrTiO}}_{3}$, ${\mathrm{SrTiO}}_{3}$:Ca, ${\mathrm{PbTiO}}_{3}$:La, Cu, and ${\mathrm{BaTiO}}_{3}$:La. We show that this anomaly arises from a low-frequency dielectric relaxation. The activation energy and the relaxation time of this process are nearly the same for all the investigated perovskites disregarding their composition, texture, and ferroelectric properties. We thus ascribe the loss anomaly to the localization of polarons on residual defects. Although the dielectric losses in ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$:Ca are qualitatively similar to other perovskites, the loss anomaly occurs at much lower temperatures: 10 instead of 40 K.
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Dielectric loss
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Using path-integral Monte Carol simulations and an ab initio effective Hamiltonian, we study the effects of quantum fluctuations on structural phase transitions in the cubic perovskite compounds SrTiO3 and BaTiO3. We find quantum fluctuations affect ferroelectric (FE) transitions more strongly than antiferrodistortive (AFD) ones, even though the effective mass of a single FE local mode is larger. For SrTiO3 we find that the quantum fluctuations suppress the FE transition completely, and reduce the AFD transition temperature from 130K to 110K. For BaTiO3, quantum fluctuations do not affect the order of the transition, but do reduce the transition temperature by 35-50 K. The implications of the calculations are discussed.
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Following the proposal by Muller, Berlinger and Tosatti on a possible coherent quantum regime in SrTiO3 below 40 K we have performed elastic measurements to look for possible related anomalies in a near-monodomain crystal. The known anomalies related to the 105 K structural transition were well reproduced. In addition, distinct anomalies were observed below 40 K, both in internal friction and in elastic compliance. The anomalies cannot be explained by phonon interaction with the soft TO mode. A different kind of excitation seems to be required. The features found bear some qualitative resemblance to what is observed in the superfluid phase of 4He.
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We propose a new interpretation of the 110\ifmmode^\circ\else\textdegree\fi{}K phase transition in SrTi${\mathrm{O}}_{3}$, in which the essential feature is a soft phonon at the corner of the cubic Brillouin zone. This interpretation is supported by new evidence from the temperature-dependent Raman spectrum as well as by results of earlier experiments and calculations. Several other experimental results are explained or predicted on the basis of our model for the phase transition.
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