Interplay between static and dynamic polar correlations in relaxor $\text{Pb}\left({\text{Mg}}_{1/3}{\text{Nb}}_{2/3}\right){\text{O}}_3$

We have characterized the dynamics of the polar nanoregions in $\text{Pb}\left({\text{Mg}}_{1/3}{\text{Nb}}_{2/3}\right){\text{O}}_3$ through high-resolution neutron-backscattering and spin-echo measurements of the diffuse-scattering cross section. We find that the diffuse-scattering intensity consists of both static and dynamic components. The static component first appears at the Curie temperature $\Theta \sim 400\text{K}$ while the dynamic component freezes completely at the temperature $T_f\sim 200\text{K}$; together, these components account for all of the observed spectral weight contributing to the diffuse-scattering cross section. The integrated intensity of the dynamic component peaks near the temperature at which the frequency-dependent dielectric constant reaches a maximum $\left(T_{\text{max}}\right)$ when measured at 1 GHz, i.e., on a time scale of $\sim 1\text{ns}$. Our neutron-scattering results can thus be directly related to dielectric and infrared measurements of the polar nanoregions. Finally, the global temperature dependence of the diffuse scattering can be understood in terms of just two temperature scales, which is consistent with random-field models.

Figure 1

(a) The square of the soft, transverse-optic mode frequency is shown as a function of temperature (data taken from Refs. 4, 5). (b) The frequency dependence of the dielectric constant of PMN (data taken from Ref. 6). (c) The inverse of the 100 kHz dielectric susceptibility as a function of temperature. The dashed line represents a high-temperature fit and the Curie-Weiss temperature $\left(\Theta \right)$ is indicated. The data were taken from Ref. 7.

Figure 2

(Color online) (a) Diffuse-scattering intensity contours measured near $\vec{Q}=\left(100\right)$ on the DCS spectrometer located at NIST; the circles illustrate where in reciprocal space. the measurements on IN10 and IN11 were conducted. (b) Backscattering spectra measured at several temperatures and summed over the $Q$ positions indicated as IN10 in panel (a). The error bars are related to the square root of the total number of neutron counts.

Figure 3

(Color online) Time dependence of the normalized intermediate scattering function $\mathfrak{R}\left[I\left(Q,t\right)/I\left(Q,0\right)\right]$ at various temperatures. Both dynamic and static components are observed for $200<T<450\text{K}$ but only the static component is present at 200 K. The error bars are related to the square root of the total number of neutron counts.

Figure 4

(Color online) Temperature dependence of the static and dynamic components extracted from fits to the data in Fig. 3. (a) compares the static intensities measured with SPINS $\left(\delta E=100\mu \text{eV}\right)$, IN10 $\left(\delta E=0.5\mu \text{eV}\right)$, and IN11. Panel (b) plots the dynamic component of the intensity as a function of temperature. The value of $T_{\text{max}}$ from Ref. 6 measured at 1 GHz is represented by a vertical line. We emphasize that all data was taken on the same PMN sample.

Figure 5

(Color online) (a) The decay time $\tau$ is plotted as a function of temperature. The solid line is a fit to an Arrhenius law $\left(\tau ={\tau }_{\circ }{e}^{U/k_{b}T}\right)$ with $U=1100\text{K}$. (b) The fitting parameter $\alpha$ is plotted as a function of temperature.