Neutron and x-ray diffraction study of cubic [111] field-cooled $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$

Neutron and x-ray diffraction techniques have been used to study the competing long- and short-range polar order in the relaxor ferroelectric $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$ (PMN) under a [111] applied electric field. Despite reports of a structural transition from a cubic phase to a rhombohedral phase for fields $E>1.7\mathrm{kV}∕\mathrm{cm}$, we find that the bulk unit cell remains cubic (within a sensitivity of 90°$-\alpha =0.03°)$ for fields up to $8\mathrm{kV}∕\mathrm{cm}$. Furthermore, we observe a structural transition confined to the near surface volume or “skin” of the crystal where the cubic cell is transformed to a rhombohedral unit cell at $T_c=210\mathrm{K}$ for $E>4\mathrm{kV}∕\mathrm{cm}$, for which 90°$-\alpha =0.08\pm 0.03°$ below $50\mathrm{K}$. While the bulk unit cell remains cubic, a suppression of the diffuse scattering and concomitant enhancement of the Bragg peak intensity is observed below $T_c=210\mathrm{K}$, indicating a more ordered structure with increasing electric field yet an absence of a long-range ferroelectric ground state in the bulk. The electric field strength has little effect on the diffuse scattering above $T_c$, however, below $T_c$ the diffuse scattering is reduced in intensity and adopts an asymmetric line shape in reciprocal space. The absence of hysteresis in our neutron measurements (on the bulk) and the presence of two distinct temperature scales suggests that the ground state of PMN is not a frozen glassy phase as suggested by some theories but is better understood in terms of random fields introduced through the presence of structural disorder. Based on these results, we also suggest that PMN represents an extreme example of the two-length scale problem, and that the presence of a distinct skin may be necessary for a relaxor ground state.

Figure 1

The diffuse scattering in zero-field-cooled and field-cooled states around the (001) Bragg peak. The dark regions represent high intensity contours in comparison to lighter regions. The dashed lines illustrate the line scans conducted to investigate the temperature dependence of the intensity.

Figure 2

(a) The temperature dependence of the diffuse scattering is plotted for several field-cooled values. Panel (b) illustrates the Bragg peak intensity as a function of applied electric field at $50\mathrm{K}$.

Figure 3

The diffuse scattering near $\vec{Q}=\left(003\right)$ under the application of an $8\mathrm{kV}∕\mathrm{cm}$ electric field along [111]. The left-hand side shows diffuse contours plotted on a logarithmic scale at temperatures above $\left(250\mathrm{K}\right)$ and below $\left(50\mathrm{K}\right)$ $T_c$. The dark regions represent high intensity contours in comparison to lighter regions. The right hand panels display linear scans through the diffuse scattering and are represented by the dotted line in the contour plots.

Figure 4

(Color online) The temperature dependence of the diffuse scattering near $\vec{Q}=\left(003\right)$. Panel (a) is a contour plot (on a linear scale) of scans along $(H,H,2.9)$ measured in a field of $8\mathrm{kV}∕\mathrm{cm}$ as a function of temperature. The dark regions represent contours of high intensity compared with lighter regions. Panels (b)–(d) show examples of linear scans at 500, 225, and $50\mathrm{K}$. The panels show the suppression of one wing of the diffuse scattering below $T_c$.

Figure 5

Panel (a) plots the diffuse scattering intensity at $\vec{Q}=(0.05,0.05,2.9)$ as a function of time. The electric field was abruptly turned off and the leads electrically shorted to ground at the time indicated by the dashed line. Panels (b) and (c) show examples of linear scans of the diffuse scattering before and after the field is turned off. The open circles in panel (b) show the diffuse scattering measured with the field turned back on $\sim 70\min$ after the field was turned off. The diffuse scattering reproduces the field-cooled intensity.

Figure 6

Longitudinal $\left(\theta \text{−}2\theta \right)$ and transverse $\left(\omega \right)$ scans through the (111) Bragg peak at 100 and $500\mathrm{K}$ are displayed. No strong distortion at low temperatures is observed.

Figure 7

The lattice strain is plotted in the upper panel as a function of temperature for field cooling with electric fields of 4 and $8\mathrm{kV}∕\mathrm{cm}$. The values for $d_0$ are taken as the measured lattice constant in zero-field-cooled conditions at the given temperature. The longitudinal width as a function of temperature for the $\vec{Q}=\left(111\right)$ Bragg peak is plotted in the lower panel. No change in the longitudinal linewidth or anomalous strain is observed in the bulk under field-cooled conditions.

Figure 8

The lattice strain is plotted in the upper panel as a function of temperature for field cooling with electric fields of 3 and $8\mathrm{kV}∕\mathrm{cm}$. The values for $d_0$ are taken as the lattice constants measured under zero-field-cooling conditions at the given temperature. The lower panel plots the linewidth as a function of temperature for cooling under electric fields of 0 and $8\mathrm{kV}∕\mathrm{cm}$. The data show a clear anomaly in both the lattice strain and the linewidth at $T_c$ for cooling under an $8\mathrm{kV}∕\mathrm{cm}$ field.

Figure 9

Panel (a) plots the lattice strain under field cooling $(8\mathrm{kV}∕\mathrm{cm})$ and zero-field warming conditions. The data show that the distortion remains on removal of the electric field at low temperatures. Panel (b) plots the measured value of $\alpha$ as a function of electric field at $T=50\mathrm{K}$. Panels (c)–(e) show $\theta \text{−}2\theta$ scans through the (111) Bragg peak at 450, 250, and $75\mathrm{K}$.