Freezing of the local dynamics in the relaxor ferroelectric [Pb(Zn${}_{1/3}$Nb${}_{2/3}$)O${}_3$]${}_{0.955}$[PbTiO${}_3$]${}_{0.045}$

We report measurements of the neutron diffuse scattering in a single crystal of the relaxor ferroelectric material 95.5$\%$Pb(Zn${}_{1/3}$Nb${}_{2/3}$)O${}_3$-4.5$\%$PbTiO${}_3$ (PZN-4.5$\%$PT). We show that the diffuse scattering at high temperatures has a quasielastic component with energy width $\gtrsim$0.1 meV. On cooling the total diffuse scattering intensity increases, but the intensity and the energy width of the quasielastic component gradually diminish. At 50 K the diffuse scattering is completely static (i.e., the energy width lies within the limits of our instrumental resolution). This suggests that the dynamics of the short-range correlated atomic displacements associated with the diffuse scattering freeze at low temperature. We find that this depends on the wave vector $q$ as the quasielastic diffuse scattering intensities associated with $\langle 001\rangle$ (T1-type) and $\langle 110\rangle$ (T2-type) atomic displacements vary differently with temperature and electric field.

Figure 1

Schematic diagram of the scattering geometry in which measurements were made in the ($H0L$) plane with an electric field applied along [001]. The gray butterfly-shaped region represents constant-intensity contours of the T2-diffuse scattering centered at $\mathbf{Q}=\left(001\right)$. The red-shaded ellipse represents similar constant-intensity contours of the T1-diffuse scattering centered at the same Bragg peak. The small squares show the locations in Q of the BASIS detectors for elastically ($\hslash \omega =0$) scattered neutrons.

Figure 2

Diffuse scattering intensities are plotted versus $\hslash \omega$ at 500 K (red), 400 K (green), 300 K (blue), and 50 K (black) for the (a) T1 component, measured at $\mathbf{Q}=(0.05,0,1)$, and the (b) T2 component, measured at $\mathbf{Q}=(-0.1,0,1.1)$. The solid lines are based on the least-square fits to the data described in the text. The error bars represent the square root of the number of counts.

Figure 3

Diffuse scattering intensities are plotted versus $\hslash \omega$ at 400 K after zero-field cooling (ZFC: black, open symbols) and field cooling (FC: red, solid symbols). Data are shown for the (a) T1 component, measured at $\mathbf{Q}=(0.05,0,1)$, and the (b) T2 component, measured at $\mathbf{Q}=(-0.1,0,1.1)$. The solid lines are based on the least-square fits to the data described in the text. The error bars represent the square root of the number of counts.

Figure 4

(a) Energy width $\hslash \Gamma$ (half-width at half-maximum) of the quasielastic diffuse scattering versus temperature for the T1 component (ZFC $=$ red, open circles; FC $=$ red, solid circles) and the T2 component (ZFC $=$ blue, open diamonds; FC $=$ blue, solid diamonds). The black triangles are data points taken from spin-echo measurements, where open symbols are ZFC data and filled symbols are the FC data.[15] (b) Temperature dependence of the integrated intensities of the quasielastic diffuse scattering. (c) Temperature dependence of the integrated intensities of the “elastic” component of the diffuse scattering. The Curie temperature T${}_C$ and the (estimated) Burns temperature[8, 15] $T^{*}$ are also shown in the figure.