Cold neutron study on the diffuse scattering and phonon excitations in the relaxor $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$

Cold neutron scattering experiments have been performed to explore the energy, temperature, and wave-vector dependence of the diffuse scattering and the transverse acoustic (TA) phonons in the relaxor $\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3$. We have observed a weak diffuse scattering cross section above the Burns temperature $T_d\sim 600\mathrm{K}$. This cross section, which is most likely caused by chemical short-range order, persists down to $100\mathrm{K}$, and coexists with the much stronger diffuse scattering that is attributed to the polar nanoregions. A systematic study of the TA phonon around (1, 1, 0) has also been carried out. The phonon is well defined for small wave-vectors $\mathbf{q}$, but broadens markedly around $\mathbf{q}=(0.1,-0.1,0)$.

Figure 1

Temperature dependence of the elastic diffuse scattering intensity measured at $\zeta =0.05$ and 0.1. Data are normalized at $100\mathrm{K}$. The solid and broken lines are guides to the eyes. Open diamonds show the results from TOF measurements (Ref. 10).

Figure 2

Thermal evolution of the elastic diffuse scattering around (1, 1, 0) along the intensity “ridge” direction (thick line, inset).

Figure 3

Intensity contours of the elastic diffuse scattering well below $T_d$ (left column) and just above $T_d$ (right column), around the (1, 0, 0) and (1, 1, 0) Bragg peaks.

Figure 4

(Color) Temperature variation of diffuse scattering contours near (1, 1, 0). The background level is $\sim 20$ counts per $10\mathrm{s}$. Tuned high-temperature contours measured at $650\mathrm{K}$ in (d) (1, 1, 0) and (e) (1, 0, 0) zones.

Figure 5

Temperature variation of constant-$\mathbf{Q}$ scans measured at small $\mathbf{q}$ near (1, 1, 0). Fits are described in the text.

Figure 6

$\mathbf{q}$ variation of constant-$\mathbf{Q}$ scans measured at $300\mathrm{K}$ near (1, 1, 0).

Figure 7

Constant-$\mathbf{Q}$ scans at $\zeta =0.1$ for three temperatures. The incoherent scattering is shown by a thin line only in (a).

Figure 8

The energy-integrated intensity of the diffuse scattering as a function of temperature. The shaded region represents the contribution from the broad central component. The resolution-limited elastic component is shown by the solid line. All curves are guides to the eye.