Soft Mode Doublet in ${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathbf{O}}_3$ Relaxor Investigated with Hyper-Raman Scattering

Hyper-Raman scattering experiments suggest that a splitting of the lowest $F_{1u}$-symmetry mode of ${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_3$ crystal occurs in a wide temperature range around its Burns temperature $T_d\approx 630\mathrm{K}$. The upper-frequency component, earlier investigated by inelastic neutron scattering experiments above $T_d$, appears to be underdamped even hundred of degrees below $T_d$. The lower-frequency component, known below $T_d$ from far-IR spectroscopy, actually becomes underdamped above $T_d$. This suggests that the lower-frequency mode is the “primary” polar soft mode of ${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_3$, responsible for the Curie-Weiss behavior of its dielectric permittivity above $T_d$.

Figure 1

(a) Unpolarized ($\mathrm{V}+\mathrm{H}$) HRS spectra of PMN at 748 K compared with INS data at 750 K taken from Ref. 12 (●). (b) Temperature evolution of unpolarized HRS PMN spectra. Inset : 473 K spectra together with the instrumental function (thin line).

Figure 2

VVV (left) and HVV (right) hyper-Raman spectra of PMN at various temperatures fitted to the model described in the text (full lines). Dashed and dash-dotted lines show DHO components corresponding to the $E_1$ and the $A_1$ modes, respectively.

Figure 3

Temperature dependence of $E_1$ and $A_1$ frequencies ${\omega }_0$ and damping (in the inset) compared to the INS data of Refs. 7, 8 and IR of Ref. 9. The lower line ($E_1$) corresponds to a fit with a Cochran law.

Figure 4

Top: Temperature dependence of the $E_1$ mode frequencies ${\omega }_0$, ${\omega }_{\mathrm{rel}}$, ${\omega }^{\prime }$, and ${\omega }^{\prime \prime }$, defined in the text. The lines stand for a Cochran-like law ${\omega }^2\propto (T-T_0)$. (b) and (c) show the polarization ratio $\rho$ of the normalized HRS intensities of the $E_1$ and $A_1$ components, respectively. The lines are guides for the eyes. Insets show $I_N(\mathrm{VVV})$ (full symbols) and $I_N(\mathrm{HVV})$ (open symbols) for the two components separately.