Intrinsic ferroelectric instability in $\mathrm{Pb}\left({\mathrm{In}}_{1∕2}{\mathrm{Nb}}_{1∕2}\right){\mathrm{O}}_3$ revealed by changing B-site randomness: Inelastic x-ray scattering study

Antiferroelectric (AFE), ferroelectric (FE), or relaxor states can appear in $\mathrm{Pb}\left({\mathrm{In}}_{1∕2}{\mathrm{Nb}}_{1∕2}\right){\mathrm{O}}_3$ (PIN) depending on the perovskite B-site randomness. We studied the effects of this randomness on the dynamics of PIN by high resolution inelastic x-ray scattering using ordered PIN (AFE) and disordered PIN (relaxor) single crystals. We have found a clear softening of a transverse optic mode at the $\Gamma$ point in both samples, indicating a robust and intrinsic ferroelectric dynamical correlation regardless of the actual ground state. We believe that the correlation results in a FE instability mode, which gives yield to the FE and relaxor states. We interpret that AFE is stabilized only when In and Nb ions are spatially ordered enough to overwhelm the FE instability. As the B-site randomness becomes larger, AFE is suppressed and the hidden FE state starts appearing. Ultimately, the randomness begins to predominate over the development of FE regions and blocks a long range FE order, which we believe yields polar nanoregions resulting in relaxor behaviors.

Figure 1

$S_2-\mathrm{AnT}-T$ phase diagram of PIN (Ref. 4).

Figure 2

(Color online) Mesh scan results of (a) O-PIN and (b) D-PIN. $\frac{h}{4}0\frac{l}{4}$ superlattice spots for O-PIN and a strong, butterfly-shaped diffuse scattering for D-PIN were observed.

Figure 3

(Color online) IXS profiles of transverse modes for O-PIN and D-PIN and fits with Eq. (2) using a least-squares method. The fitting results are shown by a red solid line. The components of the calculated profile are also shown by black (elastic), green (TA mode), and blue (TO mode) solid lines.

Figure 4

Phonon dispersions of transverse modes of (a) O-PIN and (b) D-PIN and longitudinal modes of (c) O-PIN and (d) D-PIN. The solid and open circles represent the transverse and longitudinal modes, respectively. Two solid curves in each figure are guides to the eye with the aim of comparing O-PIN and D-PIN. Note that the full energy scale for the transverse modes is different from that of the longitudinal modes.

Figure 5

(a) Longitudinal phonon modes of O-PIN. Folded branches are estimated as shown by dotted and solid curves. A dark gray curve represents the estimated LA dispersion, which is the same as that of LA of D-PIN. The inelastic profiles of the longitudinal modes of (b) O-PIN and (c) D-PIN are shown. The dotted lines are for a guide to the eyes.

Figure 6

Normalized line widths $(\Gamma ∕E)$ of the transverse optic mode of (a) O-PIN and (b) D-PIN. A trend of the overdamping toward the $\Gamma$ point (waterfall-like behavior) is seen in both O-PIN and D-PIN.