Neutron scattering study of ferroelectric Sn${}_2$P${}_2$S${}_6$ under pressure

Ferroelectric phase transition in the semiconductor Sn${}_2$P${}_2$S${}_6$ single crystal has been studied by means of neutron scattering in the pressure-temperature range adjacent to the anticipated tricritical Lifshitz point ($p\approx 0.18$ GPa, $T\approx 296$ K). The observations reveal a direct ferroelectric-paraelectric phase transition in the whole investigated pressure range ($0.18–0.6$ GPa). These results are in a clear disagreement with phase diagrams assumed in numerous earlier works, according to which a hypothetical intermediate incommensurate phase extends over several or even tens of degrees in the 0.5 GPa pressure range. Temperature dependence of the anisotropic quasielastic diffuse scattering suggests that polarization fluctuations present above $T_{\mathrm{C}}$ are strongly reduced in the ordered phase. Still, the temperature dependence of the ($\overline{2}$00) Bragg reflection intensity at $p=0.18$ GPa can be remarkably well modeled assuming the order-parameter amplitude growth according to the power law with logarithmic corrections predicted for a uniaxial ferroelectric transition at the tricritical Lifshitz point.

Figure 1

Schematic temperature-composition phase diagram for the system Sn${}_2$P${}_2$(Se${}_x$S${}_{1-x}$)${}_6$ according to Refs. 9 and 18. Dashed line is the second-order phase transition and the solid line is the first-order phase transition.

Figure 2

Accessible part of the $a$*$c$* scattering plane with schematic representation of neutron scattering intensities of principal Bragg reflections in the paraelectric phase. The areas of the circles are proportional to absolute values of neutron scattering structure factors (a) in the present experiment at $p=0.6$ GPa and $T=220$ K and (b) $p=0$ GPa and $T=383$ K values recalculated from the x-ray data of Ref. 39 using the Jana2006 computer program[42] with the neutron wave number set to $k_f=1.48$ Å${}^{-1}$.

Figure 3

Temperature dependence of the $\left(\overline{2}00\right)$ reflection intensity (a) at 0.18 GPa and (b) at 0.6 GPa. The full points and solid lines refer to the fits using Eqs. (4) and (5) with and without logarithmic corrections, respectively.

Figure 4

Zero-energy-transfer scans in the $\left(\overline{2}00\right)$ Brillouin zone of the Sn${}_2$P${}_2$S${}_6$ crystal taken in the vicinity of the ferroelectric phase transition (at 0.6 GPa; near $T_{\mathrm{C}}=205.3$ K). (a) Scans in the $[-0.03,0,1]$ direction (approximately along the diffuse streak), and (b) scans in the $[1,0,0.05]$ direction (across the diffuse streak). Measured scan trajectories are schematically indicated in the insets. Solid lines are just guides for the eye.

Figure 5

Schema of reciprocal-space trajectories of data scans shown in Fig. 4, superposed with contour plots of the critical diffuse scattering known from ambient pressure x-ray diffraction measurements of Ref. 43. Full triangles indicate positions of incommensurate satellite reflections of the ambient-pressure incommensurate phase of the related compound Sn${}_2$P${}_2$Se${}_6$, as reported in Ref. 20.

Figure 6

Temperature dependence of both elastic and quasielastic scattering in the $\left(\overline{2}00\right)$ Brillouin zone at 0.6 GPa: (a) selected constant-Q scans for several temperatures and (b) principal Bragg reflection intensity at q $=(0,0,0)$ and elastic diffuse scattering at q $=(0.02,0,-0.07)$.

Figure 7

Temperature-pressure phase diagram of Sn${}_2$P${}_2$(Se${}_x$S${}_{1-x}$)${}_6$ solid solution.[20, 27, 28, 36, 44] The shaded areas indicate intermediate phases between high-temperature paraelectric and low-temperature ferroelectric phases for given concentrations $x$. The stars stand for Lifshitz points of solid solution with $x$ equals 1, 0.28, 0.2 0.04, and 0 (from left to right). Temperature ranges of neutron scattering measurements reported in this work are indicated by vertical rectangular areas.