Vibrational properties of ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ across the ferroelectric transition

In order to explore the properties of a two-sublattice ferroelectric, we measured the infrared and Raman scattering response of ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ across the ferroelectric and glassy transitions and compared our findings to a symmetry analysis, calculations of phase stability, and lattice dynamics. In addition to uncovering displacive character and a large hysteresis region surrounding the ferroelectric transition temperature $T_{\mathrm{C}}$, we identify the vibrational modes that stabilize the polar phase and confirm the presence of two ferroelectric variants with opposite polarizations. Below $T_{\mathrm{C}}$, a poorly understood relaxational or glassy transition at $T_{\mathrm{g}}$ is characterized by local structure changes in the form of subtle peak shifting and activation of low frequency out-of-plane Cu- and In-containing modes. The latter are due to changes in the Cu/In coordination environments and associated order-disorder processes. Moreover, $T_{\mathrm{g}}$ takes place in two steps with another large hysteresis region and significant underlying scattering. Combined with imaging of the room temperature phase separation, this effort lays the groundwork for studying ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ under external stimuli and in the ultrathin limit.

Figure 1

The double-well potential energy profile computed by freezing the polar ${\mathrm{\Gamma }}_2^{-}$ phonon mode in the paraelectric phase as a function of the phonon distortion amplitude. Crystal structures of the paraelectric ($C2/c$) and ferroelectric ($Cc$) phases of ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ are shown in the inset. Black arrows denote the displacement of Cu ions corresponding to the ${\mathrm{\Gamma }}_2^{-}$ mode distortion. Purple arrows denote the relatively small displacement of In ions. The net polarization of individual ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ layers is along the direction of the blue arrows.

Figure 2

The PBE-D3 calculated (a) infrared and (b) Raman spectra for the paraelectric ($C2/c$) and ferroelectric ($Cc$) phases of ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ at 0 K. The symmetries of the major infrared and Raman peaks in the paraelectric and ferroelectric phases are marked in blue and red, respectively. Some peaks are unmarked for clarity. These unmarked peaks contain mixed contribution from both IR active or both Raman active modes in their respective plots, similar to the marked peaks with mixed contributions. The $*$ sign denotes the potential signature modes of the ferroelectric phase, which are absent in the paraelectric phase. The intensities were normalized between zero and one. A detailed list of each infrared- and Raman-active phonon mode frequency along with its associated atomic-displacement pattern is provided in the Supplemental Material [50] (see, also, Refs. [29, 31, 35, 41, 43, 67, 72, 73, 74, 75, 76, 77, 78, 79, 80]).

Figure 3

(a, d) Close-up view of the far infrared response of ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ as a function of temperature. High temperatures are indicated in red, and low temperatures are indicated in blue. The peaks are labeled using $C2/c$ and $Cc$ space group symmetries in the high and low temperature phases, respectively. Panels (b) and (c) highlight the behavior for the ferroelectric modes in panel (a), whereas panels (e) and (f) display peak position vs temperature of the ferroelectric modes highlighted in panel (d). The vertical gray bars define the transition regions, and the open to closed data points denote the $C2/c\to Cc$ space group change. There is a significant hysteresis depending upon direction of temperature sweep. The measurements shown here are taken with increasing temperature.

Figure 4

(a) Raman scattering of ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ as a function of temperature. High temperatures are indicated in red, and low temperatures are indicated in blue. The peaks are labeled using $C2/c$ and $Cc$ space group symmetries in the high and low temperature phases, respectively. Panels (b)–(g) highlight the behavior of several different Raman-active modes, many of which are sensitive to $T_{\mathrm{C}}$. The vertical gray bars define $T_{\mathrm{C}}$ and $T_{\mathrm{g}}$. The open to closed data points indicate the $C2/c\to Cc$ transition. There is a significant hysteresis effect depending upon direction of temperature sweep. This is seen very clearly in the Raman scattering response when rendered as a contour plot (Fig. S3, Supplemental Material [50]). The measurements shown here correspond to a temperature up-sweep.

Figure 5

Infrared (a–c) and Raman scattering (d–f) response of ${\mathrm{CuInP}}_2{\mathrm{S}}_6$ across the relaxational or glassy phase transition, $T_{\mathrm{g}}$. High temperatures are shown in red, and low temperatures are shown in blue. The peaks are labeled using symmetries of the $C2/c$ and $Cc$ space groups in the high and low temperature phases, respectively. Panel (a) summarizes the infrared spectrum as a function of temperature, and panels (b) and (c) show peak position vs temperature to highlight the infrared-active modes most influenced by $T_{\mathrm{g}}$. The curves in panel (a) are offset for clarity. Panel (c) summarizes the variable temperature Raman scattering response as a contour plot, and panels (e) and (f) deepen our understanding of the local structure transition at $T_{\mathrm{g}}$ by examining phonon lifetime trends as discussed in the text. There is a significant hysteresis effect in both $T_{\mathrm{C}}$ and $T_{\mathrm{g}}$ depending upon direction of temperature sweep (Fig. S3, Supplemental Material [50]). These measurements correspond to a temperature up-sweep.