# Vibrational properties of CuInP2S6 across the ferroelectric transition

Sabine N. Neal  Department of Chemistry, University of Tennessee, Knoxville,
Tennessee 37996, USA  Sobhit Singh  Department of Physics and Astronomy,
Rutgers University, Piscataway, New Jersey 08854, USA  Xiaochen Fang
Department of Physics and Astronomy, Rutgers University, Piscataway, New
Jersey 08854, USA  Rutgers Center for Emergent Materials, Rutgers University,
Piscataway, New Jersey 08854, USA  Choongjae Won  Laboratory for Pohang
Emergent Materials and Max Plank POSTECH Center for Complex Phase Materials,
Pohang University of Science and Technology, Pohang 790-784, Korea  Fei-ting
Huang  Department of Physics and Astronomy, Rutgers University, Piscataway,
New Jersey 08854, USA  Rutgers Center for Emergent Materials, Rutgers
University, Piscataway, New Jersey 08854, USA  Sang-Wook Cheong  Department of
Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
Rutgers Center for Emergent Materials, Rutgers University, Piscataway, New
Jersey 08854, USA  Laboratory for Pohang Emergent Materials and Max Plank
POSTECH Center for Complex Phase Materials, Pohang University of Science and
Technology, Pohang 790-784, Korea  Karin M. Rabe  Department of Physics and
Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA  David
Vanderbilt  Department of Physics and Astronomy, Rutgers University,
Piscataway, New Jersey 08854, USA  Janice L. Musfeldt<EMAIL_ADDRESS>Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996,
USA  Department of Physics and Astronomy, University of Tennessee, Knoxville,
Tennessee 37996, USA

###### Abstract

In order to explore the properties of a two-sublattice ferroelectric, we
measured the infrared and Raman scattering response of CuInP2S6 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 $T_{\rm C}$, we identify the
vibrational modes that stabilize the polar phase and confirm the presence of
two ferroelectric variants with opposite polarizations. Below $T_{\rm C}$, a
poorly understood relaxational or glassy transition at $T_{\rm g}$ 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, $T_{\rm g}$ 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 CuInP2S6 under external stimuli
and in the ultra-thin limit.

## Introduction

The past decade has witnessed exceptional progress in revealing the potential
and inner workings of complex chalcogenides, especially those belonging to the
metal phosphorous trisulfide family ($M$PS3, with $M$ = Mn, Fe, Ni) Burch2018
; McGuire2020 ; Wang2020 . Exciting properties under external stimuli include
sliding, metallicity, piezochromism, and superconductivity under pressure
Haines2018 ; Wang2018b ; Harms2020 ; Coak2021 , reentrant phases in high
magnetic fields Wildes2020 ; Wang2021 ; McCreary2020 ; Alliati2020 , tunable
band gaps Wang2018a , and strongly anisotropic thermal conductivity Kargar2020
. These systems can also be exfoliated into few- and single-layer sheets that
host novel magnetic excitations and states as well as symmetry breaking
Kaul2014 ; Huang2017 ; Kim2019 ; Long2017 ; Sun2019 ; Zhang2015 ; Kuo2016 ;
Lee2016_nano ; Zhong2017 ; Chu2020 . While simple metal site substitution is
well-studied in the $M$PS3 series, bimetallic substitution is relatively
unexplored even though lower symmetry may promote useful properties such as
ferroelectricity Singh2008 ; Swamynadhan2021 ; Kurumaji2015 ; Xu2017 ;
Osada2019  along with different types of structural phase transitions. Dual-
sublattice analogs such as bimetallic CuInP2S6 and AgInP2S6 offer flexible
platforms for the discovery of tunable states of matter under external stimuli
and the development of structure-property relations. CuInP2S6, for instance,
hosts a quadruple-well potential with two distinct polar phases and four
different polarization states under strain Brehm2020 ; NeumayerACSami2020 .

CuInP2S6 is a layered van der Waals system with a paraelectric
$\leftrightarrow$ ferroelectric transition near $T_{C}$ = 310 K Grzechnik998 ;
Simon1994 ; MAISONNEUVE1995 ; Fagot_Revurat_2003 ; Liu2016 ; Belianinov2015 ;
Dziaugys2020 . Although the terms “ferrielectric” and “ferroelectric” are both
used in the CuInP2S6 literature Grzechnik998 ; Dziaugys2010 ;
MaisonneuvePRB1997 ; Belianinov2015 ; Bercha2015 ; Simon1994 ; Brehm2020 ;
NeumayerPRA2020 , we have adopted the latter usage here. Our choice is
motivated by the observation that there is no In off-centering instability in
the absence of Cu off-centering. This contrasts with the case of a
ferrimagnet, in which magnetic moments would still appear on either magnetic
sublattice even if suppressed on the other sublattice. Here, instead, the
small In displacements seem more analogous to the anionic displacements that
are also induced by the Cu off-centering. In any case, the polarization in
CuInP2S6 is stable and switchable, although switching under high bias is
associated with Cu+ ion mobility Belianinov2015 ; Zhang2021 . The latter has a
two-step path that involves both in-plane and out-of-plane hopping of Cu+ ions
Zhang2021 . In the high temperature paraelectric phase, the system is in the
$C2/c$ space group, whereas the polar phase has $Cc$ symmetry Dziaugys2010 .
Individual layers of CuInP2S6 consist of Cu+ and In3+ ions surrounded by
sulfur octahedra with P–P dimers filling the octahedral voids. Along with the
primary driver - which is distortion of cations from their centrosymmetric
positions - the symmetry reduction from $C2/c$ $\rightarrow$ $Cc$ is thought
to occur with ordering of the copper occupancies Dziaugys2010 . This provides
a natural explanation for the high bias ionic conductivity. Variable
temperature Raman scattering suggests an order-disorder component to the
ferroelectric transition as well Vysochanskii1998 .

Because $T_{\rm C}$ is just above room temperature, there are a number of
intriguing properties at 300 K. For example, CuInP2S6 displays a room
temperature electrocaloric effect that may prove useful for solid-state
refrigeration Si2019 . The system also hosts sizable intrinsic negative
longitudinal piezoelectricity Brehm2020 ; Youeaav3780 . Further, CuInP2S6
single crystals exhibit polar domain structure that gets smaller and then
disappears in flakes thinner than 50 nm Belianinov2015 ; Chyasnavichyus2016 ;
Chen2019 . CuInP2S6 is also being prepared in thin film form. In fact, when
sandwiched with germanene as a two-dimensional van der Waals heterostructure,
electric field can drive a metal-semiconductor transition via control over the
polarization direction Zhu2019 . CuInP2S6 has been incorporated (along with
MoS2) in a negative capacitance field effect transistor as well Wang2019 .
Dielectric dispersion studies reveal a broad relaxation near 150 K, although
the exact position, amplitude, and shape depends upon the measurement
frequency Dziaugys2010 . This relaxation is attributed to a dipolar glass
transition due to freezing of the electric dipole Dziaugys2010 . Finally, we
note that this system hosts a first order monoclinic $\leftrightarrow$
triclinic structural transition at 4 GPa Grzechnik998 .

In this work, we combine infrared absorption and Raman scattering
spectroscopies to reveal symmetry-breaking and local lattice distortions
across the ferroelectric and relaxational or glassy phase transitions in
CuInP2S6. We compare our findings with complementary lattice dynamics
calculations, mode displacement patterns, and an analysis of the energy
landscape. Interestingly, we identify several different infrared- and Raman-
active modes in this system that appear below the ferroelectric transition,
although of course only the odd-symmetry features contribute to the
development of electric polarization. The mechanism of the $C2/c$
$\rightarrow$ $Cc$ transition is displacive, and comparison with the $M$PS3
family of materials reveals that bimetallic $A$-site substitution is what
enables the polar ground state to emerge Singh2008 ; Swamynadhan2021 . The 150
K order-disorder transition, on the other hand, does not take place with a
change in space group. Yet, it is characterized by subtle peak shifting  and
activation of low-frequency out-of-plane Cu- and In-containing modes that
arise due to differences in the local bonding environment. Thus in addition to
order-disorder and glassy character to the transition near 150 K, there is a
weak structural component due to Cu site disorder. The strong hysteresis as
well as the two-step character of $T_{\rm g}$ are also consequences of
bimetallic substitution and the resulting Cu site disorder. We further
investigate the tendency toward chemical-phase separation using a combination
of vibrational spectroscopies as well as piezoforce and transmission electron
microscopies uncovering the signatures of the highest quality CuInP2S6
crystals and imaging their two polarization domains. Going forward, these
studies will enable rapid verification of crystal quality.

## Methods

##### Crystal growth and characterization:

CuInP2S6 single crystals were grown by vapor transport methods as follows.
Copper powders, indium shots, a phosphorus lump, and sulfur flakes were loaded
into an evacuated quartz tube with $\approx$10-5 torr pressure and then heated
with a temperature gradient between both ends of the quartz ampule. The sealed
tube was held at $\approx$1023 K for 10 days and then cooled to room
temperature. The single crystal flakes were mechanically extracted from the
entangled bulk. As detailed in the Supporting Information, there is a strong
tendency toward chemical phase separation in CuInP2S6-like materials. In fact,
until the crystals are rigorously tested, they should be regarded as
Cu1-xIn1+x/3P2S6. Chemical vapor transport growth of CuInP2S6 results in thin,
orange, transparent flakes. We call these single phase platelets Type I
crystals. Type II crystals on the other hand contain CuInP2S6 \+ non-
ferroelectric In4/3P2S6 as a secondary phase. All of the spectroscopic work
reported here was performed with Type I single crystals.

The exceptional phase complexity makes growth of high-quality stoichiometric
crystals quite challenging, and we strongly urge that each crystal be tested
for phase purity as discussed in the Supporting Information. There are a
number of tests that can be used to confirm sample quality and purity. In this
work, we performed energy dispersive x-ray analysis (EDX), piezoforce
microscopy, and transmission electron microscopy. The vertical piezoforce
microscopy (PFM) experiments were performed on freshly exfoliated surfaces of
CuInP2S6 using the MultiModeTM atomic force microscope by Veeco/Digital
Instruments. Thermally cured gold paste was used to mount the sample and act
as the bottom electrode. All PFM measurements were conducted using between 3
and 5 V a.c. The voltage was applied to a conducting contact mode AFM tip, and
the bottom electrode was grounded. The vertical piezoelectric response signal
was extracted using a NanoScopeTM controller and a lock-in amplifier. Crystal
structure, electron diffraction, and domain character were examined by
JEOL-2010F field-emission transmission electron microscopy (TEM) in plane-view
specimens. In4/3P2S6-containing regions were observed by selecting (002) spots
of In4/3P2S6.

##### Vibrational spectroscopies:

Prior to our spectroscopic measurements, a Type I single crystal of CuInP2S6
was exfoliated to reveal a clean, smooth $ab$-plane sample surface. This
crystal was adhered to a round pinhole aperture. Infrared measurements were
performed in transmittance mode using a Bruker IFS 113V infrared spectrometer
equipped with a low noise He-cooled bolometer detector over the frequency
range of 20-700 cm-1 with 2 cm-1 resolution. The measured transmittance was
converted to absorption: $\alpha$($\omega$)=
-$\frac{1}{\textit{d}}$ln($\mathcal{T}$($\omega$)), where
$\mathcal{T}(\omega)$ is measured transmittance, and d is the crystal
thickness. This work was carried out on the $ab$-plane, without polarizers.
Note that the $c$-axis is not perpendicular to the $ab$-plane, so there is a
residual contribution from the $c$-axis in our spectroscopic results. This is
fortunate, because we were unable to polish a crystal to fully expose the
$c$-axis. Raman scattering measurements were performed in a back-scattering
geometry on a Horiba LabRAM HR Evolution Raman spectrometer over a 50-750 cm-1
frequency range. We used an excitation wavelength of 532 nm at a power of 0.1
mW, an 1800 line/mm grating, a 50 cm-1 notch filter, and a liquid N2 cooled
CCD detector. We used the same orientation of the CuInP2S6 crystal on the pin
hole as described above, with light incident onto (and scattered from) the
$ab$-plane. No polarizers or analyzers were employed because the instrument
does not have them. As a result, the spectra average over the Raman tensor
components. Table S1 in the Supporting information summarizes the symmetries
of the allowed excitations in the high and low temperature phases of CuInP2S6.
In each case, an open flow cryostat provided temperature control.

##### Electronic structure calculations:

All the first-principles density-functional theory (DFT) calculations were
performed using the Projector Augmented Wave (PAW) method as implemented in
the Vienna Ab initio Simulation Package (VASP) Kresse96a ; Kresse96b ;
KressePAW . The number of valence electrons in the considered PAW
pseudopotentials were 11 ($3d^{10}\,4s^{1}$), 3 ($5s^{2}\,5p^{1}$), 5
(3$s^{2}\,3p^{3}$), and 6 ($3s^{2}\,3p^{4}$) for Cu, In, P, and S atoms,
respectively. The exchange-correlation functional was computed using the
generalized-gradient approximation (GGA) as parameterized by Perdew-Burke-
Ernzerhof (PBE) PBE . The zero-damping D3 method of Grimme (PBE-D3) was
employed to describe the weak van der Waals interactions between the CuInP2S6
layers Grimme_D3 . This method has been reported to correctly predict a wide
range of physical and chemical properties of CuInP2S6 Tawfik2018 ; Reimers2018
. The energy convergence criterion for self-consistent DFT calculations was
set at $10^{-7}$ eV and force convergence criterion for relaxation of atomic
coordinates was set at $10^{-3}$ eV/Å. The reciprocal space was sampled using
a Monkhorst-pack k-mesh MP1976  of size 8$\times$8$\times$4 along with a
kinetic energy cutoff of 650 eV for the plane waves.

The optimized lattice parameters and cell angles of the paraelectric $C2/c$
phase are $a=b=6.069$ Å, $c=13.159$ Å, $\alpha=\beta=94.5^{0}$, and
$\gamma=119.9^{0}$. The ferroelectric $Cc$ phase was obtained after applying a
polar $\Gamma_{2}^{-}$ distortion on the high-symmetry $C2/c$ phase. A further
free relaxation was performed of the local minimum structure ($Cc$) shown in
Fig. 1. The resulting cell parameters and cell angles of the $Cc$ phase are
$a=b=6.112$ Å, $c=13.360$ Å, $\alpha=\beta=94.3^{0}$, and $\gamma=120.0^{0}$,
which are in good agreement with the experimental data reported at 296 K
SZhou2021 . The Phonopy package was employed to calculate the zone-center
phonon frequencies and phonon eigenvectors of the DFT optimized structures at
0 K using the finite-displacement approach phonopy . The Bilbao
Crystallographic Server was utilized to analyze the symmetry of phonon modes
bilbao2003 . The theoretical infrared (IR) spectra were calculated by
computing the mode dynamical charge associated with each phonon
eigendisplacement, and the theoretical Raman spectra were simulated by
appropriately averaging the Raman activity tensor calculated for each Raman-
active phonon eigenmode at zone center Skelton2017 .

## Results and Discussion

###  .1 Analyzing the symmetries and properties of CuInP2S6

####  .1.1 Energy landscape and ferroelectricity

Figure 1:  The double-well potential energy profile computed by freezing the
polar $\Gamma_{2}^{-}$ 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 CuInP2S6 are shown in the inset.
Black arrows denote the displacement of Cu ions corresponding to the
$\Gamma_{2}^{-}$ mode distortion. Purple arrows denote the relatively small
displacement of In ions. The net polarization of individual CuInP2S6 layers is
along the direction of the blue arrows.

Before we present our infrared and Raman spectroscopies, let us start by
briefly describing the essential details of the crystal structure,
ferroelectricity, and vibrational properties of the paraelectric and
ferroelectric phases of CuInP2S6. The inset of Fig. 1 shows the crystal
structure of the paraelectric and two equivalent ferroelectric phases of
CuInP2S6, which belong to space groups $C2/c$ (no. 15) and $Cc$ (no. 9),
respectively. The bulk unit cell of both phases contains two weakly
interacting single layers of CuInP2S6, $i.e.$, 2 f.u., stacked along the
c-axis. In the paraelectric phase, the vertically stacked CuInP2S6 layers are
related by an in-plane $C_{2}$ rotation followed by a translation $\tau(c/2)$
operation along the $c$-axis. This structure resembles a lamellar structure
composed of a sulfur framework in which the metal cations and P-P dimers fill
the octahedral voids within each layer Maisonneuve1993 ; Simon1994 ;
MAISONNEUVE1995 ; MaisonneuvePRB1997 ; Fagot_Revurat_2003 ; Babuka2019 . The
P-P dimers act as vertical pillars separating the top and bottom sulfur planes
in each layer. By contrast, the Cu and In metal cations reside exactly at the
midplane of the layers, marked by dashed horizontal black lines in the inset
of Fig. 1, lying between two vertically stacked sulfur planes and passing
through the P-P dimer at its half bond length within each CuInP2S6 layer.

The paraelectric phase is stable only at high temperatures ($T>310\,K$)
Grzechnik998 ; Dziaugys2010 ; Belianinov2015 ; Bercha2015 ; Simon1994 ;
MAISONNEUVE1995 ; MaisonneuvePRB1997 ; Fagot_Revurat_2003 . Below 310 K, this
phase transforms into a ferroelectric $Cc$ phase having a net polarization
primarily along the out-of-plane direction of each CuInP2S6 layer Simon1994 ;
MAISONNEUVE1995 ; MaisonneuvePRB1997 ; Fagot_Revurat_2003 ; Babuka2019 , which
occurs due to the polar displacements of the Cu and In sublattices in an
antiparallel fashion relative to the midplane of each CuInP2S6 monolayer, as
shown in Fig. 1.

From the group theory perspective, the paraelectric and ferroelectric phases
are related by a zone center polar optic phonon mode distortion,
$\Gamma_{2}^{-}$ mode ($B_{u}$ symmetry). This mode is unstable in the
paraelectric phase having frequency $50.3i$ cm-1 and it primarily represents
an in-phase vertical displacement of two Cu ions located in the adjacent
CuInP2S6 layers, as denoted using two parallel black arrows in the insets of
Fig. 1 (left and right panels). The calculated potential energy profile
obtained by freezing the the $\Gamma_{2}^{-}$ mode as a function of the phonon
distortion amplitude is shown in Fig. 1. The magnitude of the energy barrier
is comparable with the data reported in Refs. Brehm2020 ; NeumayerACSami2020 .
Notably, in Refs. Brehm2020 ; NeumayerACSami2020 , the authors reported the
presence of two polar phases ($Cc$) with four different (two high and two low)
polarization states under local strain conditions. No local strain was applied
in our work.

We find that, in response to the polar displacement of Cu ions ($\sim$ $1.54$
Å), In ions exhibit a relatively small ($\sim$ $0.20$ Å) but nonzero polar
displacement in the antiparallel direction to that of the displacement of Cu
ions, as shown by purple arrows in the insets of Fig. 1 (left and right
panels). Such a behaviour of In sublattice has been attributed to the second-
order Jahn-Teller effects MaisonneuvePRB1997 ; Vysochanskii1998 ;
Fagot_Revurat_2003 . Although, technically speaking, CuInP2S6 has two polar
sublattices, Cu and In, yielding a ferrielectric ordering in each CuInP2S6
layer, only Cu sublattice has a polar instability. In displacement occurs as a
response to the polar displacement of Cu ions. In other words, there is no In
off-centering instability in the absence of Cu off-centering. Therefore, it is
more natural to refer CuInP2S6 as a ferroelectric.

We further compute the magnitude of the net polarization ($\mathbf{P}$) in the
$Cc$ phase using the Berry-phase approach KSandDV1993 ; RestaRMP1994 . The
theoretically obtained value is
$\mathbf{P}=(0.13,\,0.00,\,3.43)\,\mu\text{C/cm}^{2}$, which is in excellent
agreement with the experimental data reported by Maisonneuve et al.
($P_{z}\sim 3.5\,\mu\text{C/cm}^{2}$ at 150 K) MaisonneuvePRB1997 .
Interestingly, our calculations predict a nonzero in-plane polarization
component $P_{x}$, which has not been discussed in the existing literature, to
the best of our knowledge.

Figure 2:  The PBE-D3 calculated (a) infrared and (b) Raman spectra for the
paraelectric ($C2/c$) and ferroelectric ($Cc$) phases of CuInP2S6 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 $\ast$ 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 Supporting
Information Supporting .

####  .1.2 Selection rules in the paraelectric and ferroelectric phases

Since the primitive cell contains two formula units, $i.e.,$ 20 atoms/cell,
there are sixty allowed phonon modes in CuInP2S6. According to the group
theory, the allowed acoustic and optical vibrations at zone center can be
described using the irreducible representations given below.

For the paraelectric phase ($C2/c$):

$\displaystyle\Gamma\textsubscript{acoustic}=\emph{A}\textsubscript{u}\oplus
2\emph{B}\textsubscript{u},\text{~{}and}$ (1)
$\displaystyle\Gamma\textsubscript{optical}=14\emph{A}\textsubscript{g}\oplus
13\emph{A}\textsubscript{u}\oplus 16\emph{B}\textsubscript{g}\oplus
14\emph{B}\textsubscript{u}.$

For the ferroelectric phase ($Cc$):

$\displaystyle\Gamma\textsubscript{acoustic}=2\emph{A${}^{\prime}$}\oplus\emph{A${}^{\prime\prime}$},\text{~{}and}$
(2) $\displaystyle\Gamma\textsubscript{optical}=28\emph{A${}^{\prime}$}\oplus
29\emph{A${}^{\prime\prime}$}.$

In the paraelectric phase, only _A_ g and _B_ g modes are Raman active while
_A_ u and _B_ u optical modes are infrared active. In the ferroelectric phase,
all the _A ′_ and _A ′′_ optical modes are both Raman and infrared active.
Figure 2 shows the simulated infrared and Raman spectra for the paraelectric
(red) and ferroelectric (blue) phases. A list of the mode symmetries along
with their frequencies is provided in the Supporting Information Supporting .
Some distinct features can be noticed in the simulated peak positions of the
infrared and Raman spectra which may facilitate the experimental
identification of the paraelectric and ferroelectric phases. In Fig. 2, we
marked some Raman and infrared peak positions using $\ast$ signs, which denote
the potential signature modes of the ferroelectric phase. For instance, the
$B_{u}$ infrared peak located near $536$ cm-1 converts into two $A^{\prime}$
and $A^{\prime\prime}$ peaks located at $\sim$ 514 cm-1 and $\sim$ 564 cm-1
upon the paraelectric $\rightarrow$ ferroelectric phase transition [see Fig.
2(a)]. Also, a convoluted shoulder consisting of the $A^{\prime}$ and
$A^{\prime\prime}$ modes develops near $316$ cm-1 frequency in the
ferroelectric phase, which is absent in the infrared spectrum of the
paraelectric phase. Moreover, the unstable polar soft $B_{u}$ mode
($\Gamma_{2}^{-}$) of the paraelectric phase becomes stable in the
ferroelectric phase with a predicted frequency of $\sim$50 cm-1 and
$A^{\prime}$ symmetry. This is also among the signature modes of the
ferroelectric phase and should in principle appear in both infrared absorption
and Raman scattering. This mode is near the low frequency limit of our
instruments, so we do not unambiguously detect it in our measurements.

Figure 3: (a, d) Close-up view of the far infrared response of CuInP2S6 as a
function of temperature. High temperatures are indicated in red, and low
temperatures are indicated in blue. The peaks are labeled using $C$2/$c$ and
$Cc$ space group symmetries in the high and low temperature phases,
respectively. Panels (b, c) highlight the behavior for the ferroelectric modes
in panel (a), whereas (e, 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 $C2/c$
$\rightarrow$ $Cc$ space group change. There is a significant hysteresis
depending upon direction of temperature sweep. The measurements shown here are
taken with increasing temperature.

On the other hand, the simulated Raman spectrum shows distinct signatures for
the paraelectric and ferroelectric phases [see Fig. 2(b)]. For instance, new
Raman peaks are predicted to appear in the ferroelectric phase near
frequencies $72$, $110$, $311$, $434$, and $564$ cm-1 which are absent in the
Raman spectrum of the paraelectric phase. We note that in the ferroelectric
phase, except for a few infrared and Raman active peaks, most of the simulated
peaks contain contribution from $A^{{}^{\prime}}$ and $A^{{}^{\prime\prime}}$
modes. This is mainly due to the fact that the difference in the frequency of
most of the $A^{{}^{\prime}}$ and $A^{{}^{\prime\prime}}$ modes is practically
negligible owing to the weak coupling between the adjacent CuInP2S6 layers.
The simulated Raman spectra of the paraelectric and ferroelectric phases
appears to be in reasonable agreement with our experimental data as well as
with the data reported by Vysochanskii et al. Vysochanskii1998 . A detailed
comparison of the experimental and theoretical data is provided in the
Supporting Information Supporting .

Table 1: Infrared-active vibrational modes that are sensitive to the ferroelectric phase transition in CuInP2S6. Frequencies shown for $C2/c$ are at $T$ $\textgreater$ 310 K. For the $Cc$ phase, $T$ $\textless$ 300 K. All values are in cm-1. Corresponding DFT calculated frequencies ($\omega$) are given in parentheses. $C2/c$ | $Cc$ |
---|---|---
$\omega$ experiment | symmetry |  $\omega$ experiment | symmetry |  displacement patterns
65 (63) | $B_{u}$ | - | - |  in-plane twist of P-P dimers + out-of-plane vibration of S
- | - | 66 (64) | $A^{\prime}$ |  out-of-plane polar displacement Cu
- | - | 71 (71) | $A^{\prime}$ |  in-plane Cu + In + P + out-of-plane S
101 (100) | $B_{u}$ | 102 (102) | $A^{\prime}$ |  out-of-plane rigid shift of P-P dimers (in-phase in adjacent layers) + out-of-plane vibration of S
- | - | 114 (114) | $A^{\prime\prime}$ |  in-plane Cu + In + out-of-plane S
- | - | 361 (354) | $A^{\prime}$ |  in-plane Cu + S and out-of-plane P-P stretching
372 (359) | $A_{u}$ | 373 (355) | $A^{\prime\prime}$ |  in-plane Cu + S and out-of-plane stretching of P-P dimers (opposite phase in adjacent layers)
574 (540, 541) |  $B_{u}$, $A_{u}$ | 553, 587, 611 (558, 563, 563) |  $A^{\prime\prime}$, $A^{\prime}$, $A^{\prime\prime}$ |  in-plane P-P + in-plane S vibration vibration

###  .2 Vibrational properties of CuInP2S6 across the ferroelectric transition

####  .2.1 Infrared spectroscopy probes inversion symmetry breaking

Figure 3 summarizes the infrared response of CuInP2S6 as a function of
temperature. In order to analyze the development of polar phonons across
$T_{\rm C}$, we focus on the two frequency windows displayed in panels (a, d).
At 325 K, there are two distinct phonons in the low frequency infrared
response. These include a sharp $B_{u}$ mode near 65 cm-1 as well as a very
broad $B_{u}$ mode centered around 101 cm-1. As temperature decreases across
$T_{C}$ = 310 K, there is a noticeable activation of the lower frequency
$B_{u}$ mode and the development of a shoulder on the 101 cm-1 feature [Fig. 3
(b, c)]. The appearance of new modes below 310 K is due to a change in the
space group from $C2/c$ in the high temperature paraelectric phase
$\rightarrow$ $Cc$ in the low temperature ferroelectric phase. While the 65
cm-1 feature has $B_{u}$ symmetry above $T_{\rm C}$, the peaks in the low
temperature phase are assigned as $A^{\prime}\oplus A^{\prime}$. This doublet
sharpens and continues to blueshift with decreasing temperature. At the same
time, the once-broad $B_{u}$ symmetry mode at 101 cm-1 develops a shoulder
below $T_{\rm C}$. The lower frequency component evolves as an $A^{\prime}$
mode, and the higher frequency component at 114 cm-1 transforms to
$A^{\prime\prime}$ symmetry [Fig. 3(c)]. The $A^{\prime}$ branch redshifts
below 310 K - a trend that continues to the relaxational or glassy phase
transition near 150 K - below which it blueshifts again. By contrast, the
$A^{\prime\prime}$ branch has a sharp blueshift immediately below room
temperature and continues to harden systematically to 10 K.

Figure 3(d) summarizes the infrared properties of CuInP2S6 in the 350 to 625
cm-1 range. Of the many vibrational modes present in the high temperature
phase, only one is sensitive to $T_{\rm C}$: the $A_{u}$ symmetry mode at 372
cm-1 [Fig. 3(d, e)]. A slight hardening occurs across $T_{\rm C}$ due to the
change in space group, below which the $A_{u}$ feature converts to an
$A^{\prime\prime}$ symmetry mode. Below $T_{\rm C}$, this mode downshifts
slightly before rising near 275 K, continuing to blueshift toward base
temperature. Activation of a small $A^{\prime}$ symmetry mode at 361 cm-1 can
be seen in the low temperature phase near 225 K, with an overall redshift
toward base temperature. Figure 3(d, f) also shows a broad phonon centered 574
cm-1, assigned as an $A_{u}\oplus B_{u}$ symmetry mode. This feature redshifts
slightly across $T_{\rm C}$ below which the new symmetries are assigned as
$A^{\prime}\oplus A^{\prime\prime}$. Systematic redshifting persists through
$\approx$100 K, where this broad feature separates slightly into two
individual symmetry components: $A^{\prime}$ (587 cm-1) and $A^{\prime\prime}$
(553 cm-1). Both features redshift slightly to 10 K. The spectra also reveal
an $A^{\prime\prime}$ mode at 611 cm-1 that emerges just below 300 K. The
appearance of this feature is in line with our theoretical predictions. This
mode sharpens and increases in frequency toward 10 K. A comprehensive table of
mode assignments and displacement patterns is available in the Supporting
Information.

Figure 4:  (a) Raman scattering of CuInP2S6 as a function of temperature. High temperatures are indicated in red, and low temperatures are indicated in blue. The peaks are labeled using $C$2/$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 $T_{\rm C}$. The vertical gray bars define $T_{\rm C}$ and $T_{\rm g}$. The open to closed data points indicate the $C2/c$ $\rightarrow$ $Cc$ 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, Supporting Information]. The measurements shown here correspond to a temperature up-sweep.  Table 2: Raman-active vibrational modes that are sensitive to the ferroelectric phase transition in CuInP2S6. Frequencies shown for $C2/c$ are at $T$ $\textgreater$ 310 K. For the $Cc$ phase, $T$ $\textless$ 300 K. All values are in cm-1. Corresponding DFT calculated frequencies ($\omega$) are given in parentheses. $C2/c$ | $Cc$ |
---|---|---
$\omega$ (experiment) | symmetry |  $\omega$ (experiment) | symmetry |  displacement patterns
67 (66) | $B_{g}$ | - | - |  in-plane Cu + P and out-of-plane S vibration
- | - | 68 (64), 67 (70) |  $A^{\prime}$, $A^{\prime\prime}$ |  out-of-plane Cu +S vibration
100 (108) | $B_{g}$ | 103 (102) | $A^{\prime}$ |  out-of-plane In + P + S
113 (130) | $A_{g}$ | 114 (114), 116 (117) |  $A^{\prime}$, $A^{\prime\prime}$ |  in-plane displacement Cu + In + S, out-of-plane S
161 (175) | $A_{g}$ | - | - |  in-plane Cu + P and out-of-plane S
- | - | 162 (160) | $A^{\prime}$ |  out-of-plane P-P + in-plane S
262 (254) | $A_{g}$ | - | - |  in-plane Cu + P + out-of-plane S
- | - | 264 (263) | $A^{\prime\prime}$ |  in-plane S motion
446 (429) | $B_{g}$ | 450 (435) | $A^{\prime\prime}$ |  out-of-plane P + S
544 (534) | $A_{g}$ | 550 (558, 558) |  $A^{\prime}$, $A^{\prime\prime}$ |  in-plane P-P stretching + S vibration
557 (539) | $B_{g}$ | 558 (562, 563) |  $A^{\prime}$, $A^{\prime\prime}$ |  in-plane P-P + S vibration

The development of a polar state requires inversion symmetry breaking, so we
are naturally interested in the behavior of the odd-symmetry vibrational modes
across $T_{\rm C}$. Our infrared work demonstrates that CuInP2S6 hosts five
polar modes in reasonable overall agreement with the theoretical results in
Fig. 2(a). These include features near 65 and 103 cm-1 that appear to split
below $T_{\rm C}$ due to the activation of new modes, the 372 cm-1 feature
which blueshifts across the ferroelectric transition, and two additional
features near 361 and 611 cm-1 are activated in the low temperature phase. All
infrared-active polar modes, along with their symmetries and displacement
patterns, are listed in Table 1. The predicted $A^{\prime}$ symmetry soft mode
near 50 cm-1 is not unambiguously observed in our spectra - probably due to
the low frequency limit of our instruments.

####  .2.2 Raman scattering spectroscopy across $T_{\rm C}$

Figure 4(a) summarizes the Raman scattering response of CuInP2S6 along with
mode assignments for the various phonons as a function of temperature. Even-
symmetry modes also change across $T_{\rm C}$ although they do not break
inversion symmetry. For instance, the 68 cm-1 $B_{g}$ symmetry mode in the
high temperature paraelectric phase transforms to give $A^{\prime}\oplus
A^{\prime\prime}$ symmetry modes in the low temperature ferroelectric phase
[Fig. 4(b)]. The upper frequency branch is relatively consistent in terms of
size and position until 150 K, below which the peak position hardens toward 75
K and then softens again. The lower frequency branch systematically blueshifts
toward base temperature. Figure 4(c) displays the behavior of the $A_{g}\oplus
B_{g}$ high temperature doublet. The $B_{g}$ component near 103 cm-1 hardens
toward $T_{\rm C}$ then remains relatively constant (although the symmetry
becomes $A^{\prime}$). Below 300 K, the $A_{g}$ peak converts to an
$A^{\prime}$ branch near 113 cm-1 and an $A^{\prime\prime}$ branch near 116
cm-1. Moving on to the $A_{g}$ feature at 162 cm-1 [Fig. 4(d)], we note a 4
cm-1 blueshift across the ferroelectric transition as the mode changes to
$A^{\prime}$ symmetry. The peak position remains relatively constant, shifting
only slightly with decreasing temperature. Figure 4(e) displays the frequency
vs. temperature trend for the $A_{g}$ symmetry mode near 264 cm-1. It hardens
across the $C$2/$c$ $\rightarrow$ $Cc$ transition and is reclassified as
$A^{\prime\prime}$ which has a fairly continuous up-shift to base temperature.
The blueshift near the ferroelectric transition is even more noticeable in the
$B_{g}$ symmetry mode near 450 cm-1 [Fig. 4(f)]. Below 310 K, the feature
hardens steadily until 150 K where there is a slight cusp and then an overall
blueshift toward base temperature. Finally, we turn our attention to Fig. 4(g)
which tracks the high frequency $A_{g}\oplus B_{g}$ doublet. The higher
frequency branch has an even clearer blueshift across $T_{\rm C}$ although
both features move systematically below 310 K, with a slight frequency upturn
below 25 K. A full list of symmetries and mode assignments as well as the
relevant mode displacement patterns are available in the Supporting
Information.

Figure 5: Infrared (a-c) and Raman scattering (d-f) response of CuInP2S6
across the relaxational or glassy phase transition, $T_{\rm g}$. High
temperatures are shown in red, and low temperatures are shown in blue. The
peaks are labeled using symmetries of the $C$2/$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, c) show peak
position vs. temperature to highlight the infrared-active modes most
influenced by $T_{\rm g}$ . The curves in panel (a) are off-set for clarity.
Panel (c) summarizes the variable temperature Raman scattering response as a
contour plot, and panels (e, f) deepen our understanding of the local
structure transition at $T_{\rm g}$ by examining phonon lifetime trends as
discussed in the text. There is a significant hysteresis effect in both
$T_{\rm C}$ and $T_{\rm g}$ depending upon direction of temperature sweep
[Fig. S3, Supporting Information]. These measurements correspond to a
temperature up-sweep.

As previously mentioned, several even-symmetry Raman-active modes change
across $T_{\rm C}$ although they do not break inversion symmetry or contribute
to the electric polarization in CuInP2S6. Our Raman scattering work reveals
activation of additional modes related to the 67 and 113 cm-1 phonons below
$T_{\rm C}$. This is in line with theory for a displacive transition, which
predicts new peaks in the ferroelectric phase. Other Raman-active phonons
including those at 100, 161, 262, 446, and the 544–557 cm-1 doublet reveal
sharp frequency shifts near 310 K as well. Frequency shifts are also evident
in the predicted Raman spectra [Fig. 2(b)]. All Raman-active modes that are
sensitive to $T_{\rm C}$, along with their symmetries and displacement
patterns, are summarized in Table 2. Raman scattering nicely shows the
hysteresis across $T_{\rm C}$ as well [Fig. S3, Supporting Information].

####  .2.3 Bimetallic $A$-site substitution introduces ferroelectricity

Returning to a comparison of $M$PS3 systems ($M$ = Mn, Ni, Fe) and dual
sublattice analogs such as CuInP2S6 and AgInP2S6, we immediately see that the
most important consequence of the bimetallic nature is the introduction of
ferroelectricity. $A$-site size disorder has been predicted produce polar
behavior in other materials as well Singh2008 ; Swamynadhan2021 . That $T_{\rm
C}$ is slightly above room temperature is already providing the basis for a
number applications. Examples include electrocaloric effects for
refrigeration, negative longitudinal piezoelectricity, and a negative
capacitance field effect transistor Si2018 ; Si2019 . Unfortunately, Cu site
disorder demonstrably broadens the ferroelectric and relaxational or glassy
phase transitions. This is seen very clearly in the Raman scattering response
when rendered as a contour plot Fig. 5(d) and [Fig. S3, Supporting
Information]. It also hinders the formation of larger polarization in
CuInP2S6. The $M$PS3 materials obviously do not have $A$-site disorder. They
also lack ferroelectricity (although MnPS3 may be ferrotorroidic)
Ressouche2010 . Another useful point of comparison in these structure-property
relationships is CrPS4, a related chalcogenide with slightly different
stoichiometry and $C2$ symmetry Neal2021 . This system appears to be both
polar and chiral. There is no $A$-site disorder, and the P–P dimer is absent.
Clearly, subtle structural changes have important consequences for properties
in this family of materials.

###  .3 Vibrational properties of CuInP2S6 across the low temperature
relaxational transition

In addition to the well-defined ferroelectric transition, CuInP2S6 displays a
weak relaxational or glassy transition ($T_{\rm g}$) near 150 K. By
comparison, this transition is more subtle and much less studied than the
displacive $C$2/$c$ $\rightarrow$ $Cc$ ferroelectric transition. Although
$T_{\rm g}$ does not alter the $Cc$ space group, there is a local
rearrangement of the structure in which the relative inter-atomic coordinates
of Cu and In are different. The weak structural component is probably due to
the existence of multiple competing $Cc$ phases with varying monoclinic cell
angle SZhou2021 . This gives the transition local structure aspects as well as
order-disorder or glassy character due to freezing of ferroelectric domains
Dziaugys2010 .

Figure 5 summarizes the infrared absorption and Raman scattering response of
CuInP2S6 across the relaxational transition. We can track how the various
modes evolve across $T_{\rm g}$ using frequency vs. temperature and phonon
lifetime vs. temperature plots. The latter is calculated from the phonon
linewidth and is an expression of Heisenberg uncertainty principle Sun2013 .
The spectroscopic signatures of $T_{\rm g}$ tend to appear below 200 cm-1.
These modes are mostly due to out-of-plane motions of indium and copper [Table
S2 and S3, Supporting information]. They are labeled with symmetries of the
$Cc$ space group.

Interestingly, Raman scattering spectroscopy reveals that the structural
aspects of $T_{\rm g}$ may take place in two distinct steps. This is
particularly noticeable in the contour plot [Fig. 5(d)] as well as Fig. S3 in
the Supporting Information. Significant broadening of all three phonons is
observed around 175 and 150 K - in addition to underlying scattering intensity
consistent with order-disorder processes Vysochanskii1998 . The increase in
the background scattering across $T_{\rm g}$ may be due to critical scattering
(opalescence) from the microdomains.

Taken together, we see that while many infrared- and Raman-active phonons
drive the ferroelectric transition, the relaxational or glassy transition in
CuInP2S6 is discernible only through subtle peak shifting and mode activation.
This is because $T_{\rm g}$ is not associated with a change in the space
group. Instead, our spectroscopic work reveals local lattice distortions
associated with Cu site disorder. These effects appear only in phonons below
200 cm-1, suggesting that $T_{\rm g}$ involves local rearrangements of the Cu+
and In3+ coordination environments (which may impact the polarization) as well
as order-disorder processes that involve freezing of the Cu+ ions.
Interestingly, the two-step character of $T_{\rm g}$ [Fig. 5(d) and Fig. S3 in
the Supporting Information] is consistent with the low frequency dielectric
dispersion of CuInP2S6 which shows a broad transition region near 155 K along
with evidence for a possible two-step aspect to the relaxation embedded in the
overall shape of the response at certain frequencies Dziaugys2010 . In the
$M$PS3 family of materials ($M$ = Mn, Fe, Ni), only MnPS3 hosts a comparable
process with spin-phonon coupling across the antiferromagnetic ordering
transition Vaclavkova2020 .

## Summary and Outlook

In order to explore the properties of complex chalcogenides, we measured the
infrared absorption and Raman scattering response of CuInP2S6 across the
ferroelectric and glassy phase transitions and compared our findings with a
symmetry analysis and complementary lattice dynamics calculations. Several
different infrared- and Raman-active modes drive the ferroelectric transition
whereas the relaxational or glassy phase transition involves local lattice
distortions and is characterized by much more subtle peak shifting and
activation. This is because $T_{\rm C}$ is a displacive transition whereas
$T_{\rm g}$ is due to Cu site disorder. Both transitions have large hysteresis
regions - probably on account of the bimetallic nature of this system. The
glassy transition is especially interesting because, while there is no change
in space group, order-disorder processes lead to local structure differences
at the Cu and In sites that arise from varying coordination environments. In
addition to providing evidence for a two-step transition, the spectral
response across $T_{\rm g}$ is hysteretic and has significant underlying
scattering intensity - consistent with glassy character. We also investigated
the tendency toward chemical phase separation in these materials and, using a
combination of optical microscopy, piezoforce microscopy, transmission
electron microscopy, and vibrational spectroscopies, we unravel the signature
of the highest quality crystals. This work provides guidance on how to
identify high quality single crystals and, at the same time, places the
vibrational properties of ferroelectric CuInP2S6 on a firm foundation to
support future work to reveal the symmetry and dynamics of few- and single-
layer systems.

## Acknowledgements

Research at the University of Tennessee is supported by the U.S. Department of
Energy, Office of Basic Energy Sciences, Materials Science Division under
award DE-FG02-01ER45885. Work at Rutgers University is funded by the NSF-DMREF
program (DMR-1629059) and ONR grants N00014-16-1-2951 and N00014-19-1-2073.
Work at Pohang University of Science and Technology was supported by the
National Research Foundation of Korea (NRF) funded by the Ministry of Science
and ICT (No. 2016K1A4A4A01922028). This work was supported by the U.S.
Department of Energy (DOE), Office of Science, Basic Energy Sciences under
award DE-SC0020353 (S. Singh).

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