# Pressure-induced insulator-to-metal transition in van der Waals compound
CoPS3

Takahiro Matsuoka<EMAIL_ADDRESS>Department of Materials Science and
Engineering, University of Tennessee, Knoxville, TN 37996, USA  Rahul Rao
Materials and Manufacturing Directorate, Air Force Research Laboratory,
Wright-Patterson Air Force Base, OH 45433, USA  Michael A. Susner  Materials
and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson
Air Force Base, OH 45433, USA  Benjamin S. Conner  Sensors Directorate, Air
Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA
National Research Council, Washington D.C. 20001, USA  Dongzhou Zhang  Hawaii
Institute of Geophysics and Planetology, University of Hawaii at Manoa, 1680
East-West Road, Honolulu, HI 96822  GSECARS, University of Chicago, 9700 S
Cass Ave, Argonne, IL 60439  David Mandrus<EMAIL_ADDRESS>Department of
Materials Science and Engineering, University of Tennessee, Knoxville, TN
37996, USA  Department of Physics and Astronomy, University of Tennessee,
Knoxville, TN 37996, USA  Materials Science and Technology Division, Oak Ridge
National Laboratory, Oak Ridge, TN 37831, USA

###### Abstract

We have studied the insulator-to-metal transition and crystal structure
evolution under high pressure in the van der Waals compound CoPS3 through in-
situ electrical resistance, Hall resistance, magnetoresistance, X-ray
diffraction, and Raman scattering measurements. CoPS3 exhibits a $C2/m$
$\rightarrow$ $P\overline{3}$ structural transformation at 7 GPa accompanied
by a 2.9$\%$ reduction in the volume per formula unit. Concomitantly, the
electrical resistance decreases significantly, and CoPS3 becomes metallic.
This metallic CoPS3 is a hole-dominant conductor with multiple conduction
bands. The linear magnetoresistance and the small volume collapse at the
metallization suggest the incomplete high-spin $\rightarrow$ low-spin
transition in the metallic phase. Thus, the metallic CoPS3 possibly possesses
an inhomogeneous magnetic moment distribution and short-range magnetic
ordering. This report summarizes the comprehensive phase diagram of $M$PS3
($M$ = V, Mn, Fe, Co, Ni, and Cd) that metalize under pressures.

##  I INTRODUCTION

The transition metal thiophosphates MPS3 (M = V, Mn, Fe, Co, Ni, and Cd)
compounds form a family of quasi-two-dimensional (2D) compounds. They are
isostructural in a monoclinic $C2/m$ symmetry, with individual lamellae
composed of slightly distorted octahedral sites circumscribed by the S atoms
bordering the van der Waals gap which are, in turn, arranged in a honeycomb
lattice. Of the octahedra, 2/3 can be described as a +2 metal cation in an
$M$S6 cage. The remaining 1/3 of the octahedra are filled with P-P dimers that
form a [P2S6]${}^{4}-$ anionic sublattice that charge balances the
aforementioned metal cations. The anionic sublattice is common to all of these
compounds; the cations in turn impart the various functionalities native to
these systems, including magnetism [1, 2]. In this particular subset of the
metal thiophosphate family, all compounds form a Mott insulating state at low
temperatures and exhibit 2D antiferromagnetic (AFM) behavior, except for the
Cd, which in the +2 oxidation state has a closed $d$-shell [3, 4, 5, 6, 7].
The 2D magnetism in these materials has attracted recent attention due to the
ability to study the effects of extreme anisotropy in low dimensions. The MPS3
family thus offers an enticing materials platform to study novel magnetic
phenomena in low-dimensional materials in addition to the promise for
applications in magnetic and spintronic devices because they can be exfoliated
down to thin films [8, 9, 10, 11]. Therefore, elucidating these interesting 2D
magnetic materials’ physical properties is vital for future applications. In
particular, it is essential to consider the structural and magnetic changes
induced by imparting pressure to these materials.

External pressure is an effective perturbation tool because van der Waals
compounds are highly compressible, especially in the inter-layer direction.
Thus far, the structural, magnetic, and electronic evolutions under
compression have been extensively studied for the MPS3 (M = V, Mn, Fe, Ni, Cd)
and their analogous selenophosphate counterparts MPSe3. Researchers have
commonly observed that these materials exhibit an insulator-to-metal
transition at high pressures (12-28 GPa) [12, 13, 14, 15, 16, 17, 7, 18].
Additionally, spin-crossover (high to low-spin state) occurs in FePS3 (FePSe3)
and MnPS3 (MnPSe3) concomitantly with the insulator-to-metal transition [13,
14]. Finally, FePSe3 becomes superconducting with a superconducting transition
temperature of 2.5 K at 9 GPa (increasing to 5.5 K at 30 GPa) [14]. Evidence
for a metallization has also been reported recently in a bimetallic metal
thiophosphate, Cu-deficient CuInP2S6 [19]. External pressure induces inter-
layer sliding transitions, followed by a 10-20$\%$ volume collapse across the
insulator-to-metal transition at room temperature [12, 18, 13, 4, 15, 20, 21,
17]. Other transitions can be more subtle. For example, the MPS3 (M = Fe, Mn)
and V0.9PS3 compounds change from $C2/m$ to a $C2/m$ with a different
monoclinic angle ($\beta$) or a trigonal $P\overline{3}1m$ [12, 22, 23, 18,
13, 24, 14, 4, 21]. CdPS3 changes from $C2/m$ to a trigonal $R\overline{3}$
[20]. Previous studies of NiPS3 observed up to five high-pressure phases
($P\overline{3}$, $P\overline{3}m1$, $P3m1$, $P3$, and $P1$) between ambient
pressure and 39 GPa, making this composition unique among these van der Waals
gapped magnetic materials [25]. Clearly, pressure-driven structural phase
transitions are critical as drivers of new states of matter with the potential
to host emergent properties.

Focusing on the last of these properties, the trigonal distortion present in
the octahedra bounding the metal cations (where the trigonal axis is parallel
to the stacking direction) affects the degeneracy of the energy states
associated with the octahedral crystal field splitting, thus creating highly
anisotropic effects in the magnetism of these compounds [1] that in turn
contribute to their interesting behavior. From a structural perspective, the
magnetic MPS3 or MPSe3 can be grouped into three main categories. In all
compounds, spins are pointed along the $c$-axis except for NiPS3 and CoPS3,
where spins are pointed parallel and antiparallel to the $a$ direction.

The first grouping is MnPS3 and MnPSe3; both of these compounds are co-linear
antiferromagnets with propagation vectors of $\bm{q}$ $=[0\ 0\ 0]$ [26, 27,
28]. We note that other works state that $\bm{q}=[0\ 1\ 0]$ for MnPS3 [5]. The
second main grouping contains CoPS3 and NiPS3; they exhibit $\bm{q}=[0\ 1\ 0]$
[6, 3]. In CoPS3, though the orientation of the moments is mostly along the
$a$-axis, a small component may be along the $c$-axis as well [3]. Finally,
the third grouping comprises the compounds FePS3 and FePSe3. The sulfide has
been shown to have an incommensurate $\bm{q}=[1/2\ 1/2\ 0.34]$ [29] while the
selenide has a vector of $\bm{q}=[1/2\ 0\ 1/2]$ [27, 28]. The careful reader
may note that V0.8PS3 [30], NiPSe3 [31], and many of the quarternary magnetic
compounds [1] have yet to be fully characterized in terms of magnetic
structure and may yield fruitful investigations themselves if suitably sized
crystals can be synthesized.

To date, the effects of high pressure on CoPS3 have not been experimentally
reported, probably due to the significant difficulty in the synthesis and
single crystal growth of this compound. CoPS3 is antiferromagnetic at ambient
pressure with a Neel temperature of TN = 122 K and a Weiss temperature of
$\theta$ $=-116$ K [32]. Its effective moment is 4.9 $\mu$B, slightly larger
than the expected value for a pure spin moment of a Co2+ ($S=$$\frac{3}{2}$)
cation [32], implying some degree of orbital contribution to the
magnetization. A first-principles calculation, the only dedicated article to
the pressure effects in CoPS3, predicts a pressure-driven isostructural Mott
transition accompanied by a spin-crossover [33].

In this study, we successfully grew large single crystals of CoPS3. Our
electrical resistance, Raman scattering, and X-ray diffraction (XRD)
measurements reveal an insulator-to-metal transition around 7 GPa, coinciding
with a $C2/m$ $\rightarrow$ $P\overline{3}$ structural transformation and a
2.9$\%$ reduction in the volume per formula unit. Hall effect measurements
find the metallic phase is a hole-dominant conductor. The linear magnetic
field dependence of the magnetoresistance, combined with the small volume
collapse at the metallization, suggests an incomplete high-spin $\rightarrow$
low-spin crossover in the metallic phase. Thus, metallic CoPS3 may possess an
inhomogeneous magnetic moment distribution and short-range magnetic ordering
due to the coexisting high- and low-spin Co2+ ions. This report summarizes the
comprehensive phase diagram of $M$PS3 that metalize under compression.

##  II EXPERIMENTAL METHOD

We synthesized single crystals of CoPS3 using the general procedures outlined
in Refs. [3, 1]. Co powder (Alfa Aesar Puratronic, 22 mesh, 99.998%, reduced),
P chunks (Alfa Aesar Puratronic, 99.999%), and S (Alfa Aesar Puratronic,
99.9995%) were combined in a near-stoichiometric ratio to form CoPS3 together
with an appropriate quantity of I2 as the vapor transport agent in a sealed
quartz ampoule, heated to the reaction temperature, and held there for 4 days
[34]. Typical crystals were 4-6 mm in size along the a–b planes with several
exceeding 12 mm. Typical thicknesses were $<$ 0.5 mm.

We used diamond anvil cells (DACs) for the high-pressure application. We
loaded a small single crystal of CoPS3 in a DAC and connected five electrical
probes made of platinum (Pt) for the electrical resistance, magnetoresistance,
and Hall resistance measurements. The a–b planes of the single crystals were
laid on the diamond’s flat surface to achieve a quasi-uniaxial compression. A
pre-compressed sodium chloride (NaCl) flake was placed underneath the sample,
serving as a pressure-transmitting medium and ensuring that the pressure
distribution across the sample was as homogeneous as possible. Several tiny
ruby chips (Cr: Al2O3) were added with the samples as a pressure standard
[35]. For further details, see the Supplemental material [36].

We performed Raman spectroscopy measurements on a CoPS3 crystal compressed in
a DAC, using a Renishaw inVia Raman microscope with a 632.8 nm excitation
laser at room temperature. The pressure-transmitting medium was a 4:1 ratio
methanol/ethanol solution. The power of the excitation laser was tuned to
$\sim$1 $\mu$W to minimize heating.

We conducted the XRD measurements at beamline 13BM-C at the Advanced Photon
Source (APS), Argonne National Laboratory, utilizing a focused (12 $\mu$m (H)
$\times$ 18 $\mu$m (V)) X-ray beam (wavelength $=$ 0.4340 Å) in all
measurements. Potassium chloride (KCl) was the pressure-transmitting medium.
We collected diffraction data on a flat panel detector array (Dectris Pilatus
1M-F, pixel size: 172 $\times$ 172 $\mu$m2) in the forward scattering geometry
at room temperature. We used Dioptas for two-dimensional XRD data reduction
[37]. We obtained lattice constants ($a$, $b$, and $c$) by the least-square-
fitting of peak positions using PDindexer [38].

##  III RESULTS

###  III.1 Resistance vs. Pressure and Temperature

Fig. 1a shows the pressure dependence of the electrical resistance (Rxx) of
CoPS3 at room temperature without applying an external magnetic field. To
estimate the figure of electrical resistivity ($\rho$xx), we calculated
$\rho$xx for sample #1 using the area/length ratio, $wt/l$ where $w=55$ $\mu$m
is the width of the sample, $t=20$ $\mu$m is the thickness, and $l=50$ $\mu$m
is the separation between electrical leads measured before applying pressure.
Since the separation between electrical leads does not change significantly
(Fig. 1a), we assume that most of the change in $\rho$xx comes from the
reduction of $t$. From the XRD results (Fig. 2b) discussed later, the $c$-axis
shrinks 20$\%$ from the ambient pressure to the highest pressure (17 GPa).
Although the error does not affect the conclusion of the current report,
readers are noted that a maximum of 20$\%$ of error should be included in the
$\rho$xx in Fig. 1a. We also note that we obtained the pressure by averaging
the pressure values measured at room temperature before and after each
temperature cycle for the electrical resistance measurements. The actual
pressures at low temperatures are thought to be somewhat different from the
indicated values.

The Rxx decreases into the measurable range of our transport measurement
system (maximum 2 M$\Omega$) above 2 GPa. The Rxx shows a significant decrease
up to 7 GPa by three orders of magnitude. Then it abruptly decreases by five
further orders of magnitude when applying an additional mere 1 GPa. Above 10
GPa, Rxx becomes almost independent of the external pressure. The $\rho$xx
reaches around 200 $\mu$$\Omega$cm, suggesting a metallic conductivity. The
similarities in the trends from two independent samples, #1 and #2, show good
reproducibility of the transport results (Fig. 1a). The insets of Fig. 1a show
microphotographs of CoPS3 at 4.5 GPa and 12 GPa under epi-illumination. Here
we see that the light reflection increases with pressure. The sample at 12 GPa
is shiny and comparable to the Pt metal of the electrical probes, thus
indicating a major electronic transition.

Upon releasing the pressure, the $R$xx traces back the $R$xx vs. P curve of
the compression down to 8 GPa. Below 8 GPa, the $R$xx stays much lower (one to
3 orders of magnitude) than the compression, showing a large hysteresis.
However, at 0 GPa, the compressed and decompressed lines are extrapolated to
merge. This large hysteresis between compression and decompression implies the
presence of a first-order transition.

To see if there are any temperature-dependent resistance effects, in Fig. 1b
(top panel), we show $R$xx vs. T at various pressures (Sample #1) without an
external magnetic field. The CoPS3 exhibits insulating or semiconducting
behavior at 7.4 GPa and also displays a negative slope (d$R$xx/dT). The origin
of the hump at 7.4 GPa and 50 K is as of yet unknown. Above 10 GPa, d$R$xx/dT
becomes positive along the entirety of the probed temperature range, thus
revealing that CoPS3 is metallic under these pressures. We see no
superconducting transition down to 2 K. When we plot the $R$ as a function of
T2 (inset in the bottom panel of Fig. 1b), we see that d$R$xx/dT fits the
Fermi-liquid theory at temperatures below 15 K. Thus, we conclude that CoPS3
exhibits a pressure-induced insulator-to-metal transition around 7 GPa. At 3.5
GPa on decompression, CoPS3 exhibits an insulator behavior (Fig. 1b).

Figure 1: (color online) (a) Rxx and $\rho$xx vs. P at room temperature. The
data of samples #1 and #2 are plotted for compression and decompression. The
dotted lines are guides for the eyes. The vertical and horizontal solid lines
indicate the structural phase diagram confirmed by our XRD and Raman
scattering measurements. The inset pictures show sample $\sharp$1 at
pressures. (b) $R$xx vs. T at pressures obtained for Sample $\sharp$1 without
an external magnetic field. All data plots are taken on warming. The inset
figure plots the $R$xx vs. T2.

###  III.2 XRD

Figure 2a displays the representative XRD patterns of CoPS3 at 0.5 and 17 GPa.
We note that the observed XRD patterns are affected by the orientation
reflecting the initial geometry of the single crystal when loaded in the DAC.
In our measurements, the a-b plane of the layered structure is perpendicular
to the X-ray beam. Although we rotated the DAC as much as allowed by the
beamline instruments and the DAC opening angle, the diffraction peaks from
($hkl$) with large l ($>$2) are invisible, limiting the number of peaks.
Additionally, the single crystal partially broke into several pieces during
compression. Therefore, the relative intensity between the diffraction peaks
is inaccurate because the obtained XRD results are not in the form of even-
intensity powder rings. See the Supplementary Material for the XRD image
recorded on a detector [36]. At 0.5 GPa, the XRD peak positions agree well
with the previously reported monoclinic $C2/m$ ($a$ = 5.844(1) Å, $b$ =
10.127(1) Å, $c$ = 6.562(4) Å, $\beta$ = 107.04(2)∘) [3]. At 17 GPa, we can
index the XRD pattern to a trigonal structure with lattice constants $a=b=$
5.570(5) Å, $c=$ 5.13(2) Å. We name the high-pressure trigonal phase HP-I in
this report.

Figure 2b shows the pressure dependencies of volume per formula unit (Vf.u.)
and the lattice constants, $a$, $b$, and $c$. The Vf.u. is obtained by
dividing a unit cell volume by the number of CoPS3 units. For the comparison
between $C2/m$ and HP-I, we reduce the trigonal unit cell to a monoclinic unit
cell ($\beta$ = 90∘) using the relation bmono. $=2a$tri.$\times$cos30∘. In
agreement with the electrical transport measurements, the structure changes
from $C2/m$ to HP-I at 7 GPa. Concomitantly, the Vf.u. abruptly decreases by
2.9% (84.690 Å3 $\rightarrow$ 82.269 Å3) at 7 GPa. All the lattice constants
$a$, $b$, and $c$ show a sharp discontinuity, with $c$ exhibiting the largest
reduction ($\Delta$$c$ = 1.4 Å).

Here, we focus on the observed reduction in the Vf.u.. Isostructural materials
MnPS3 and FePS3 commonly collapse a volume by 10-20% simultaneously with a
spin-crossover, and the insulator-to-metal transition [15, 13, 14]. This study
has not performed a direct measurement, such as X-ray absorption and Mössbauer
spectroscopy, to investigate the electronic configuration of Co. However, from
the observed volume collapse and comparing FePS3 and MnPS3, it is reasonable
to conclude that CoPS3 exhibits the spin crossover ($S=$ 3/2 $\rightarrow$
1/2) accompanied by the metallization at 7 GPa.

On the other hand, the ovserved volume reduction (2.9%) of CoPS3 is much
smaller than MnPS3 (19.7%) and FePS3 (10.6%) [15, 13, 14]. The ionic radii of
high- (HS, 0.89 Å) and low-spin (LS, 0.79 Å) Co2+ ions [39] make the HS
$\rightarrow$ LS radius reduction by 11.2%, which is not much smaller than
that of Mn2+ (HS: 0.97 Å, LS: 0.81 Å, 16.5%) and Fe2+ (HS: 0.92 Å, LS: 0.75 Å,
18.5%) [39]. Thus, the slight volume reduction of CoSP3 cannot be explained
simply by the difference between HS and LS radii.

In Fig. 2b, it is also noticeable that the $V$f.u. and $c$ in the HP-I phase
show a steeper compression between 7 GPa and 12 GPa followed by moderate
compression above 12 GPa, indicating a sign of $V$($P$) stabilization. These
series of changes in compression behavior suggest an electronic transition
takes place in the HP-I phase. On decompression, the HP-I phase remains down
to 2 GPa, displaying a large hysteresis in $V$f.u. and $c$ below 12 GPa.
Considering the significant hysteresis observed in $R$xx vs. $P$, the $C2/m$
$\rightarrow$ HP-I transition is considered first-order. We later discuss
those anomalous compressions concerning electronic transformations, the HS to
LS crossover, and the volume collapse.

Figure 2: (color online) Structure analysis of CoPS3 by XRD under pressure.
(a) XRD patterns of the $C2/m$ (0.5 GPa) and HP-I (17 GPa) phases. Note that
KCl changes from B1 to B2 type structure at 2 GPa. (b) Pressure evolution of
Vf.u. and lattice constants. The trigonal structure of HP-I is reduced to a
monoclinic lattice ($\beta$ = 90∘) for comparison. The open and closed data
points indicate compression and decompression, respectively. The error bars
are inside the data markers at most pressures except for 6.8 GPa. The broken
and dashed curves are guides for the eyes. The vertical dotted line is the
structural phase boundary.

###  III.3 Raman scattering

To obtain further insights into changes to the symmetry of the crystal
structure under compression, we performed pressure-dependent Raman scattering
measurements. Fig. 4a displays the evolution of the Raman spectra from CoPS3
under quasi-hydrostatic compression at room temperature. Based on the previous
theoretical and experimental reports, we anticipate eight Raman active modes
(5Eg \+ 3Ag) for bulk CoPS3 at room temperature [40]. At pressures below 6.7
GPa (in the stability region of $C2/m$), we observe all eight peaks in
agreement with the previous reports [40]. The peak at 110 cm-1 is not observed
at atmospheric pressure but becomes visible above 1.2 GPa, suggesting that a
preferential alignment of layers could cause this peak to be more prominent at
higher pressures. Up to 6.7 GPa, all the peaks blueshift in frequency with
increasing pressure, as expected for phonon modes under compression. Between
6.7 GPa and 7.5 GPa, the Raman spectrum changes abruptly with the loss of
peaks and the appearance of new peaks (Fig. 3a and 3b). Accompanied by the
Raman spectral change, the sample becomes lighter in color and more reflective
under epi-illumination (Fig. 3a, photographs), in agreement with the visible
observations during our transport measurements (Fig. 1a). The abrupt Raman
spectra and reflectivity changes give further evidence of the $C2/m$
$\rightarrow$ HP-I structural change coinciding with the ITM transition.
Similar to what our electrical resistance measurements observe, the transition
in the Raman spectra takes place within a narrow pressure range of 0.8 GPa,
strongly suggesting the absence of an intermediate phase between $C2/m$ and
HP-I phases. At 18.7 GPa, all peaks diminish significantly and are replaced by
a broad peak between 300-400 cm-1, except for the peak near 120 cm-1. We
consider two possibilities for the cause of broadening. One is the
solidification of the pressure-transmitting medium near 10 GPa, and the
developing non-hydrostatic condition that induces the inhomogeneous strain in
the crystal [41, 42, 43]. Another possibility could be the indication of
further structural transformation. Future studies would address the question.

Figure 3b, left panel, shows the pressure-dependent frequencies of the Raman
peaks. The right panel in Fig. 3b shows a magnified view of the ambient
pressure phase. Based on the previous literature, we assign the peak P4 near
245 cm-1 to the out-of-plane bending (A1g) of P2S64- dimer units. It has the
highest pressure coefficient, reflecting the large compressibility in the
$c$-axis (Fig. 3b) [40]. P8 near 560 cm-1 is the out-of-plane stretching of
P-P dimer (Eg) [40]. The peak shows a sharp increase in the frequency at the
start of compression. Contrary, P6 near 380 cm-1 representing in-plane
stretching of P2S64- units (A1g) has the lowest pressure coefficient [40].
Overall, the compression affects out-of-plane phonon modes more than in-plane
modes.

Figure 3: (color online) Raman scattering measurements of CoPS3 under
pressures. (a) The pressure evolution of the Raman scattering spectra at
ambient temperature. Pictures show CoPS3 at 1.3 GPa and 18.7 GPa. Atm.;
atmospheric pressure (b-left) Pressure dependencies of the Raman scattering
peaks. Dashed vertical lines show the structural phase boundaries. (b-right)
The close-up view of the left panel. See the Supplemental Material for the
peak-fitting analysis [36].

Next, we try to understand the $C2/m$ $\rightarrow$ HP-I transition. We first
track the peak frequency changes across the structural transition. P1 near 115
cm-1 (complex vibrations along all three axes of Co and S, Eg) blue shifts
with pressure up to 7 GPa, above which it redshifts in frequency (labeled
P${}_{1^{\prime}}$ in Fig. 3b). P2 near 145 cm-1 (in-plane Co-Co stretching,
Eg) and P3 near 238 cm-1 (out-of-plane stretching of P2S64-, Eg) behave
similarly to P1, blueshifting up to 7 GPa, followed by slight discontinuities
and are designated as P${}_{2^{\prime}}$ and P${}_{3^{\prime}}$in the HP-I
phase, respectively. P4 near 240 cm-1merges with P5 near 280 cm-1 (in-plane
S-S vibration in P2S64- units, Eg) up to 7 GPa. In the HP-I phase, the merged
peak is designated P${}_{4^{\prime},5^{\prime}}$ near 300 cm-1. P6 near 380
cm-1 (in-plane S-S vibration, A1g) exhibits a sharp discontinuity across the
phase transition and appears at a lower frequency 400 cm-1 labeled as
P${}_{6^{\prime}}$. P7 near 545 cm-1 (complex stretching mode of P2S64-, Eg)
and P8 come closer up to 7 GPa. Across the critical pressure, these peaks
disappear, and the highest frequency peak in HP-I appears at a much lower
frequency 510 cm-1, designated as P${}_{7^{\prime},8^{\prime}}$. The merging
and newly appeared peaks provide evidence for both increasing and decreasing
symmetry.

We next consider the evidence for increased symmetry. As mentioned above,
several Raman peaks merge with increasing pressure up to 7 GPa (P4+P5
$\rightarrow$ P${}_{4^{\prime},5^{\prime}}$, and P7+P8 $\rightarrow$
P${}_{7^{\prime},8^{\prime}}$). This means that in addition to the mirror
planes, axial glides, inversion centers, two-fold rotations, and the two-fold
screw axes that characterize the $C2/m$ space group, the system gains
additional symmetry elements across 7 GPa. Examination of the $C2/m$ group
$\leftrightarrow$ supergroup relationships provides several higher symmetry
candidates such as $P\overline{3}1m$, $P\overline{3}m1$, and $Cmmm$. Since our
XRD result suggests a trigonal structure, we can exclude $Cmmm$. See the
Supplemental Material of Ref. [25] for the summarized subgroup/supergroup
symmetry relations relevant to the $M$PS3 compounds.

Next, we investigate the evidence for symmetry breaking. The newly emergent
peak PA (near 140 cm-1) in the HP-I phase indicates the rise of the out-of-
phase intralayer Co translational mode. PB and PC are considered to be related
to the S-S vibrations from their frequencies in the lower-pressure phase. To
unravel how these modes correspond to the change in crystal symmetry, we
consider the relevant mode displacement patterns and how they impact different
symmetry elements. These include some newly established symmetry elements of
$P\overline{3}1m$ and $P\overline{3}m1$, such as axial glide planes, two-fold
rotations, and two-fold screw axes. Therefore, candidate subgroups include
$P31m$, $P\overline{3}$, $P3m1$, and $P312$. In the Raman spectra, we do not
see a significant increase in the overall number of peaks, suggesting the
retention of the inversion center. Of the four candidate subgroups,
$P\overline{3}$ retains the inversion center. We, therefore, conclude the
$C2/m$ $\rightarrow$ $P\overline{3}$ transformation.

Figure 4 summarizes the crystal structures of CoPS3 in the $C2/m$ and
$P\overline{3}$. Note that we did not refine the atomic positions in the
$P\overline{3}$ due to the limitation mentioned above in the obtained XRD data
[36].

We calculated the mode Grüneisen parameter for each phonon mode using the
pressure dependence of the Raman frequencies and the $V$f.u.. See the
Supplemental Materials for the analysis and results [36].

Figure 4: (color online) The crystal structure of A.P.-phase ($C2/m$) and the
suggested $P\overline{3}$ structure for HP-I phase visualized using VESTA[44].

###  III.4 Transverse transport measurements

Now that we have confirmed the existence of a new metallic phase at high
pressure in CoPS3, we turn our attention to its electronic properties.
Transverse transport measurements, including Hall resistance and
magnetoresistance (MR), are essential probes because it gives us information
about the Fermi surface [45]. Fig. 5a and Fig. 5b display the Hall resistivity
($\rho$xy) and MR ($\Delta$$\rho$xx($B$)$/$$\rho$xx(0)) of sample #1 at 10,
13, and 15 GPa and temperatures ranging from 1.8 to 160 K. The $\rho$xy shows
positive and mostly linear magnetic field dependence at all temperatures and
pressures (Fig. 5a). Besides, it does not saturate at this study’s highest
field (9 T). If a material is ferromagnetic, the anomalous Hall effect is
anticipated with saturation at a high field. Our Hall resistance data thus
indicate that CoPS3 is not ferromagnetic. CoPS3 is likely a hole-dominant
conductor that requires a multiple-conduction band model. We also notice that
$\Delta$$\rho$xx($B$)$/$$\rho$xx(0) exhibits a positive and linear magnetic
field dependence (linear magnetoresistance: LMR) at all pressures and
temperatures (Fig. 5b).

Generally, a multi-band analysis based on a semi-classical description
utilizes information such as carrier density and mobility on the Fermi surface
from the Hall resistivity and MR. However, the obtained results tend to become
ambiguous because of hypothesizing the number of carrier types. The LMR in
this study makes the analysis even more complicated because it is far from the
quadratic behavior anticipated by a semi-classical description. Here, we
employ a simple one-band model analysis and estimate the orders of density
($n$e,av.) and mobility ($\mu$e,av.), on average, for all carriers. From the
relation $1/eR$H = $n$e,av., the Hall coefficient (RH) and the electron charge
($e$) provide the estimation $n$e,av. = 1.41$\times$1021 cm-3 at 10 GPa and
1.8 K. This value is slightly smaller than that a Hall effect measurement
expects for general metals (1022 cm-3). Using the relation $\sigma$ =
$\mu$e,av.$n$e,av., the $\mu$e,av. = 138 cm2$V$-1$s$-1 can be extracted, where
$\sigma$ is a conductivity. The $n$e,av and $\mu$e,av are within the range of
1.4 - 2.9$\times$1021 cm-3 and 55 - 138 cm2$V$-1$s$-1 at 2 K for all
pressures, respectively.

Here, we analyze the observed LMR (Figs. 5b and 5c). The semi-classical model
predicts that the $\rho$xx evolves quadratically with a magnetic field,
saturating at high fields if the hole and electron densities are not
compensated [46, 47]. At the low-field limit, $\omega$c$\tau$$\ll$ 2$\pi$,
where $\omega$c is the cyclotron frequency and $\tau$ is the relaxation time,
the leading term in $\rho$xx becomes $\Delta$$\rho$ =
$\rho$($B$)$-$$\rho$($B$=0) $\sim$ $H$2 due to Onsager reciprocity relation,
which requires $\sigma$ij(B) = $\sigma$ji($-\textit{{B}}$) [46, 47]. The
$\rho$xx of CoPS3 evolves almost linearly with the field contrary to the semi-
classical description. The LMR is observable down to low fields: 0.7 T at 10
GPa, 2 T at 13 GPa, and 3 T at 15 GPa (Fig. 5c) followed by the asymptotic
curves approaching zero near zero field. Elevated temperature suppresses the
increase of the $\rho$xx vs. $B$ curves. At higher pressures, the parabolic
shape in the $\rho$xx vs. $B$ becomes more evident at lower fields. To obtain
further insight into the linear term in the $\rho$xx vs. $B$ relation, we
adopt a phenomenological approach to disentangle these components, fitting the
measured MR as $\rho$xx($H$, various $T$) = $\rho$xx($T$, $H=0$) + $A$($T$)$H$
\+ $B$($T$)$H$2 [48]. We perform the fitting below 4 T where the quadratic
component is visible. Fig. 5d plots $A(T)$ and $B(T)$ as a function of
temperature. The $A(T)$ saturates below 10 K, significantly decreasing with
increasing temperature. At low temperatures, the $A(T)$ decreases with
pressure from 10 to 13 GPa. However, the change becomes diminished between 13
and 15 GPa. By comparison, the $B(T)$ does not change appreciably over a wide
range of temperatures. We try to discern the origin of LMR in the following
section.

Figure 5: (color online) Transverse transport data from metallic CoPS3 at 10, 13, and 15 GPa. (a) The $\rho$xy at different temperatures. The data at 1.8 K and 20 K at 10 GPa overlap (top panel). The data at 1.8 K and 10 K at 13 GPa overlap (middle panel). (b) The $\Delta$$\rho$xx($B$)/$\rho$xx($B=0$). The dotted (black) and dashed (blue) lines in the top panel indicate the linear fit, ${y=Ax+C}$ with $A=$ 1.927(3)$\times$10-3, $C=-$7.7772(3)$\times$10-3) and quadratic-fits (quad.-fit, ${y=Bx}$2 with ${B=}$4.82(4)$\times$10-3) to the data at 10 GPa and 1.8 K. (c) $\Delta$$\rho$xx($B$)/$\rho$xx($B=0$) at low field. (d) The linear and quadratic components of MR under a field of 4 T for CoPS3. The broken lines are a guide for eyes. Table 1: Structural and electronic phase diagram of $M$PS3s that metalize under compression. AFMout and AFMin mean that the magnetic moments are pointing mostly out-of-plane and in-plane directions, respectively. The Pc is the pressure where crystal structures start transformations. $\Delta$$V$ is the volume reduction at insulator-to-metal transition. | A.P. | H.P. |  |  |  | Ref. / Note
---|---|---|---|---|---|---
V0.9PS3 |  $C2/m$ ($\beta$$\sim$107∘) |  $C2/m$ ($\beta$$\sim$90∘) |  |  |  | [12, 22]
| AFMNA111N.A.: information Not-Available, $\textit{{q}}=[010]$, ins. | ins.222ins.: insulator | met.333met.: metal |  |  |
Pc | $-$ | 2.6 GPa | 12 GPa |  |  |
|  |  |  $\Delta$$V$$\sim$0.8% |  |  |
MnPS3 |  $C2/m$ ($\beta$$\sim$107∘) | $P\overline{3}1m$ |  $C2/m$ ($\beta$$\sim$90∘) |  |  | [23, 18, 13, 24]
| AFMout, $\textit{{q}}=[010]or[000]$, ins. | ins. | met. |  |  | spin crossover
Pc | $-$ | 10 GPa | 28 GPa, $\Delta$$V$$\sim$19.7% |  |  | at 28 GPa
FePS3 |  $C2/m$ ($\beta$$\sim$107∘) |  $C2/m$ ($\beta$$\sim$90∘) | $P\overline{3}1m$ |  |  | [23, 14, 4, 24, 21]
| AFMout, $\textit{{q}}=[01\frac{1}{2}]$, ins. | AFM, $\textit{{q}}=[010]$, ins. | met. |  |  | spin crossover
Pc | $-$ | 2 GPa | 14 GPa, $\Delta$$V$$\sim$10.6% |  |  | at 14 GPa
CoPS3 |  $C2/m$ ($\beta$$\sim$107∘) | $P\overline{3}$ |  |  |  | [23, 3]
| AFMin, $\textit{{q}}=[010]$, ins. | met. |  |  |  | this study
Pc | $-$ | 7 GPa, $\Delta$$V$$\sim$2.9% |  |  |  |
NiPS3 |  $C2/m$ ($\beta$$\sim$107∘) | $P\overline{3}$ | $P\overline{3}1m$ | $P3m1$ |  | [23, 25, 17, 16]
| AFMin, $\textit{{q}}=[010]$, ins. | ins. | ins. | met. |  |
Pc | $-$ | 7.2 GPa | 15 GPa | 23 GPa |  |
|  |  |  |  $\Delta$$V$$\sim$2.8% |  |
CdPS3 |  $C2/m$ ($\beta$$\sim$107∘) | $R\overline{3}$ | $R\overline{3}$ |  |  | [23, 20]
| ins. |  |  |  |  |
Pc | $-$ | 0.25 GPa | 8.7 GPa |  |  |

##  IV Discussion

Here, we discuss the electronic configuration of the metallic CoPS3,
discerning the source of the observed pressure dependence of $V$f.u. and the
LMR. First, we focus on the $V$f.u. reduction at $C2/m$ $\rightarrow$
$P\overline{3}$ transformation. As discussed earlier, we concluded HS
$\rightarrow$ LS spin crossover takes place at the insulator-to-metal
transition and structural transformation. However, the relatively small
reduction in the $V$f.u. is not explained simply by the decrease in the ionic
radius of Co2+. Remarkably, the theoretical study predicts that the magnetic
moment in CoPS3 is much more robust than Fe2+ and Mn2+ under pressure [33].
The study suggests that the CoPS3 in either the $R\overline{3}$ or $C2/m$
($\beta$$\sim$90∘) phases above 12.5 GPa is ferromagnetic. The magnetic
moments of Co2+ decrease significantly with increasing pressure but do not
achieve $S=1/2$ even at 50 GPa [33]. Although the predicted crystal structure
differs from the one our experiments determine, we then raise the possibility
that the $P\overline{3}$ phase is in the middle of spin crossover where the
HS- and LS-Co2+ coexist.

We turn our eyes to the pressure dependence of the $V$f.u. in the
$P\overline{3}$ phase. Looking at several Fe-bearing compounds and (Mg, Fe)O
forsterite, we find the changes in the pressure dependence of the volume due
to the interplay between the compressibility and spin variation effect on the
Fe3+ ionic radius [49, 50, 51]. Considering the incomplete spin crossover
discussed above, the significant reduction of $V$f.u. between 7 and 12 GPa is
potentially due to the proceeding HS $\rightarrow$ LS crossover. Then, the
moderate $V$f.u. vs. $P$ slope above 12 GPa suggests the spin crossover’s
completion or moderate progress. The significant hysteresis between the
$V$f.u. of $P\overline{3}$ upon compression and decompression, especially
below 12 GPa, could be because the sample on compression has a bigger fraction
of HS than decompression.

Next, we try to discern the source responsible for LMR. LMR has been observed
in a growing number of novel materials and often invoked as evidence for some
exotic quasiparticles in materials [52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 48, 67, 56]. At the high-field limit $\omega$c$\tau$ $\gg$
2$\pi$, where $\omega$c is the cyclotron frequency, and the $\tau$ is the
relaxation time, there have been several suggested electronic and geometric
mechanisms that satisfy the criteria for a quantum LMR. The first is special
features on the Fermi surface, including the linear dispersion from a Dirac
cone with infinitesimally small carrier mass [68, 69, 70, 71]. The second is
principally geometric in nature, including an average over a combination of
open and closed electron trajectories in polycrystals [47, 72, 73, 64, 74].

On the other hand, the disorders of density and spin have been suggested as
universal mechanisms. The density disorder provides an inhomogeneous
distribution of charge concentration and affects the conduction carrier path,
admixing the Hall resistance component with MR [69, 67, 74]. Similarly, the
LMR due to the magnetic disorder has been observed for several 3$d$
ferromagnets and the antiferromagnetic normal conducting state of FeSe [75,
76]. Another is the LMR in CDW and SDW containing materials [48]. From their
nature, those three are applicable to the LMR to low-filed limit
$\omega$c$\tau$ $\ll$ 2$\pi$.

To examine the suggested mechanisms, we first estimate an average for all
carriers $\omega$c$\tau$ = $B$/$\rho$$nec$ = 2.75$\times$10-2 at 2 T (10 GPa,
1.8 K) for CoPS3. The criteria for quantum LMR ($\omega$c$\tau$ $\gg$ 2$\pi$)
(Ref. [69]) are thus not satisfied under our measurement conditions.
Additionally, CDW and SDW are not likely, judging from the featureless
$\rho$xx vs. $T$. Also, we do not observe the appearance of satellite peaks in
XRD, which is suggestive of CDW. Finally, the rapid diminution of $A(T)$ (Fig.
5d) at elevated temperatures argues against the phonon- [70] or the
excitation-based [66] scattering mechanisms.

We next test the density fluctuation scenario. Since our sample is under non-
hydrostatic stress, it is the most straightforward one to consider. However,
the estimated $n$e,av. and $\mu$e,av. are far bigger and smaller than that of
the high-mobility and low-carrier density materials where the density
fluctuation effects become more prominent [67, 77, 78, 74]. Besides, since the
pressure gradient in the sample generally develops with pressure in a non-
hydrostatic condition, a more amplified density fluctuation and even more
linear MR are expected, contrary to our experimental results. Thus, we defer
concluding the density fluctuations as the dominant source.

Finally, we consider the spin-disordered mechanism [75, 76]. In this model,
ions with different magnetic moments coexist randomly. The inhomogeneously
distributed magnetic moments possibly affect the conduction carrier
trajectories allowing irregular current paths and the LMR. Based on our
conclusion of the incomplete HS $\rightarrow$ LS spin crossover, it can be
thought that HS- and LS-Co2+ ions coexist and are arranged in a disordered
manner, possibly possessing a short-range magnetic ordering. In Fig. 5c and
5d, we see the quadratic component of the LMR becomes more evident in the
$\rho$xx vs. $B$ at higher pressure, implying a more homogeneous magnetic
moment distribution promoted by pressure. Besides, the linear component at 13
GPa and 15 GPa possess almost the same value. Those observations are
consistent with the interpretation that the spin crossover proceeds with
pressure up to 12 GPa and stops or progresses moderately above 12 GPa in the
$P\overline{3}$ phase.

The remaining question is how the insulator-to-metal transition, the
structural transition, and the spin crossover relate to each other in CoPS3.
We propose two scenarios. The first is that the insulator-to-metal transition
occurs simultaneously with the structural transition. The second is that
metallization originates within the $P\overline{3}$ phase. This scenario
arises from the observation that CoPS3 is still a semiconductor at 7.4 GPa,
while our Raman and XRD measurements suggest that the structural
transformation occurs at 7 GPa and completes within 1 GPa. Besides, upon
decompression, CoPS3 reverts to an insulator at 3.5 GPa, preceding the
$P\overline{3}$ $\rightarrow$ $C2/m$ transition observed below 2 GPa.
Currently, we do not have precise and detailed data to address the discrepancy
in the transition pressures. The off-stoichiometry of the sample may also
affect the transition pressures. Future detailed studies including the
simultaneous measurements of electrical transport and crystal structure would
provide an unambiguous answer.

Table 1 summarizes the structural and electronic evolution of $M$PS3 ($M$ = V,
Mn, Fe, Co, Ni, Cd) reported to date. All $M$PS3 exhibit $C2/m$
($\beta$$\sim$107∘) to trigonal structural transition when subjected to
pressure, decreasing their monoclinic angle to 90∘ as a consequence of the
inter-layer sliding. The insulator-to-metal transition commonly occurs when
$M$PS3 compounds are in the trigonal or $C2/m$ with $\beta$$\sim$90∘
symmetries.

The question is how the electronic configuration, magnetism, and structure
correlate. We see that $M$PS3 compounds, as far as the available experimental
data display, can be classified into two groups concerning their pressure
transformations. The first contains MnPS3 and FePS3 and exhibits the
transformation between symmetries in the group-subgroup relation ($C2/m$
$\leftrightarrow$ $P\overline{3}1m$). These compounds align their magnetic
moments mainly in the out-of-plane direction. The second group is comprised of
CoPS3 and NiPS3. These materials have moments aligned largely in-plane.
Contrary to the first group, the transition process from the lower-pressure
phase ($C2/m$) to the first high-pressure phase is not in the simple group-
subgroup relation. As discussed, CoPS3 transforms from $C2/m$ (14) to
$P\overline{3}$ (147) via a higher-symmetry phase such as $P\overline{3}1m$
(162). NiPS3 is an insulator in the $P\overline{3}$ phase. Thus, Ni2+ ions in
the $P\overline{3}$ phase may possibly be in the HS state. The potentially
remaining magnetic moments of Co2+, and possibly Ni2+, are likely to affect
the high-pressure phase that succeeds the $C2/m$.

Figure 6 is the visual summary of the $T$Ns and $V$f.u. shown in Table I as a
function of the ionic radius of $M$ in HS states. In Fig. 6, the two groups
(Mn and Fe, Co and Ni) discussed for the pressure-induced structural
transition are noticeable in the $T$N and $V$f.u. The $V$f.u.s of NiPS3 and
CoPS3 at 1 bar are similar. However, the $V$f.u. shows an obvious increase
from FePS3 to MnPS3 while the ionic radius difference between Fe2+ and Mn2+ is
smaller than between Ni2+ and Co2+. The $T$N decreases moderately with ionic
radius from Ni2+ to Co2+, followed by a steep decline from Fe2+ to Mn2+.
Remarkably those two groups are also observable in the volume reduction from
the insulator to the metallic phases at the metallization pressure. NiPS3 and
CoPS3 commonly show a smaller reduction than another group (Fe and Mn). In
$M$PS3 compounds, the $t$2g and $e$g orbitals play roles in bonding, and the
hopping integrals between $t$2g and $e$g show different anisotropy [7]. Thus,
the occupation of the electron orbitals, partially filled $t$${}_{2}g$ and
$e$g orbitals of FePS3 and filled $t$2g in NiPS3 for example, has a direct
influence on the physical characteristics, making this group of compounds a
rich platform to explore novel quantum phenomena. Fig. 6 reveals that the
electronic configurations at ambient pressure influence the high-pressure
properties. We also notice that MnPSe3 and FePSe3 possess similar $T$N with
their analogous MnPS3 and FePS3. If Ni and Co follow this trend, we may expect
$T$Ns of NiPSe3 and CoPSe3 to be close to NiPS3 and CoPS3.

Figure 6: (color online) $M$PS3 phase diagram with temperature and volumes
along the vertical axes and transition metal ($M$2+) ionic radius in HS state
(except for V) along the horizontal axis. Data are taken from Ref.[12, 22, 23,
18, 13, 24, 14, 4, 3, 17, 16, 20, 14, 39, 79]. The solid marks in the upper
panel indicate the $V$f.u. at 1 bar (square), insulator phases (triangle), and
metallic phases (circle). In the lower panel, the $T$N of $M$PS3 are plotted
with MnPSe3 and FePSe3.

##  V SUMMARY

We have successfully grown high-quality single crystals of CoSP3 suitably
large enough for conducting various high-pressure experiments. We studied the
electrical transport and structural evolution of CoPS3 under quasi-uniaxial
pressure along the layer-stacking direction through electrical resistance,
Hall resistance, magnetoresistance, Raman scattering, and XRD measurements.
Electrical resistance significantly decreases as the pressure increases,
consistent with the rise of the optical reflectivity of the sample. CoPS3
becomes metallic above 7 GPa, accompanied by the monoclinic $C2/m$
$\rightarrow$ trigonal $P\overline{3}$ structural transition. Metallic CoPS3
shows no superconducting transition down to 2 K. The $C2/m$ $\rightarrow$
$P\overline{3}$ transformation induces a 2.9% reduction in $V$f.u., much
smaller than that of the Mn and Fe analogous. The Hall effect data indicate
the metallic CoPS3 is a hole-dominant conductor. We observed the linear
magnetoresistance in a wide range of magnetic fields. The linear
magnetoresistance, the small volume reduction across the structural
transition, and the previous theoretical prediction [33] suggest the
coexistence of HS- and LS-Co2+ ions and the inhomogeneous magnetic moment
distribution with a possible short-range magnetic ordering. Furthermore, the
anomalous compression behavior of $V$f.u., and the pressure evolution of the
electrical resistance and linear magnetoresistance suggest the possibility
that the metallization occurs within the $P\overline{3}$ and the spin
crossover completes up to 12 GPa, or the progresses becomes moderate above the
pressure in the $P\overline{3}$. By revealing the high-pressure phase and
electrical transport property of CoPS3, this report summarizes the
comprehensive phase diagram of $M$PS3 ($M$ = V, Mn, Fe, Co, Ni, Cd) that
metalize under compression. $M$PS3 at ambient pressure has been an excellent
platform for exploring emergent quantum phenomena due to their various
electronic configurations. The phase diagram reveals that the electronic
configurations at ambient pressure strongly influence the structural and
electronic properties of $M$PS3 at high pressures, making this series of
compounds suitable platforms for exploring new physical properties under
compression.

###### Acknowledgements.

This research is funded by the Gordon and Betty Moore Foundation’s EPiQS
Initiative, Grant GBMF9069 to D.M. XRD experiments in this study were
performed at GSECARS (Sector 13), Advanced Photon Source (APS), Argonne
National Laboratory. GSECARS is supported by the National Science Foundation –
Earth Sciences (EAR-1634415). This research used resources of the Advanced
Photon Source, a U.S. Department of Energy (DOE) Office of Science User
Facility operated for the DOE Office of Science by Argonne National Laboratory
under Contract No. DE-AC02-06CH11357. Crystal growth and Raman
characterization were performed under Air Force Office of Scientific Research
(AFOSR) grant LRIR 23RXCOR003 and AOARD-MOST Grant Number F4GGA21207H002. Part
of the XRD experiment was supported by COMPRES under NSF Cooperative Agreement
EAR-1606856. We thank Dr. Antonio M. dos Santos and Prof. Maik Lang for
providing us with the DACs for the XRD measurements. We thank Prof. Heung-Sik
Kim and Dr. Sungmo Kang for the fruitful comments and discussions.

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