# Pressure-driven phase transitions in bulk $\text{HfS}_{2}$

M. Grzeszczyk  Institute of Experimental Physics, Faculty of Physics,
University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland  J. Gawraczyński
Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warsaw,
Poland  T. Woźniak  Department of Semiconductor Materials Engineering, Faculty
of Fundamental Problems of Technology, Wrocław University of Science and
Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland  J. Ibáñez
Geosciences Barcelona (GEO3BCN), CSIC, Lluís Solé i Sabarís s.n., 08028,
Barcelona, Catalonia, Spain  Z. Muhammad  Hefei Innovation Research Institute,
School of Microelectronics, Beihang University, Hefei 230013, P. R. China  W.
Zhao  Hefei Innovation Research Institute, School of Microelectronics, Beihang
University, Hefei 230013, P. R. China  M. R. Molas  Institute of Experimental
Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw,
Poland  A. Babiński  Institute of Experimental Physics, Faculty of Physics,
University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland

###### Abstract

The effect of hydrostatic pressure up to 27 GPa on the Raman scattering (RS)
in bulk $\text{HfS}_{2}$ is investigated. There are two transformations of RS
spectra, which take place during compression at pressure between 5.7 GPa and
9.8 GPa as well as between 12.8 GPa and 15.2 GPa. Seven vibrational modes can
be observed after the transformation, as compared to four modes before the
transformation. The observed change suggests structural change in the material
of yet unknown nature. The frequencies of the RS modes observed above the
transformation change linearly with pressure and corresponding pressure
coefficients have been determined. The other transition manifests itself as a
change in the RS lineshape. While a series of well-defined RS modes are
observed under pressure below the transition, broad spectral bands can be seen
at higher pressure. The overall lineshape of the spectra resembles that of
disordered materials. The lineshape does not change during decompression,
which suggests permanent nature of the high-pressure transition.

Raman scattering, hydrostatic pressure, transition metal dichalcogenides

##  I Introduction

Layered transition metal dichalcogenides (TMDs) and in particular their few-
layer structures have been drawing the attention of researchers for more than
a decade now. While about 60 layered TMDs are recognized, until now, the
attention of researchers is focused on Mo- and W-based compounds. Although
basic properties of several TMDs in their bulk form are known for years Wilson
and Yoffe (1969), there is still room for studies of $e.g.$ their properties
under hydrostatic pressure.

In this work we address the effect of hydrostatic pressure on hafnium
disulphide ($\text{HfS}_{2}$ ), a member of group IVB TMD. $\text{HfS}_{2}$
has been recently shown to have very effective electrical response Xu  _et
al._ (2015); Kanazawa  _et al._ (2016), which justifies a need to uncover
basic properties of the material. The evolution of lattice dynamics of
$\text{HfS}_{2}$ with hydrostatic pressure is studied. We follow RS spectra as
a function of pressure to investigate possible structural transformations of
the material as a first-order phase transition has been recently reported in
Ref.Ibáñez  _et al._ (2018).

##  II Samples and experimental setups

Figure 1: Raman scattering spectrum of bulk $\text{HfS}_{2}$ at ambient
pressure. Figure 2: Raman scattering spectra of bulk $\text{HfS}_{2}$ as a
function of hydrostatic pressure for compression (a) and decompression (b)
cycle

Single crystals of $\text{HfS}_{2}$ have been synthesized in two-zone chemical
vapour transport (CVT) furnace. First, precursor materials were sealed in
quartz tubes 25 cm long and of diameter of 8 cm. Iodine was used as a
transport agent. The reaction and growth temperatures were set to 1050 K and
950 K, respectively. The growth was performed continuously for 120 hours. With
higher stability of $\text{HfS}_{2}$ against iodine, CVT growth first starts
at elevated temperatures. In the vapour phase HfI and HfI2 can also dominate
the direction of reaction. After 120 hours the reaction was stopped
automatically and the reactor was cooled down to room temperature in 5 hours.
High quality $\text{HfS}_{2}$ single crystals of 0.8-1 cm2 size were grown in
the low-temperature part of the reactor. The pattern of powder X-Ray
diffraction (XRD) of the investigated material was found to be in perfect
agreement with that of the of the octahedral 1T phase of $\text{HfS}_{2}$
Lucovsky  _et al._ (1973). A very minor amount of an unidentified phase was
also detected in the crystal by XRD technique Ibáñez .

The high-pressure RS measurements were conducted at room temperature in a
nonmagnetic diamond anvil cell (DAC) made of BeCu alloy. Crystallographic oil
was adopted as the pressure transmitting medium. The fluorescence line of ruby
was used to calibrate pressure. RS spectra were excited using $\lambda$=561 nm
(2.21 eV) radiation from a diode-pumped laser. The excitation light was
focused by means of a 50x long-working distance objective with a 0.42
numerical aperture (NA) producing a spot of about 1 $\upmu$m diameter. The
signal was collected via the same microscope objective, sent through 0.75 m
monochromator and then detected by using a liquid nitrogen-cooled charge-
coupled device (CCD) camera. The spectral resolution of the setup in the
studied energy range of the RS experiment was equal to 0.7 cm-1.

##  III Results

There are six normal vibrational modes at the $\Gamma$ point of
1T-$\text{HfS}_{2}$ Lucovsky  _et al._ (1973):

$\Gamma=A_{1g}+E_{g}+2A_{2u}+2E_{u}$

The A1g and Eg modes are Raman-active, the infrared-active modes A2u and Eu
are split into LO and TO branches (for the atom displacement pattern see
$e.g.$ Neal  _et al._ (2021)), and other A2u and Eu modes are acousticLucovsky
_et al._ (1973) .

The measured RS spectrum of bulk $\text{HfS}_{2}$ at ambient pressure consists
of four modes (see Fig. 1), the frequencies of which equal approx. to: 141
cm-1, 266 cm-1, 325 cm-1, and 344 cm-1. This is consistent with previous
studies Ibáñez  _et al._ (2018); Roubi and Carlone (1988); Cingolani  _et al._
(1987). There is an agreement in literature on the attribution of peaks at 266
cm-1 and 344 cm-1 to in-plane Eg and out-of-plane A1g Raman-active modes,
respectively. The peak at 325 cm-1 is attributed to infrared-active Eu (LO)
Cingolani  _et al._ (1987); Neal  _et al._ (2021) or A2u(LO) Roubi and Carlone
(1988) alike mode. Despite the formal Raman-inactivity, both LO and TO
components of infrared-active modes may be observed in RS spectrum due to long
range Coulomb forces resulting from charges localised on atoms Roubi and
Carlone (1988). A resonant nature of RS involving such phonons was previously
reported in Ref. 10. Temperature-dependent RS measurements Gołasa  _et al._
(2017) or measurements with modulation of excitation light Molas  _et al._
(2017) might help to verify the attribution of the mode. For the sake of this
work, we assume the latter attribution to A2u(LO) Ibáñez  _et al._ (2018).

The assignment of the weak feature at 141 cm-1, previously reported in Ref. 4,
is also not clear. Its attribution to a second-order difference processes was
suggested, as such peaks can be observed in RS spectra of some TMDs Chen and
Wang (1974); Gołasa  _et al._ (2013). The Eu(TO) was also suggested as the
signature of the mode Roubi and Carlone (1988); Neal  _et al._ (2021). The
peak in this work will be referred to as $\omega_{1}$.

The effect of hydrostatic pressure on RS spectra of bulk $\text{HfS}_{2}$
during compression and decompression can be appreciated in Fig. 2(a) and (b),
respectively. Let us first focus on the results obtained during compression
process. The lineshape of the RS spectra does not significantly change up to
5.7 GPa. The observed mode experience blueshifts with increasing of the
hydrostatic pressure. Moreover, a substantial enhancement of the A1g peak can
be noticed in the spectrum at 5.7 GPa.

Figure 3: The evolution of the Raman scattering peak energies in bulk
$\text{HfS}_{2}$ with hydrostatic pressure. Straight lines correspond to
linear fits to experimental data.

It was found that the energies of the observed modes increase linearly with
increasing pressure, which can be appreciated in Fig. 3. Assuming the linear
dependence of the energies on pressure:

$E(P)=E_{0}+\alpha P$

one can fit the experimental data with the results shown in Table 1.

The obtained pressure coefficients are in general agreement with those
recently reported by Ibáñez and coworkers Ibáñez  _et al._ (2018). The initial
values $E_{0}$ and pressure coefficients $\alpha$ for the observed modes span
from 1.59 cm-1/GPa to 4.36 cm-1/GPa for A1g mode.

Table 1:  Results of linear fits to the pressure evolution of the Raman scattering peaks in bulk $\text{HfS}_{2}$ Peak | $E_{0}$ | $\alpha$
---|---|---
| [cm-1] | [cm-1/GPa]
$\omega_{1}$ | 141.4 | 1.59
Eg | 266.1 | 2.14
A2u(LO) | 325.5 | 2.63
A1g | 344.0 | 4.36
I | 95.1 | -0.13
II | 101.8 | 0.69
III | 142.0 | 0.75
IV | 151.6 | 0.77
V | 277.3 | 1.68
VI | 315.3 | 1.69
VII | 334.9 | 2.61
Figure 4: Raman scattering spectrum of bulk $\text{HfS}_{2}$ in hydrostatic
pressure of 9.8 GPa.

Substantial change in the line-shape of the RS spectrum can be observed at
pressure of 9.8 GPa, which corresponding spectrum is presented in Fig. 4. It
can be appreciated in the Figure that the A1g mode substantially weakens.
Simultaneously Eg, A2u(LO), and $\omega_{1}$ disappear from the spectra and a
set of new lines emerge in their stead. The peaks are denoted with I-VII.
Similar lineshape of the spectra can be observed under hydrostatic pressure up
to 12.8 GPa with the A1g mode completely vanishing above 10 GPa. The
structural change of $\text{HfS}_{2}$ , which affects the RS spectra, was
previously suggested in Ref. 4 with a new peak on the higher-frequency side of
the A1g mode. In our experiment, the transformation manifests itself in the
emergence of peak VII at the lower-frequency side of the A1g, as well as in
changes to the low-energy part of the spectrum, in which two pairs of lines:
I-II and III-IV can be observed. The pressure coefficients $\alpha$ of the
I-VII modes do not correspond in to those of modes detected at lower pressure.
In particular, the pressure coefficient $\alpha$ (2.61 cm-1/GPa) for mode VII
is substantially lower than the pressure coefficient for A1g mode although
both linear energy evolutions have rather similar $E_{0}$ initial values
(334.9 cm-1 for VII mode vs 344.0 cm-1 for A1g). Similar effect can observed
for Eg and V mode with $E_{0}$ and $\alpha$ equal respectively to 266.1 cm-1
and vs 277.3 cm-1 and 2.14 cm-1/GPa vs 1.68 cm-1/GPa (see Table 1). Modes II-
IV share relatively small pressure coefficient $\alpha$ equal to approx. 0.7
cm-1/GPa) which is significantly smaller than the lowest coefficient for modes
below the pressure-induced transformation. Finally, the pressure coefficient
for the I mode is negative. The properties substantially differ from those
observed at lower pressure one can conclude that the phase transition of yet
unknown origin takes place between 5.7 GPa and 9.8 GPa.

Next transformation of the RS spectrum can be observed above 15.2 GPa (see
Fig. 2(a)). Instead of seven well-defined vibrational modes present in the RS
spectrum at lower pressure, broad spectral bands can be detected at 15.2 GPa
or higher pressures. The overall lineshape of the RS spectra at highest
hydrostatic pressure resembles that of disordered materials Gołasa  _et al._
(2015); Mignuzzi  _et al._ (2015). The disorder and/or defects affecting
crystalline structure can localize phonons allowing for momentum non-
conserving processes. As a result, the inelastic scattering is possible with
phonons from whole Brilloiun zone. Therefore the RS spectrum of disordered
materials reflect the total density of phonon modes. Adopting such an approach
one can conclude that the low-energy band (below 150 cm-1) corresponds to
acoustic phonons and the high-energy band (at approx. 300 cm-1) is due to
optical vibrations. The emergence of the disorder-like RS under highest
hydrostatic pressure may be related to the contribution of an undefined phase
observed in X-ray diffraction measurements as it was mentioned earlier. As can
be appreciated in the Fig. 2(b), the lineshape of RS spectra does not change
during decompression process. It suggests permanent nature of the high-
pressure transition, most likely into an amorphous phase.

##  IV Conclusions

We have studied Raman scattering in bulk $\text{HfS}_{2}$ as a function of
hydrostatic pressure up to 27 GPa. There are two transformation of Raman
scattering spectrum observed during compression between 5.7 GPa and 9.8 GPa as
well as between 12.8 GPa and 15.2 GPa. The spectrum after the lower-pressure
transformation consists of seven well-defined vibrational modes as compared to
four modes observed below the transformation. The modification in the spectrum
suggests structural change in the material. Frequencies of the modes observed
above the transformation change linearly with pressure and the corresponding
pressure coefficients have been determined. Eelatively small (II-IV) or
negative pressure coefficients (I) of the vibrational modes in the low-energy
part of the spectra have been noticed. The high-pressure transformation of the
Raman scattering spectrum results in the change of its lineshape. While a
series of well-defined vibrational modes are observed under pressure below the
transition, broad spectral bands can be detected at higher pressure. The
lineshape of the spectra resembles that of disordered materials, which
suggests amorphisation process involved. The lineshape does not change during
decompression confirming permanent nature of the high-pressure transition.

## Acknowledgment

The work has been supported by the National Science Centre, Poland (grants no.
2017/27/B/ST3/00205 and 2018/31/B/ST3/02111). Z.M. and W.Z. acknowledge
support from the National Natural Science Foundation of China (Grants No.
61627813 and 61971024), the International Collaboration Project (No. B16001),
the Beihang Hefei Innovation Research Institute (project no. BHKX-19-02).

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