Pressure-induced optical anisotropy of HfS₂

Transition metal dichalcogenides (TMDs) have emerged as an exciting class of materials with a layered van der Waals (vdW) structure. Their unique properties, which are strongly dependent on the thickness of the structure and the relatively easy exfoliation, have recently become a hot topic in materials research. Moreover, their layered structure makes them very sensitive to the interlayer spacing, which can be modulated by temperature or strain. This explains the interest in strain engineering of TMDs as an effective way to modify their properties.^1–4 In this study, we address the properties of hafnium disulfide (⁠ $H f S 2$⁠), a less studied member of the TMD family. Interest in this material is driven by its promising electrical properties. According to theoretical calculations, the room-temperature electron mobility in $H f S 2$ is much higher than in the most studied $MoS 2$⁠.⁵ Field-effect transistors based on few-layer $H f S 2$⁠, fabricated by Kanazawa et al.,⁶ exhibit high drain currents and mobility, a transistor on/off current ratio greater than $10 4$⁠, and good responsivity (⁠ $∼$1.6  $μ A W − 1$⁠) in a transfer-free photodetector,⁷ making them notable for the development of thermoelectric and optoelectronic devices.⁸ 

The properties of $H f S 2$ are highly susceptible to changes in the temperature and pressure, including pressure-induced phase transitions.^9–13 However, there is an ongoing debate regarding the precise pressure at which the pressure-induced phase transitions occur, whether they are reversible upon pressure release, and what is the crystallographic structure of the pressure-induced phase. Under ambient conditions, $H f S 2$ belongs to the space group $P 3 ¯m1$ (No. 164). The onset of the phase transition was reported at $P∼$11 GPa based on Raman scattering (RS) measurements in Ref. 10. The RS spectroscopy of $H f S 2$ permitted the earlier reporting on two phase transitions,¹¹ which were observed at $P∼$9.8 GPa and $P∼$15.2 GPa. The distinctive feature of the study in which silicone oil was used as the pressure transmitting medium (PTM) was the emergence of several new high-pressure (HP) peaks in the RS spectra above the phase transformation. A reversible transformation to the 3D orthorhombic $Immm$ (No. 71) structure accompanied by semiconductor-to-semiconductor transition was reported in Ref. 14 at approximately 12 GPa of pressure, which was mediated by neon gas as the PTM. Notably, the authors observed that the RS measurements reflected the transition under pressure as low as $∼$9.2 GPa, which corresponds to other reports.^15,16 Hong et al.¹⁵ reported two structural phase transitions at $P∼$8.0 GPa and $P∼15.2$ GPa as well as metallization at $P$ = 20.5 GPa using helium as the PTM. They also showed that upon decompression, the characteristic RS peaks, which emerged above the transformation, persisted down to $P∼1.4$ GPa, indicating a significant pressure hysteresis effect for $H f S 2$⁠. Quite recently, Zhang et al.¹⁶ have also reported two structural transitions at approximately $P$ = 11.0 GPa and $P$ = 35.5 GPa using silicone oil as the PTM. The former transformation was related to the transition to the orthorhombic $Pnma$ (No. 62) phase, while the latter was linked to a structural transition from the $Pnma$ phase to the tetragonal $I4/mmm$ (No. 139) phase. The pressure-induced transition from the $P 3 ¯m1$ to $Pnma$ phase under pressure was also corroborated by first-principles calculations.¹⁷ 

The motivation of our work is to provide more information on the pressure-induced structural changes of $H f S 2$ upon compression by probing a local symmetry of the related Raman-active vibrations. To this end, we report on polarization-sensitive room-temperature RS measurements as a function of pressure up to $P$ = 10.5 GPa. Our focus is on the effect of pressure hydrostaticity on the phase transition, with particular examination of the results of experiments performed with two PTMs. No apparent phase transition is observed when using the 4:1 methanol–ethanol (ME) mixture, which ensures hydrostatic conditions of pressure within the investigated pressure range. In contrast, a substantial change in the RS spectrum of $H f S 2$ was observed at approximately $P$ = 7 GPa with silicone oil as the PTM. Similarly to the observation by Hong et al.,¹⁵ a large hysteresis effect was observed, and the phase transition is shown to be reversible upon full decompression. The angle-resolved polarized RS (ARPRS) measurements performed at $P$ = 7.4 GPa revealed a strong in-plane anisotropy of the observed RS modes. We discuss the possible origin of the anisotropy, emphasizing the crucial effect of non-hydrostaticity on the phase transitions in $H f S 2$ under external pressure. The results of our study are explained in terms of a distorted $Pnma$ phase as a possible pressure-induced phase of $H f S 2$⁠.

The results of the measurements show that the $A 1 g$ intensity is independent of the relative polarization of the incoming and scattered light for the XX configuration and practically vanishes for the XY configuration (although some signal can still be observed, which might be due to light traveling slightly out of the perpendicular direction). On the contrary, the $E g$ intensity in both XX and XY configurations is practically independent of the polarization of the incoming light. The ARPRS polar plot of $A 1 g$ and $E g$ mode intensities at ambient pressure is shown in Fig. 2. The full and open circles represent the results of measurements for the XX and XY configurations, respectively.

The evolution of RS spectra with pressure transmitted by the ME mixture, which generally provides hydrostatic conditions up to approximately $P$ = 10 GPa,²² is presented in Fig. 3. The line shape of the RS spectra does not change significantly with pressure up to $P$ = 9.6 GPa with a systematic blueshift of the observed RS peak energies. In particular, the $A 1 g$ peak energy is characterized by a linear dependence throughout the entire range of applied pressures (see Fig. S2 in the supplementary material).

The evolution of the RS spectra during compression with silicone oil as the PTM up to $P$ = 10.5 GPa is shown in Fig. 4(a). The RS spectrum measured under $P$ = 0.2 GPa, in the experiment with silicone oil PTM, is similar to that obtained under ambient conditions [compare Fig. 4(a) with Fig. 1]. The effect of increasing pressure up to $P$ = 6.5 GPa is primarily manifested by the blueshift of the LP modes and slight changes in their relative intensities. In contrast, a substantial change in the RS line shape is observed at $P$ = 7.4 GPa, with two well-resolved peaks: I (89  $cm − 1$⁠) and II (100  $cm − 1$⁠) emerging in the low-frequency range of the spectrum. The modification of the RS spectra is followed by the emergence of additional peaks: III (142  $cm − 1$⁠), IV (151  $cm − 1$⁠), V (291  $cm − 1$⁠), VI (324  $cm − 1$⁠), and VII (352  $cm − 1$⁠). The I–VII peaks will, henceforth, be referred to as HP modes. It is evident from Fig. 4(a) that under pressure exceeding $P$ = 7.4 GPa, all HP peaks exhibit a notable increase in the intensity in comparison to their LP counterparts. With increasing pressure, the $A 1 g$ and $E g$ modes continuously disappear from the spectra, becoming barely discernible at $P$ = 10.5 GPa and $P$ = 8.1 GPa, respectively.

To assess the reversibility of the structural transformation of $H f S 2$ under pressure, the RS spectra were also recorded during the decompression cycle. The corresponding selected RS spectra are displayed in Fig. 4(b). The HP RS modes can be observed in the spectra under pressure as low as $P$ = 1.2 GPa [see the black line in Fig. 4(b)] at which A $1 g$ and E $g$ recover. Although the A $1 g$ mode emerges as a separate feature at $∼$350  $cm − 1$⁠, the quenching of the V peak is accompanied by the reemergence of the E $g$ feature, as manifested by a change in the broadening of the peak at $∼$270  $cm − 1$⁠. The energies of the RS peaks measured under the compression (full circles) and decompression (open squares) cycles are shown in Fig. 5. An inspection of the pressure evolution of the $A 1 g$ energy reveals a slope change at approximately $P$ = 5 GPa. An apparently non-monotonic evolution of peaks V and VII is observed at 280 and 340  $cm − 1$ in the pressure range of 7.3 GPa $<P<$ 8.9 GPa (for the determination of their energies, see Fig. S4 in the supplementary material). This behavior cannot be observed during decompression, as the energies of both peaks follow a monotonic dependence down to $P$ = 1.2 GPa. In contrast, the evolution of I, II, IV, and VI during decompression reflects those of the compression procedure down to $P$ = 1.2 GPa.

To gain further insight into the $H f S 2$ structure under pressure with silicone oil as the PTM, the polarization-related properties of the observed RS modes were investigated under $P$ = 7.4 GPa during the compression cycle and at $P$ = 1.2 GPa during the decompression cycle. Let us first address the polarization dependence of the $A 1 g$ intensity, which is still present in the RS spectrum at $P$ = 7.4 GPa [see Fig. 6(a)]. A fourfold symmetry of the $A 1 g$ intensity is observed for both the XX and XY configurations. The main axis of the A $1 g$ intensity for the XY configuration is rotated by 45 $°$ with respect to the main axis for the XX configuration. It should be noted that only minor deviations from the circular dependence of the A $1 g$ intensity can be observed at $P$ = 1.2 GPa in the XX configuration. For the XY configuration, the $A 1 g$ mode has a significantly lower intensity with a negligible angle dependence.

Let us restrict our discussion to light traveling along the z axis, perpendicular to the crystal planes, and adopt the counterclockwise chirality in our setup. In this case, the XX configuration sets the electric field of the incident light (⁠ $e ^ i$⁠) and the scattered beam (⁠ $e ^ s$⁠) as $e ^ i= e ^ s$ = (cos $θ$⁠, sin $θ$⁠). The XY configuration is achieved by rotating the detection polarizer by 90 $°$⁠, resulting in $e ^ s$ = (⁠ $−$sin $θ$⁠, cos $θ$⁠).

The analysis of our observations begins with an examination of the emergence of the anisotropic components of the Raman tensor. In our opinion, they must result from the anisotropy induced by the PTM used in our experiment. The silicone oil is known to introduce a non-hydrostatic component to the pressure. The anisotropy is removed during the decompression cycle at approximately $P$ = 1.2 GPa, as clearly demonstrated in Fig. 6(b). The use of silicone oil in pressure experiments strongly affects the pressure value at which the phase transition occurs. We also found that with the use of the ME, the phase transition is not apparent up to $P$ = 9.6 GPa (Fig. 3). The non-hydrostatic component of pressure clearly leads to the distortion of the 1T- $H f S 2$ crystallographic structure, as observed by the anisotropic RS spectrum of the A $1 g$ mode obtained at $P$ = 7.4 GPa (Fig. 6). The Raman tensor, which can be used to interpret the results, suggests that $H f S 2$ has an orthorhombic crystal structure of the distorted. Similar anisotropy has been reported in a series of different layered materials, e.g., $WTe 2$⁠,²⁹ black phosphorus,³⁰ black arsenic,^31, $α$ $MoO 3$⁠,^32, $ReS 2,$³³ or GeS.³⁴ 

The Raman tensors, which describe the polar dependence of the II, III, and IV HP peaks, correspond to the orthorhombic structure, while those describing the I, V, and VII HP peaks correspond to the triclinic structure. We cannot offer a firm explanation for this observation. However, the energy coincidence of the III and $ω 1$ peaks may suggest that peaks III and IV are split features, which evolve from the $ω 1$ vibration in the unaffected $H f S 2$ crystal. Similarly, peak II may be attributed to another mode that is not optically active in the original $H f S 2$ crystal and became visible in the distorted structure. The fit for peak I is not very conclusive, as the off-diagonal element (⁠ $d/a$⁠) is much smaller than the diagonal (⁠ $b/a$⁠) one. Additionally, the intensity for peak VI was insufficient for the comprehensive analysis. This would leave peaks V and VII to plausibly attributed to a distorted orthorhombic symmetry of the HP phase of $H f S 2$⁠. We propose that this is a distorted $Pnma$ phase.

There are two strong $A g$ modes with energies at 269 and 324  $cm − 1$⁠, while the other $A g$ and $B 1 g$ modes are much weaker. As illustrated in Table I, their energies coincide with the extrapolated zero-pressure energies of peaks V and VII. We note that the polarization-resolved dependence of the intensities of peaks V and VII corresponds well to the triclinic crystal symmetry, which may result from the pressure-induced distortion of the orthorhombic structure. Quantitative correspondence with the experimental results cannot be expected, as our calculations are made for the ambient pressure at $T$ = 0 K. Moreover, the local density approximation (LDA) functional is used, which is known to underestimate the lattice constants that affect the frequencies and intensities of the modes. Additionally, possible resonant conditions are also neglected. Nevertheless, the observed correspondence strongly suggests that the HP phase should be attributed to the distorted $Pnma$ phase of $H f S 2$⁠.

The scattering of the bulk $H f S 2$ was investigated using the $λ$ = 633 nm excitation at room temperature under external pressure up to $P$ = 10.5 GP applied under hydrostatic and non-hydrostatic conditions, which were provided by ME and silicone oil, respectively. No significant RS spectrum line shape was observed with a systematic blueshift of the RS features under hydrostatic conditions. A phase transition in $H f S 2$ was observed at $P≈7$ GP when a non-hydrostatic environment was provided. The phase transition manifested itself with the appearance of seven new modes in the RS spectrum. The angle- and polarization-dependent RS spectroscopic study conducted at $P$ = 7.4 GPa clearly demonstrated anisotropic behavior for all observed RS modes. It was proposed that the original ambient-pressure 1T- $H f S 2$ phase was distorted under pressure, leading to the orthorhombic crystal structure. Concurrently, a new phase emerged, which was associated with a distorted $Pnma$ phase. The pressure-induced phase coexisted with the ambient-condition phase up to $P$ = 10.5 GPa and persisted during the decompression down to $P$ = 1.2 GPa, which confirms its metastable behavior.

The $H f S 2$ crystals under investigation were obtained from 2D semiconductors. The iodine-related photoluminescence signal¹² was observed in the 2D semiconductor crystal. However, in our opinion, the presence of iodine has no significant effect within the pressure range investigated. The x-ray diffraction measurements were found to be in perfect agreement with those of the octahedral 1T phase of $H f S 2$⁠,¹⁸ although a minor amount of an unidentified phase was also detected.³⁵ 

Room-temperature optical measurements were conducted by exciting the sample with a He–Ne laser at $λ$ = 633 nm (1.96 eV), which was focused by a 50 $×$ long-working distance objective with 0.55 (NA). The excitation power focused on the sample was maintained at approximately 0.5 mW throughout all measurements, which resulted in temperature of the sample determined from the relative intensity of the anti-Stokes to the Stokes $A 1 g$ modes equal to $T$ = 291 K (see Fig. S4 in the supplementary material). The scattered light was collected in the back-scattering geometry, sent through a 0.75 m monochromator, and then detected by means of a liquid nitrogen-cooled CCD camera.

The polarization-sensitive spectroscopy was carried out by introducing a $λ/2$ plate directly on top of the objective lens in order to simultaneously rotate the incoming and scattered light with reference to the investigated in-plane crystal orientation. The experiments were conducted with the incoming and scattered light traveling along the $z$ axis. Both configurations, i.e., co- (XX) and cross-linear (XY), were probed. These correspond to the detection polarizer being aligned parallel or perpendicular to the excitation one, respectively. Further details and a schematic illustration of the experimental setup can be found in Fig. S1 of the supplementary material.

The high-pressure experiments were conducted at room temperature in a non-magnetic diamond anvil cell (SymmDAC 60 LT DAC) manufactured from the BeCu alloy.³⁶ The pressure chamber was sealed using a BeCu gasket with a height of approximately. 75  $μ$m, a diameter of 250  $μ$m, and filled with either a methanol/ethanol mixture or silicone oil. The pressure was monitored by the ruby (⁠ $Al 2 O 3$⁠: $Cr + 3$⁠) fluorescent method. The $R 1− R 2$-separation is used as a metric for uniaxial stress.³⁷ 

Density functional theory (DFT) calculations were performed in Quantum Espresso^38,39 with scalar-relativistic norm-conserving pseudopotentials.⁴⁰ The local density approximation (LDA) to the exchange-correlation functional was used. The wavefunction and charge density cutoff energies were set to 100 and 400 Ry, respectively. A $6×10×4$ $Γ$-centered Monkhorst–Pack $k$-point grid was used. The geometrical structure was fully optimized using $10 − 5$ Ry/Bohr and 0.01 kbar criteria for the interatomic forces and stress tensor components, respectively. Phonon and non-resonant Raman calculations were performed within the framework of density functional perturbation theory. A $2×2×2$ $q$-point grid was found to be sufficient for the convergence of phonon dispersion and Raman intensities.

See the supplementary material for a schematic illustration of the experimental setup, fundamental pressure features, and details related to the fitting procedure and parameter tables.

The work was supported by the “Excellence Initiative—Research University at the University of Warsaw” program. Z.M. and W.Z. acknowledge the support from the National Natural Science Foundation of China (NNSFC) (Grant No. 62150410438), the International Collaboration Project (No. B16001), and the Beihang Hefei Innovation Research Institute (Project No. BHKX-19-02). This research was carried out with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, under computational Allocation No. G95-1773.

The authors have no conflicts to disclose.

Igor Antoniazzi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Tomasz Woźniak: Data curation (equal); Formal analysis (equal); Software (equal); Writing – review & editing (equal). Amit Pawbake: Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (supporting). Natalia Zawadzka: Data curation (equal); Investigation (equal); Methodology (equal); Writing – review & editing (supporting). Magdalena Grzeszczyk: Data curation (supporting); Formal analysis (supporting); Writing – review & editing (supporting). Zahir Muhammad: Conceptualization (equal); Methodology (equal); Writing – review & editing (supporting). Weisheng Zhao: Methodology (equal); Writing – review & editing (supporting). Jordi Ibáñez: Conceptualization (equal); Writing – review & editing (equal). Clement Faugeras: Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (supporting). Maciej R. Molas: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Writing – original draft (equal); Writing – review & editing (equal). Adam Babiński: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.