MPX3 van der Waals magnets under pressure (M = Mn, Ni, V, Fe, Co, Cd; X = S, Se)

1 Introduction

Transition metal phosphorous trichalcogenides, MPX₃, where M represents a transition metal ion and X is either S or Se, are a family of semiconducting van der Waals magnets that were originally discovered in 1894 (Friedel, 1894) but were not studied intensively until the 1970s (Klingen et al., 1973). Originally, interest in these materials was sparked by their low dimensional magnetic properties (Le Flem et al., 1982) and ability to form intercalation compounds (Jophnson and Jacobson, 1982), although more recently these materials have attracted attention as single-layer magnets (Burch et al., 2018) and as highly tunable systems that undergo bandwidth-controlled Mott transitions under pressure (Kim et al., 2019).

MPX₃ materials typically crystallize in two space groups, C2/m (No. 12) for the sulfur analogs and R$\bar{3}$ (No. 148) for the selenium-containing compounds. In both cases, the M ions form a honeycomb net, and at the center of each hexagon there is a P-P dimer that extends perpendicular to the net. S or Se anions terminate each MPX₃ layer on both sides, and there is a van der Waals gap between the layers, leading to small cleavage energies and easy exfoliability. Single layers of the MPS₃ and MPSe₃ materials can also be viewed as a honeycomb net of M²⁺ ions coordinated by distorted octahedra of S/Se anions, and P-P dimers centering the hexagons and forming a [P₂S₆]⁴⁻ anionic sublattice (Figure 1). To emphasize the importance of the P-P dimers, the chemical formula of MPX₃ materials is sometimes written as M₂P₂X₆, but this is incorrect nomenclature as the chemical formula is not supposed to reflect structural features (Hiroi, 2008). These structural motifs lead to three different types of chemical bonding: ionic, covalent, and van der Waals - which makes understanding the electronic structure of this family of materials quite challenging (Dedkov et al., 2023).

Figure 1

Figure 1. (Top) Schematic diagrams of diamond anvil cells (DAC) applying hydrostatic (left) and non-hydrostatic (right) pressure to MPX₃ compounds. (Middle) An example of pressure-induced structural transition involving layer sliding and phosphorous chain formation in MPX₃. (Bottom) An Illustration of structural (metal-metal distance d_M−M, metal-sulfur distance d_M−S, and bond angle ∠MSM), orbital (L), spin (S), charge (q)), and magnetic (Mag.) degrees of freedom, which together interact to give rise to novel pressure-induced physical properties of MPX₃.

In general, MPS₃ materials with M = V, Mn, Fe, Co, and Ni are reported to be antiferromagnetic Mott insulators with variable semiconducting energy gaps and magnetic structures. CdPS₃, in contrast, has a filled d shell and is semiconducting and nonmagnetic. The Mottness and magnetism of MPS₃ compounds originates from their partially-filled d-orbital shells; this, in addition to the presence of a van der Waals gap, suggests that the MPS₃ series is an excellent platform for the study of two-dimensional correlated electron phenomena and magnetism (Figure 1).

Tuning the physical properties of these compounds is a highly contemporary research subject, allowing for the exploration of new states of matter and functionalities. Toward this end, researchers are using chemical substitution, doping and intercalation, as well as various external perturbations such as electric field, light, strong magnetic fields, and strain (Wang et al., 2018a; Pei et al., 2022). For instance, chemical substitution on the M and X sites provides the control of d-orbital filling and bandwidth, respectively, which are both important parameters to control Mottness, magnetism, and spin-orbital-lattice coupling (Lu et al., 2022; Peng et al., 2023). Even better, many MPS₃ compounds have both X = S and Se limits as stable systems, which allows continuous tuning of lattice parameters and bandwidth via synthesizing MPS_xSe_3−x samples (Basnet et al., 2022b). Even differences in X-site chemistry sometimes gives rise to interesting contrasts; for example, the presence and absence of superconductivity in pressurized FePSe₃ and FePS₃, respectively. At the same time, doping and intercalation control carrier concentration and impart new properties (Basnet et al., 2022a; Tezze et al., 2022).

Among these external stimuli, pressure is a highly effective tool for tuning the physical properties of MPX₃ materials. The interlayer van der Waals (vdW) interaction is weak; thus, the interlayer spacing can be effectively modulated by pressure. As the layers are forced closer together, layers slide with respect to each other, changing their relative orientation. Furthermore, pressure modifies the c/a ratio, reflecting the more compressible interlayer distance than the ab plane. Bond lengths and angles within the chalcogenide layers are also modified under compression (Figure 1). With the collapse of the van der Waals gap under pressure, interlayer orbital overlap increases, and the materials become more three-dimensional with enhanced bandwidth. With varying d-orbital occupancies and the resulting different orbital degrees of freedom (i.e., t_2g vs. e_g), pressure can induce drastically different responses of lattice structure, as well as electronic and magnetic properties, depending on the chemistry of the metal center and chalcogen anion.

In addition to bandwidth and dimensionality tuning, the sliding of adjacent layers and change of stacking order can create contrasting responses in electronic and magnetic properties, as recently suggested in 1T-TaS₂ with the “star of David” charge density wave formation. In MPX₃, this effect appears prominently since even hydrostatic pressure can create shear strain in the monoclinic structure of many of them (Butler et al., 2020). As we will see below, the presence of this layer-sliding in the MPS₃ series under pressure (in V_0.9PS₃, MnPS₃, FePS₃, CoPS₃, and NiPS₃) creates complicated yet rich structural, electronic, and magnetic behaviors. For example, it has been reported that the layer sliding in MnPS₃ expedites the pressure-induced Mott transition (Harms et al., 2020). At this point it is uncertain why systems show different layer-sliding responses under compression, still it is clear that pressure is a valuable tool in unlocking tremendously rich physical characteristics hidden within the MPX₃ series.

Over the past few years the evolution of the structural, magnetic, and electronic properties of MPX₃ compounds under compression have been extensively studied. Given the rapid progress in this field, the time is ripe for a short review. In the sections below, we first discuss the M = Mn, Fe, and Ni, which have been the topics of the most number of studies. We then discuss V_0.9PS₃ and CoPS₃, which have been much less studied. Lastly, we cover the non-magnetic compounds, CdPS₃ and CdPSe₃, and the structure-property relations that can be unraveled in these systems.

In addressing ongoing research topics in each system, discussions involving the following themes occur in most of the compounds: strong electron correlations from the partially-filled d-orbital shells, pressure-induced Mott insulator-to-metal transitions, the role of p-d hybridization in ground-state and optical properties via the comparison between MPS₃ and MPSe₃ systems, and the role of layer-sliding and the changes in of P-P bonding at the Mott metallization transition. These issues are discussed at appropriate points in the manuscript.

Pressure is an effective tool for tuning the properties of complex chalcogenides, but the following considerations should be kept in mind when interpreting experimental data. Below 6 or 7 GPa, pressure in the diamond anvil cell is reliably hydrostatic, although tests should be performed to confirm this expectation. Above 6 or 7 GPa, it’s very challenging to assure perfectly hydrostatic conditions. Even in a well-tested and characterized system, there may be deviations on the order of 1% or more—especially at low temperatures. Non-hydrostatic conditions can impact the properties - for instance, broadening a spectroscopic response. These signatures are most easily monitored by ruby fluorescence and are discussed in a number of references including (Musfeldt et al., 2023).

2 Properties of MPX₃ materials under pressure

2.1 MnPS₃ and MnPSe₃

MnPS₃ is the prototype in this family of materials and is therefore extensively investigated. This system crystallizes in a monoclinic C2/m structure whereas MnPSe₃ displays a trigonal R$\bar{3}$ arrangement. The P–P dimer is an important structural building block as is the ${\mathrm{P}}_2{\mathrm{S}}_6^{4-}$ cluster. These elements are crucial in defining the thickness of the chalcogen layer. Table 1 summarizes the layer thickness and van der Waals gap for MnPS₃ and MnPSe₃ and compares them to other members of this series. The C2/m vs. R$\bar{3}$ structural difference between sulfur and selenium analogs plays out in other members of the MPX₃ family of materials as well (Figure 2 and Tables 2, 3).

Table 1

Table 1. Inter-layer thicknesses distances and van der Waals (vdW) gaps of MPS₃ and MPSe₃. Data are from (Ouvrard et al., 1985b; Ouvrard et al., 1985a; Wiedenmann et al., 1981).

Figure 2

Figure 2. Crystal structures of MPS₃ (M = V, Mn, Fe, Ni, Co, Cd) family of materials in the low-pressure (LP) and high-pressure (HP) phases visualized using VESTA3 (Momma and Izumi, 2011) based upon reported experimental and theoretical results (Ouvrard et al., 1985a; Haines et al., 2018; Coak et al., 2019; Harms et al., 2020; Harms et al., 2022a; Matsuoka et al., 2023). The bottom right shows layer sliding in C2/m symmetry with decreasing monoclinic angle β under pressure. When β = 90°, the honeycomb pattern of metal ions overlaps between adjacent layers, and the system transforms to a trigonal high pressure phase.

Early neutron diffraction studies of MnPS₃ uncovered collinear Néel-type AFM order at T_N = 78 K (Le Flem et al., 1982; Kurosawa et al., 1983b; Joy and Vasudevan, 1992; Wildes et al., 1994), although there were discrepancies as to the direction of the magnetic propagation vector. A recent study revisited this problem using single crystal neutron diffraction and polarimetry (Ressouche et al., 2010). This work revealed a propagation vector k = [000] as well as magnetoelectric coupling and ferrotoroidicity (Ressouche et al., 2010). By comparison, T_N = 74 K for MnPSe₃ (Wiedenmann et al., 1981; Le Flem et al., 1982). A similar reduction of the transition temperature is observed for FePX₃ when the X is modified from sulfur to selenium. Neutron scattering of MnPSe₃ reveals an identical propagation vector (k = [000]) (Wiedenmann et al., 1981; Bhutani et al., 2020). Photoemission and x-ray absorption spectroscopy confirms a high spin Mn²⁺ configuration in MnPSe₃ (Fujii et al., 2022). Each Mn center is antiferromagnetically coupled to its three nearest neighbors (Kurosawa et al., 1983a). One surprising finding is the strong magnetic interaction between third nearest neighbors. The spin wave excitations have also been studied by Raman and neutron scattering in these materials. Major findings include: hybridization of the two-magnon excitation with phonons (which impacts the spin wave decoherence pathway) and absence of nonreciprocity in zone boundary magnons (which provides experimental limits that can be tested against theoretical predictions) (Sun et al., 2019; Vaclavkova et al., 2020; Mai et al., 2021; Wildes et al., 2021).

Several different but complementary efforts were required to unravel the sequence of events that takes place under pressure. In the first experimental work, Wang et al. uncovered a simultaneous spin-state crossover and metal-insulator transition in both MnPS₃ and MnPSe₃ (Figure 3) as well as zigzag chain formation of the Mn atoms in the metallic phase (Wang et al., 2016). The critical pressures (P_c’s) for these processes were reported to be 30 and 25 GPa for MnPS₃ and MnPSe₃, respectively. First-principles electronic structure calculations using DFT + U and DFT + DMFT techniques reproduced the insulator-to-metal transition with simultaneous spin-state transition but with a Mn-Mn dimerization at 64 GPa (Kim et al., 2019), although it was hinted that some structural components might be missing. This early experimental and theoretical work did not consider layer sliding, which turns out to modify the picture in important ways.

Figure 3

Figure 3. Magnetic moment and spin state as a function of pressure for MnPS₃, MnPSe₃, FePS₃, and FePSe₃ relative to properties at ambient conditions. Data taken from (Wang et al., 2016; Wang Y. et al., 2018).

In a significant conceptual advance, Coak et al. discovered an intermediate pressure transition in the series of MPS₃ (M = V_0.9, Mn, Fe, Ni) materials (Coak et al., 2020). This transition involves coherent layer sliding to create an alignment of P–P dimers along the layer-normal direction. This insight enabled a number of subsequent advancements. For instance, infrared, Raman scattering, and optical measurements as a function of pressure combined with first-principles calculations reveal that MnPS₃ undergoes a C2/m (LP) → P$\bar{3}$1m (HP-I, insulating, around 10 GPa) → C2/m (HP-II, metallic, around 30 GPa) with a layer-sliding between the LP and HP-I phases, similar to observed in FePS₃ (Figure 2 and Table 2). The HP-I → HP-II transition accompanies spin-state transition, collapse of MnS₆ volume, and a reduction of interlayer distance with an layer-normal P-chain formation, (Figures 2–4). The trigonal (HP-I)-to-monoclinic (HP-II) symmetry lowering transition is thought to originate from the low-spin d⁵ orbital nature of the Mn²⁺ ions, contrary to the case of FePS₃ with the same layer sliding but with C2/m (LP) → C2/m (HP-I, insulating after the layer sliding) → P$\bar{3}$1m (HP-II, metallic) transitions.

Table 2

Table 2. Crystal structures for the low pressure (LP) and high pressure (HP) phases of MPS₃.

Figure 4

Figure 4. Volume per formula unit as a function of pressure. (A) MPS₃ (M = V, Mn, Fe, Co, Ni). (B) MnPS₃ and FePS₃ with MnPSe₃ and FePSe₃ for comparison. The circles denote the low (or ambient) pressure phase, which is semiconducting, including the HP-I phases for MnPS₃ and FePS₃. The squares indicate high pressure metallic phases. The solid lines guide the eye.

We note in passing that theory tends to over-estimate the band gap and pressure of the insulator-to-metal transition in these materials (Grasso et al., 1991; Harms et al., 2020; Yan et al., 2023). Gap estimation is a well-known challenge for first-principles density functional theory-based approaches, and weak interactions with shallow potentials are notoriously difficult to calculate with accuracy. Nevertheless, these techniques nicely reveal the semiconducting behavior of the aligned phosphorous dimer phase and the metallic character of the aligned phosphorous chain phase (Figure 5A).

Figure 5

Figure 5. MnPS₃ under pressure puncture. (A) Spectral functions from DFT + DMFT calculations showing the k-resolved and orbital-projected spectral functions calculated with the aligned phosporous dimer (APD) and aligned phosphorous chain (APC), respectively (Harms et al., 2020). (B) Photographs of piezochromic MnPS₃ inside the diamond anvil cell at several characteristic pressures and also after release at room temperature. The scale bar (left panel) is 200 μm. (Harms et al., 2020).

From the optical properties point of view, MnPS₃ is a semiconductor with a 2.7 eV band gap. It hosts spin-charge coupling across the magnetic ordering transition and a set of crystal field excitations that have been widely investigated (Boerio-Goates et al., 1981; Grasso et al., 1991; Harms et al., 2020; Yan et al., 2023; Park et al., 2024). There is strong p-d hybridization which activates the d-to-d on-site excitations of the Mn²⁺ centers. There is also a broad near infrared emission band assigned as ⁴T₁ →⁶A₁ with a half life of approximately 50 μs at 77 K (Boerio-Goates et al., 1981). The ratio of the crystal field splitting to the Racah parameter (10Dq/B) is unusually large and may explain the strongly red-shifted light emission in this system. That the band gap of MnPS₃ decreases systematically under pressure suggests that this system hosts piezochromism (Harms et al., 2020). It turns out that MnPS₃ is green at ambient conditions, and as shown in Figure 5B, it is yellowish-green at 3 GPa, bright red at 8 GPa, and black by 20 GPa. The latter occurs because the band gap shifts out of the visible wavelength range, moving systematically toward closure at a rate of approximately −50 meV/GPa. This effect is quenched by the appearance of the insulator–metal transition. This high level of linear responsivity under pressure is unusual, and piezochromism of this type has applications in pressure sensing, actuation, as well as artificial skin. At this time, it is not known whether strain can drive similar effects in the bulk material, although in few- and single-sheet MnPS₃ there is a C2/m to P$\bar{3}$1m transition that may involve surface strain effects (Neal et al., 2019; Neal et al., 2020) and biaxial strain is predicted to impact the magnetic ground state in MnPSe₃ monolayers (Pei et al., 2018).

Thermal properties of these materials are also of interest from a fundamental point of view and for heat management purposes in a device. Kargar et al. find in- and out-of-plane thermal conductivities of 6.3 ± 1.7 and 1.1 ± 0.2 W/m⋅K, respectively (Kargar et al., 2019). These values are higher than what is found in the Fe analog.

2.2 FePS₃ and FePSe₃

FePS₃ and FePSe₃ are layered antiferromagnets with T_N around 120 K (Le Flem et al., 1982; Joy and Vasudevan, 1992). FePS₃ has gained significant interest recently for its Ising-like antiferromagnetic ordering in the single-layer limit (Lee et al., 2016). The d⁶ configuration of the Fe²⁺ charge status shows a high-spin configuration S = 2 with the partially-filled t_2g complex, implying anisotropic nature of magnetism as revealed by experimental and theoretical observations (Nauman et al., 2021; Zhang et al., 2021). In the presence of external pressure, like Mn-based siblings, spin-state transition and the resulting complex electronic and structural responses are expected in FePS₃ and isostructural FePSe₃. Accordingly, the responses of magnetic, electronic, and structural properties of FePS₃ and FePSe₃ have been actively investigated.

Recent x-ray, neutron scattering, and optical spectroscopy studies on the effect of hydrostatic pressure on FePS₃ reveal a sequence of structural phase transitions, (Haines et al., 2018; Coak et al., 2021; Harms et al., 2022b) analogous to MnPS₃ and V_1−xPS₃ (Coak et al., 2019; Harms et al., 2020); a gradual layer-sliding crossover from the monoclinic LP (C2/m space group) to the pseudo-hexagonal intermediate phase (HP-I, C2/m) around 2–5 GPa, and the following C2/m → P$\bar{3}$1m (HP-II) transition accompanied by the insulator-to-metal transition at 14 GPa (see Figure 2), (Coak et al., 2021). The LP and HP-I phases of FePS₃ have been reported to be insulating and antiferromagnetic with a Néel-type order. Figures 6A, B show the magnetic configurations of the LP and HP-I phases from neutron data, respectively (Coak et al., 2021). Figure 6C describes the evolution of the T_N as a function of pressure (Wang et al., 2018b; Haines et al., 2018; Coak et al., 2021). The gradual enhancement of the T_N can be attributed to the increased kinetic energy scale due to the closer Fe-Fe distances and the resulting enhanced magnetic exchange interactions.

Figure 6

Figure 6. Crystal and magnetic structures of the low-pressure (HP-0) and the first high-pressure (HP-I) phases of FePS₃. (A) The magnetic cell of FePS₃ with the k = [0 1 1/2] propagation vector - overall antiferromagnentic order, consisting of a zig-zag chain antiferromagnetically coupled to their neighbors along a-axis and between the planes (Lançon et al., 2016). (B) The magnetic unit cell with k = [0 1 0] propagation vector, where the planes are ferromagnetically aligned (Coak et al., 2021). (C) Pressure-temperature phase diagram of FePS₃ from magnetization measurements and neutron scattering experiments. Blue circles, red crosses (and squares) are from magnetization measurements and integration of neutron spectra, respectively. Dashed lines are fits to the data points, and vertical lines mark structural transitions. Inset shows normalized magnetization versus temperature with increasing pressure. The plot is from (Coak et al., 2021).

The second transition (HP-I → HP-II) accompanies the breaking of the P-P dimer structure and the formation of interlayer P-chain perpendicular to the Fe layers, in addition to a sudden collapse of the interlayer distance and volume, (Haines et al., 2018) similar to the case of MnPS₃. Harms et al. (2020) note that these observations are consistent with separate first-principles electronic structure calculation results, (Zheng et al., 2019; Deng et al., 2023) where the origin of the coexistence of the LP and HP-I phases around 2–5 GPa is suggested to be the result of the shear-induced energy barrier between the LP and HP-I phases (see Figure 7A), (Deng et al., 2023).

Figure 7

Figure 7. High-pressure electronic states of FePS₃ and superconducting FePSe₃ (A) Enthalpy difference from DFT calculations as a function of the monoclinic β angle in the C2/m structure for the ambient (LP) and HP-I AFM phases of FePS₃ at 1.0 GPa. Panel from Deng et al. (2023). (B) Heat map of magnetic peaks at 80 K in FePS₃, showing the presence of magnetic signals in the HP-II (P $>$ 15 GPa) phase. Panel from Coak et al. (2021). (C) The temperature dependence of the electrical resistance of FePSe₃ at 29.6 GPa under magnetic fields of 0, 0.1, 0.25, 0.5, 1, 2, and 5 T. Inset shows the field dependence of T_c for FePSe₃ at 29.6 GPa. (D) Temperature–pressure phase diagram of FePSe₃. Solid circles: the pressure dependence of the onset superconducting transition temperatures (5*T_c), blue triangles: the pressure dependence of Hall coefficient, T_N denoting the Néel temperature. Panel (C) and (D) from (Wang Y. et al., 2018).

From both experimental and theoretical studies, the Mott-insulating antiferromagnetic phase is reported to remain robust in the LP and HP-I phases, reflecting the quasi-two-dimensional nature (Haines et al., 2018; Zheng et al., 2019). With the formation of the interlayer P-chain in the HP-II phase this two-dimensional character breaks down, and so does the insulating behavior. The sudden collapse of the interlayer distance and cell volume at the HP-I → II transition implies a spin-state transition (see Figure 4). Indeed, an early study on pressurized phases of FePS₃ and FePSe₃ reported collapses of magnetic moments and transitions to low-spin phases around 13 and 8 GPa, respectively, Wang et al. (2018b) and additionally, the DFT study of Zheng et al. (2019) also reports the spin-state transition from the high-spin S = 2 to the low-spin S = 0 configuration of the Fe ions at the HP-I → II transition. Interestingly, on the other hand, a high-pressure neutron diffraction data by Coak et al. (2021) suggests the presence of short-range magnetic order in the HP-II phase, persisting even up to room temperature (see Figure 6C, 7B). From a detailed electronic structure calculation study, Deng et al. (2023) argues that this puzzling behavior may be explained by the potential coexistence of two metastable metallic states; the high-spin one with the intralayer P₂ dimer structure remains intact comparing the short-range order (2D-like), while the P₂ dimer breaks to form the out-of-plane P chain structure (3D-like) in the other low-spin state. A separate dynamical mean-field theory study on FePS₃ also suggests the coexistence of the two structural phases, each one hosting the normal Fermi liquid-like character (with the interlayer P-chain) and the incoherent “Hund’s metal” character (with the intralayer P-dimer) in the high-pressure regime, where the Hund’s metal phase keeps the local moments intact and induces bad-metallic behavior due to magnetic fluctuations (Kim et al., 2022).

It is interesting to note that, in Kim et al., (2022), the Hund’s metal phase with the orbital-selective correlation effects occurs only with a non-hydrostatic pressure, especially when the pressure perpendicular to the Fe layers are stronger than the in-plane counterparts. This originates from the direction-selective orbital effect under pressure, where the t_2g orbitals of Fe ions becomes more susceptible to the out-of-plane stress compared to e_g. This implies a subtle role of anisotropy and inhomogeneity in pressure, which may often occur in high-pressure experimental situations depending on the choices of pressure-transmitting medium (Matsuoka et al., 2021).

Lastly we comment on FePSe₃. This system shares a crystal structure and magnetic ground state with FePS₃, (Wiedenmann et al., 1981; Le Flem et al., 1982) and expected from theoretical calculations to show many common properties, such as layer-sliding transition to HP-I, volume collapse at the HP-I → II transition accompanying the simultaneous spin-state and insulator-metal transitions (Zheng et al., 2019). Experimentally the second transition is observed to occur at a lower pressure of around 8 GPa than that of FePS₃, which can be attributed to the larger hybridization effects from Se ions (Wang et al., 2018b). Unlike FePS₃, superconductivity of unknown origin has been reported in the HP-II metallic phase of FePSe₃ below 2.5K (see Figures 7C, D), (Wang et al., 2018b). Structural refinement in the same study suggests the formation of the zigzag chains within the Fe honeycomb layer in the HP-II phase of FePSe₃, hinting the presence of orbital physics from high-spin configuration at Fe ions and potential unconventional superconductivity.

2.3 NiPS₃ and NiPSe₃

NiPS₃ and the Se analog provide another exciting platform for exploring new states of matter under external stimuli and developing different types of structure-property relationships. The magnetic ordering temperatures are T_N = 155 and 206 K, respectively (Le Flem et al., 1982; Joy and Vasudevan, 1992; Chandrasekharan and Vasudevan, 1994), so we see that in this case, heavier anions act to raise the Neél temperature. In the low temperature phase of NiPS₃, the magnetic propagation vector k = [010]. Analysis of the integrated intensity of the (010) magnetic Bragg peak as a function of temperature reveals a critical exponent for the magnetization 2β = 0.30 away from the transition temperature, consistent with a two-dimensional universality class, and 0.30 near T_N, suggesting the importance of three-dimensional interactions in this regime (Wildes et al., 2015). There are a number of low energy excitations in this system from which competing exchange interactions can be extracted (Mehlawat et al., 2022; Wildes et al., 2023), and active pumping of orbital resonances can also manipulate magnetic order in this quasi-two-dimensional van der Waals antiferromagnet (Afanasiev et al., 2021). Solid solutions in the form of Ni_1−xMn_xPS₃ (0 ≤ x ≤ 1) can also tune the spin flop transition from approximately 7 to 2 T due to modulation of the magnetic anisotropy (Basnet et al., 2021). Intercalation is also very effective in this regard. It can even drive the ground state ferrimagnetic (Basnet et al., 2022a; Tezze et al., 2022). The magnetic properties of NiPS₃ are clearly very sensitive to chemical pressure, suggesting that there is more to learn under physical pressure. The latter is obviously a much cleaner technique as well. Light is also an important external stimuli in these materials. NiPS₃, for instance, sports laser-induced demagnetization with responsivity (lifetime) on the order of 10 ps (Kuntu et al., 2024). Photo-induced quenching of magnetic order is likely to be very sensitive to pressure.

Early high pressure x-ray diffraction work combined with first-principles calculations suggested strong similarities between NiPS₃ and the M = Mn and V analogs, with LP-to-HP-I and the HP-I-to-HP-II transitions near 15 and 27 GPa with an insulator-to-metal transition near 20 GPa (Ma et al., 2021). More recent efforts combining transport and x-ray diffraction reveal a series of different crystal structures under pressure, time-dependent and somewhat sluggish character to several of the transitions, and an insulator-to-metal transition near 30 GPa (Matsuoka et al., 2021). Systematic studies of hydrostatic pressure vs. strain demonstrates that the critical pressure of the insulator-to metal transition (as identified by transport measurements) is reduced from 30 to 12.5 GPa under uniaxial strain (Cui et al., 2021) - an observation that again emphasizes the need for hydrostatic pressure conditions. This confusing and somewhat contradictory picture was resolved by bringing together synchrotron-based infrared absorption, Raman scattering, x-ray diffraction, and first-principles calculations under pressure to show that in fact NiPS₃ is quite different from the other MPS₃ materials (Harms et al., 2022a) with a series of five different critical pressures. The set of symmetry progressions in this material is complex (involving C2/m → P$\bar{3}\to$ P$\bar{3}$m1 → P3m1 → P3 → P1 space groups) from monoclinic to trigonal to noncentrosymmetric trigonal to triclinic phases (Figures 8, 9). The insulator-to-metal transition takes place near 23 GPa as evidenced by the development of a Drude response + screening of the phonons in the infrared spectrum. This definition of the insulator-to-metal transition obviously places the critical pressure below that obtained from a transport measurement (23 vs. 30 GPa), but the development of Drude signature in the electrodynamic response is an exquisitely sensitive indicator of metallicity. In any case, it’s important to realize that several of the aforementioned space groups lack an inversion center, suggesting that NiPS₃ may be a polar metal under compression (Harms et al., 2022a). Whether the material is switchable (ferroelectric) or not switchable (pyroelectric) under these conditions (in the P3m1 phase above 23 GPa) is unexplored at present. In principle, any electric polarization should increase as the space group progresses from P3m1 → P3 → P1 (Harms et al., 2022a; Aoyama et al., 2014). Real physical examples of polar metals are rare, so it’s useful to consider how NiPS₃ hosts such a state when it has not been sighted (as of yet) in related MPX₃ systems. The current working hypothesis is that because NiPS₃ does not favor a $P\bar{3}m1$-type structure or layer-normal phosphorous chain formation, it may engage in negative charge transfer with hole formation at the S sites (Harms et al., 2022a). The optical properties of NiPS₃ have also been of sustained interest (Kim et al., 2018; Kang et al., 2020; Lane and Zhu, 2020)—both in single crystal and thin film form—although to our knowledge, there have been no studies under pressure or strain. Interestingly, electric field also drives an insulator-to-metal transition in the monolayer (Lane and Zhu, 2020), suggesting that pressure and electric field phase space may share more similarities that previously supposed.

Figure 8

Figure 8. Vibrational properties of NiPS₃ under compression. (A–D) Close-up view of the infrared absorption and frequency vs. pressure plots. (E–H) Close-up view of the Raman scattering response and frequency vs. pressure plots. Spectra for the low pressure (LP) phase are shown in gray; those for the high pressure phases (HP-I, HP-II, and HP-III) are shown in teal, green, and black, respectively. Closed and open circles represent two independent runs. Note that infrared spectra in the HP-III phase are not included because the phonons are screened by the metallic response. The critical pressures (P_C’s) separate the high pressure phases and are indicated with dashed vertical gray lines. Panels (A–H) from (Harms et al., 2022a).

Figure 9

Figure 9. High pressure x-ray diffraction results of NiPS₃ up to 39 GPa. (A) Integrated x-ray diffraction profiles at indicated pressures. The appearance of x-ray diffraction peaks at the given angle are indicated, alongside dashed lines to guide the eye. Critical pressures, dividing individual pressure phases, are indicated by solid blue horizontal lines. The space groups of individual high pressure phases are labeled. The asterisk (*) and plus (+) marks correspond to the diffraction response from NaCl in B1-type structure (below 30 GPa) and B2-type (above 30 GPa). (B) and (C) The x-ray diffraction images on the detector for HP-I (13 GPa) and HP-III (24 GPa). The peaks from NiPS₃ are enclosed with squares alongside the hkl indices for each phase. The gray labels in the panel (C) indicate the diffraction from HP-II. The Bragg diffraction from the diamond anvils is masked with red circles.Panels (A–C) from (Harms et al., 2022a).

NiPSe₃ is different, primarily because it does not have a complicated set of symmetry progressions under compression. Instead, there is a relatively simple structural sequence as shown in Figure 10 and Table 3, (Harms et al., 2022a; Sun et al., 2023). More recent efforts involving combined synchrotron x-ray diffraction and first-principles theory confirm these two structural transitions: LP to HP-I (where the honeycomb layers slide relative to each other) and HP-I to HP-II (where the structure has more three-dimensional character) (Sun et al., 2023). There is also a concomitant magnetic crossover at P_C1 where the direction of the antiferromagnetic moment switches from out-of-plane to in-plane. Complementary resistance measurements indicate a bandwidth-controlled Mott insulator-metal transition near 8.0 GPa. The latter coincides with the emergence of superconductivity with T_c ≈ 4.8 K (Sun et al., 2023). This leads to a remarkable and complex pressure-temperature phase diagram hosting coexisting zigzag antiferromagnetic order and superconductivity (Figure 11).

Figure 10

Figure 10. Crystal structures of NiPS₃ and NiPSe₃ in LP ((A) and (D)), HP-I ((B) and (E)), and HP-II ((C) and (F)) phases visualized using VESTA3 (Momma and Izumi, 2011) based on the experimental reports (Harms et al., 2022a; Sun et al., 2023). As discussed in the text, NiPS₃ displays an unusual sequence under pressure: C2/m with β ∼ 108°→ P$\bar{3}\to$ P$\bar{3}$m1 → P31m and so on. This structural sequence is not seen in other members of the MPS₃ family. On the other hand, NiPSe₃ is similar to FePS₃ (C2/m with β ∼ 108°→ C2/m with β ∼90°→ P$\bar{3}$1m) and MnPS₃ (C2/m with β ∼108°→P$\bar{3}$1m). The primary difference between the LP-phases of NiPS₃ and NiPSe₃ is the angle of the P-P dimer. The P-P dimer in NiPS₃ aligns almost perpendicular to the ab plane. On the other hand, the dimer in NiPSe₃ aligns mostly in an out-of-plane direction but with an angle.

Table 3

Table 3. Crystal structures for the low pressure (LP) and high pressure (HP) phases of MPSe₃.

Figure 11

Figure 11. Phase diagram of NiPSe₃. Structural phase boundaries are from x-ray diffraction experiments at room temperature. T_N for AFM order and T_C for superconductivity are from electrical resistance measurements and DFT calculations. Created based on data from (Sun et al., 2023).

Finally, we point out that transition metal dichalcogenides such as MoS₂ and WS₂ and related nanostructures are employed for solid state lubrication due to their ultra-low friction coefficients - especially under high shear conditions (Musfeldt et al., 2020). In an important initiative, Deng et al. (2024) are started to explore the mechanical properties of terenary chalcogenides like NiPS₃ using lateral force microscopy (Deng et al., 2024). These measurements reveal a friction coefficient of approximately 4.5 × 10⁻³ under 5 × 10⁻³ Pa with load up to 768 nN. These findings are discussed in terms of the extremely weak interlayer interactions. Table 1 summarizes other candidates with low layer thickness/van der Waals gap ratios including CdPS₃ and FePSe₃ that should be tested.

2.4 V_1−xPS₃ (x < 1)

The vanadium phosphate synthesis has been achieved with the vanadium deficiency in V_1−xPS₃ which can be explained as due to valence mixing on the vanadium site between V²⁺ and V³⁺ states (Ouvrard et al., 1985b; Ichimura and Sano, 1991). The LP-phase has an electrical conductivity higher than 10^–5 Ω⁽⁻¹⁾cm⁽⁻¹⁾, while MnPS₃, NIPS₃ and ZnPS₃ crystals lower than 10^–9 Ω⁽⁻¹⁾cm⁽⁻¹⁾ at room temperature. The high conductivity of the former crystals is attributed to their mixed valency on the metal and/or the S and P sites, which has been revealed by x-ray photoelectron spectroscopy (Ichimura and Sano, 1991). The LP → HP-I transition starts at 2.6 GPa followed by the gradual transition to HP-I completing near 8.0 GPa (Coak et al., 2019). The layers of V_0.9PS₃ shift relative to each other in a sliding motion of ∼ a/3 along the a-axis such that the S atoms become arranged in a hexagonal closed packing layout between the layers (Table 2; Figure 2), (Coak et al., 2019). In HP-I, P atoms are slightly distorted along the a-axis (the x coordinate value is 0.0074 at 17.7 GPa) of the unit cell, and this distortion results in the same C2/m symmetry (Coak et al., 2019). The volume per formula unit decreases continuously without a sudden or discontinuous changes across the gradual LP → HP-I transformation (Figure 4). Coak et al. (2019) The electrical resistance decreases significantly and continuously with increasing pressure, and then the insulator-to-metal transition occurs near 12 GPa above the pressure where the LP → HP-I transformation completes (Coak et al., 2019). Thus, the isostructural insulator-to-metal transition is concluded, suggesting a second-order transition (Coak et al., 2019). From the magnetoresistance data, Coak et al. claim the insulator-to-metal transition involves the antiferromagnetic to paramagnetic transition (Coak et al., 2019). The R vs. T curve in the metallic phase shows an upturn at low temperatures. Coak et al. (2019) suggest that Kondo effect due to the vanadium deficiency and disordered valence mixing on the vanadium sites (Coak et al., 2019). The synthesis of VPSe₃ has not been reported to the knowledge of the authors.

2.5 CoPS₃ and CoPSe₃

Like other structural siblings, CoPS₃ has gained significant interest recently for the study of two-dimensional magnetism. Since Co²⁺ ion is in the d⁷ configuration with a hole in the t_2g shell, significant effects of spin-orbit coupling on magnetism is expected. Indeed, recent theoretical studies suggested an interesting way to realize the so-called Kitaev’s exchange interactions in cobalt-based compounds, (Kitaev, 2006; Liu and Khaliullin, 2018; Sano et al., 2018) which were originally considered in heavier transition metal systems (Jackeli and Khaliullin, 2009). Several Co-based systems including CoPS₃ have been studied for the search of the Kitaev-induced frustrated magnetism (Kim et al., 2020; Kim et al., 2021; Lin et al., 2021; Kim et al., 2023; Zhang et al., 2023). Considering the presence of metastable spin states and significant spin-orbit coupling in Co ions, (Yamaguchi et al,. 1996; Zobel et al., 2002). It is expected that pressure may induce intriguing evolution of electronic and magnetic properties of CoPS₃.

CoPS₃ crystallizes in C2/m structure at ambient pressure as other MPS₃ family at ambient pressure. CoPS₃ exhibits AFM at ambient pressure with a T_N = 122 K and a Weiss temperature of θ = −166 K (Ouvrard et al., 1982; Wildes et al., 2017). Single-crystal neutron diffraction shows that the magnetic propagation vector is k = [010] with the moments mostly along the a-axis and with a small component along the c-axis (Ouvrard et al., 1982; Wildes et al., 2017). As observed for NiPS₃, this magnetic structure is in sharp contrast to MnPS₃ and FePS₃ whose moments are mostly along the c-axis. Its effective moment is 4.9 μ_B, slightly larger than the expected value for a pure spin moment of a Co²⁺ cation (Ouvrard et al., 1982), implying orbital contribution to the magnetization as mentioned above. In addition, an inelastic neutron scattering study suggests a XXZ-type antiferromagneic order in CoPS₃, signalling the presence of the spin-orbit coupling-induced magnetic anisotropy (Kim et al., 2020).

High pressure properties of CoPS₃ have not been experimentally reported until recently, probably due to the significant difficulty in the synthesis and single crystal growth of this compound. A first-principles calculation from an article dedicated to the pressure effects in CoPS₃ predicts a pressure-driven isostructural Mott transition accompanied by a spin crossover (Gu et al. 2021). x-ray diffraction and Raman scattering measurements reveal that CoPS₃ exhibits C2/m (LP) → P$\bar{3}$ (HP-I) structural transformation (Figure 2; Table 2) at 7 GPa and room temperature accompanied by the small drop (2.9%) of the volume per formula unit (Figure 4), (Matsuoka et al., 2023). This volume collapse and comparing FePS₃ and MnPS₃, it is concluded that CoPS₃ exhibits the spin crossover (S = 3/2 → 1/2) accompanied by metallization. On the other hand, the 2.9% of volume collapse is much smaller than that of FePS₃ (10.6%) and MnPS₃ (19.7%) (Figure 4), (Wang et al., 2016; Wang et al., 2018b; Haines et al., 2018; Matsuoka et al., 2023). The ionic radii of high-spin (S = 3/2, 0.89 Å) and low-spin (S = 1/2, 0.79 Å) Co²⁺ ions make the high-spin → low-spin radius reduction 11.2%, which is not much smaller than that of Mn²⁺ (S = 5/2: 0.97 Å, S = 1/2: 0.81 Å, 16.5%) and Fe²⁺ (S = 2: 0.92 Å, S = 0: 0.75 Å, 18.5%) (Shannon, 1976). Thus, the slight volume reduction of CoPS₃ cannot be explained solely by the difference between high-spin and low-spin radii. It is also noticeable that the volume per formula unit and c-axis in the $P\bar{3}$ phase show a steeper compression between 7 and 12 GPa followed by moderate compression above 12 GPa, indicating a sign of structural stabilization (Matsuoka et al., 2023). These series of changes in compression behavior suggest an electronic transition in the $P\bar{3}$ phase. Upon decompression at room temperature, the $P\bar{3}$ phase remains down to 2 GPa revealing a large hysteresis in the volume per formula unit and c-axis. Concomitantly with the structural transition, the electrical resistance decreases significantly and CoPS₃ becomes metallic (Matsuoka et al., 2023). The positive Hall resistivity reveals this metallic CoPS₃ is a hole-dominant conductor with multiple conduction bands, and its non-saturating behavior against the external magnetic field, indicating the absence of the anomalous Hall effect, suggests that the metallic CoPS₃ is not ferromagnetic (Figure 12). The linear magnetoresistance (Δρ_xy(B)/ρ_xx (B = 0), where Δρ_xx(B) = ρ_xx(B) − ρ_xx (B = 0)), along with the small volume collapse at the metallization, suggest the incomplete high-spin → low-spin transition in the metallic phase (Figure 12), (Matsuoka et al., 2023). It is expected that the metallic CoPS₃ possibly possesses an inhomogeneous magnetic moment distribution and short-range magnetic ordering (Matsuoka et al., 2023). Furthermore, the magnetoresistance changes from linear to more quadratic magnetic field dependent as pressure increases. Considering the suggested electronic transition from the volume per formula unit vs. pressure slope across 12 GPa (Figure 4), it can be thought that the spin crossover proceeds with pressure up to 12 GPa and stops or progress moderately above 12 GPa in the P$\bar{3}$ phase.

Figure 12

Figure 12. Transverse magnetotransport data from metallic CoPS₃. (A) The ρ_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 magnetoresistance. The dotted (black) and dashed (blue) lines in the top panel indicate the linear fit, y = Ax + C and quadratic fits y = Bx² to the data at 10 GPa and 1.8 K (Matsuoka et al., 2023). Reprinted (Figure 5) with permission from [Matsuoka, T., Rao, R., Susner, M. A., Conner, B. S., Zhang, D., and Mandrus, D., Pressure-induced insulator-to-metal transition in the van der Waals compound CoPS₃, 107, 165125 (2023)).] Copyright (2023) by the American Physical Society.

2.6 CdPS₃ and CdPSe₃

CdPS₃ crystallizes in the C2/m structure with the monoclinic angle β = 107.27°, possessing an insulating electrical character like other MPX₃ family members (Ouvrard et al., 1985a; Niu et al., 2022). The Raman scattering measurements combined with ab initio calculation reveal that CdPS₃ exhibits two structural transformations the LP-phase (C2/m) → HP-I phase (R$\bar{3}$) that initiates near 0.11 GPa and completes near 1.1 GPa. The HP-I (R$\bar{3}$) → HP-II (R$\bar{3}$) transition occurs from 7.35 GPa to 10.2 GPa. Niu et al. (2022) the C2/m → R$\bar{3}$ transition is obtained by sliding a single layer of the LP-phase along the b axis for a distance of about $b/6$ and simultaneously sliding it for approximately $a/3$ along the a axis. This results in the C2/m unit’s β angle changing from 107.27° to approximately 90° (Niu et al., 2022). The HP-I (R$\bar{3}$) to HP-II (R$\bar{3}$) transition is instead caused by the distortion of CdS₆ polyhedrons. The ab initio calculation suggests a small volume reduction (−2.05%) with the LP-I → HP-I transformation. On the other hand, the volume vs. pressure curves of HP-I and HP-II almost overlap across a wide pressure range (2–22 GPa), reflecting the transformation nature (Niu et al., 2022). The ab initio calculation also suggests the further transformation from HP-II to HP-III (P$\bar{3}$1m) at approximately 25 GPa. Compared with other MPS₃, it is noticeable that the LP-phase of CdPS₃ is relatively more sensitive to external pressure than other MPX₃ reported so far LP → HP-I at 0.11 GPa. This would suggest that even a slight strain can be an effective stimulus to drive the appearance of a new structural phase of CdPS₃. Finally, we note that the M = Cd system may prove a useful platform for exploring spin-orbit coupling, although it will require analogous measurements to be made on ZnPS₃ and ZnPSe₃ for comparison.

3 Summary and future prospects

Complex chalcogenides display properties and states of matter that are incredibly sensitive to external stimuli. This particular review is inspired by opportunities to employ pressure to unveil elusive states of matter and uncover charge-structure-function relationships. Compression is particularly well-suited to tuning the properties of chalcogenides because, in addition to changing bond lengths and angles, it provides deterministic control of the c/a structural ratio and the van der Waals gap. By controlling the environment around the metal center, compression also controls spin. As emphasized throughout this review, strain is likely to offer complementary advantages. At the same time, expanding the chemical phase space of the MPX₃ system to include solid solutions like (Zn,Cd)PS₃ or (Ni,Co)PS₃, heavy 4- and 5d-metal centers to enhance spin-orbit coupling, the CrPS₄ member of this family, and dual sublattice analogs such as bimetallic CuInP₂S₆ and AgInP₂S₆ provides exciting new platforms for exploring ferroelectricity, new types of photoinduced behavior, ionic motion, and even charge pumping under compression.

Author contributions

TM: Funding acquisition, Visualization, Writing–original draft, Writing–review and editing. H-SK: Visualization, Writing–original draft, Writing–review and editing, Funding acquisition. SS: Writing–original draft, Writing–review and editing. JM: Funding acquisition, Visualization, Writing–original draft, Writing–review and editing. DM: Funding acquisition, Visualization, Writing–original draft, Writing–reviewand editing.

Funding

The authors declare that financial support was received for the research, authorship, and/or publication of this article. TM is supported by the Air Force Office of Scientific Research under award number FA2386-23-1-4112, Dr. Emerlinda Roman Professorial Chair Grant awarded from University of the Philippines Foundation (2023–2024), and the NIP research contract (2023). HSK and SS are funded by the Korea Research Fellow (KRF) Program and the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education (Grant No. NRF-2019H1D3A1A01102984, 424 NRF-2020R1C1C1005900, and RS-2023-00220471). JLM is funded by Physical Behavior of Materials, Basic Energy Sciences, U.S. Department of Energy (Contract number DE-SC00023144). DGM is funded by the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant No. GBMF9069.

Acknowledgments

The authors thank our collaborators for valuable discussions: Dr. Nathan C. Harms, Dr. Amanda Haglund, Dr. Amanda J. Clune, Dr. Rui Xue, Dr. Kevin A. Smith, Dr. Kenneth R. O’Neal, and Dr. Maik Lang from The University of Tennesee Knoxville, Dr. Jesse S. Smith and Dr. Dongzhou Zhang from Argonne National Laboratory, Dr. Erxi Feng, Dr. Huibo Cao, and Dr. Antonio M. dos Santos from Oak Ridge National Laboratory, Dr. Rahul Rao, Dr. Michael A. Susner, and Dr. Benjamin S. Conner from Air Force Research Laboratory, Dr. Zhenxian Liu from The University of Illinois Chicago, Dr. Kristjan Haule and Dr. David Vanderbilt from Rutgers University.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

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