Piezochromism in the magnetic chalcogenide MnPS3

van der Waals materials are exceptionally responsive to external stimuli. Pressure-induced layer sliding, metallicity, and superconductivity are fascinating examples. Inspired by opportunities in this area, we combined high-pressure optical spectroscopies and first-principles calculations to reveal piezochromism in MnPS3. Dramatic color changes (green → yellow → red → black) take place as the charge gap shifts across the visible regime and into the near infrared, moving systematically toward closure at a rate of approximately −50 meV/GPa. This effect is quenched by the appearance of the insulator–metal transition. In addition to uncovering an intriguing and tunable functionality that is likely to appear in other complex chalcogenides, the discovery that piezochromism can be deterministically controlled at room temperature accelerates the development of technologies that take advantage of stress-activated modification of electronic structure.


INTRODUCTION
Chalcogenides are exceptionally sensitive to external stimuli. Tuning parameters like pressure and strain can alter the balance of energy scales and drive these materials into new areas of phase space where exotic properties can emerge [1][2][3][4] . Transition metal phosphorus trisulfides with chemical formula MPS 3 (M = Mn, Ni, Fe) display a number of intriguing properties under compression, including (i) insulator-metal transitions, (ii) sliding transitions, and (iii) superconductivity [5][6][7][8][9][10][11][12][13][14][15] . Another appealing aspect is pressureinduced color change [ Fig. 1]. While it is not uncommon for compression to modify electronic structure, it is unusual for the response to be controllable within the visible portion of the electromagnetic spectrum 16,17 . Pressure-induced color change in the complex magnetic chalcogenide MnPS 3 , shown in Fig. 1, can loosely be considered as a visible analog of piezoelectricity, although the mechanisms that underlie piezochromism in complex materials [18][19][20][21][22][23][24] -beyond donor-acceptor complexes, polymers, and molecular systems [25][26][27][28][29][30][31][32][33][34][35] -are highly underexplored 36 . Here, we use a combined spectroscopic and theoretical approach that builds upon recent transport, magnetic, and Xray properties work in the MPS 3 family of materials 5,[9][10][11] to reveal the electronic structure of MnPS 3 under compression, unraveling the microscopic origin of stress-activated color change, the connection of this effect to the stacking sequence, and the nature of chemical bonding in the high-pressure metallic state. At the same time, we unveil a functionality that is likely to emerge in other complex chalcogenides under pressure or strain control.

RESULTS AND DISCUSSION
Force-activated color change in MnPS 3 Figure 2a displays the optical response of MnPS 3 as a function of pressure. At ambient conditions, the absorbance increases rapidly above 2.64 eV, in reasonable agreement with prior determinations of the direct band gap [37][38][39][40] . As discussed in greater detail below, the absorption edge is comprised primarily of charge transfer excitations from the 3p valence band of sulfur to the localized 3d manganese bands [37][38][39][40] . The literature also reveals that the spectrum contains vibronically activated d-to-d on-site Mn 2+ excitations at 1.92, 2.40, and 2.64 eV [37][38][39][40] . These features are relatively weak in our data due to optical density effects. Thus, the color properties of MnPS 3 are primarily defined by the charge transfer excitations that determine the fundamental band gap. The absorption edge moves to lower energy with increasing pressure.
The band gap of MnPS 3 can be extracted from the optical response using Tauc plots as: where α(E) is the absorbance, E g,dir is the direct gap energy, E g,ind is the indirect gap energy, E ph is the mediating phonon energy, and both A and B are constants 41,42 . This model was originally developed for traditional semiconductors with simple single parabolic band structures. More recently, it has been extended to accommodate a variety of more complex materials 43 41,42 . We carried out this analysis for MnPS 3 and find a 2.64 eV direct gap at ambient conditions-in excellent agreement with prior work [37][38][39][40] . We also find that the direct band gap of MnPS 3 decreases systematically from 2.64 eV at ambient conditions to 2.15 eV at 11.5 GPa [ Fig. 2a, b]. In other words, it closes at the rate of -50 meV/GPa through the optical range. This trend is consistent with the images in Fig. 1. Figure 2c displays the band gap of MnPS 3 as a function of pressure. The gap traverses most of the visible range in a systematic manner. Hence, this complex chalcogenide is an agile and controllable piezochromic material with an operating range from bright green (at ambient conditions), to yellow-green (at 3 GPa), to ruby red (at 8 GPa), and to midnight black (above 20 GPa). These effects are reversible within our sensitivity. As it has a precisely controllable piezochromic response over a wide range of the visible and into the near infrared, MnPS 3 is a promising candidate for opto-electronics, spintronics, catalysis, and pressure sensor applications 6,[44][45][46] .
A simple linear extrapolation of the band gap vs. pressure trend reveals two interesting energy scales. First, the gap moves outside the visible range at 20 GPa, consistent with our photographic data [ Fig. 1]. Second, if the band gap were to continue closing at the same rate (−50 meV/GPa), we would anticipate full closure near 55 GPa-in reasonable agreement with theoretical predictions for the formation of metallic Mn dimers from the ambient pressure phase 11 . Of course, MnPS 3 probably undergoes a sliding transition that aligns the sulfur centers along the c-axis, similar to that in the Fe analog 10 . As discussed below, we expect that (i) the sliding transition raises the symmetry of MnPS 3 due to removal of monoclinicity by layer stacking and that (ii) the electronic structure of this phase collapses at much lower pressure. Consistently, our measurements reveal that the band gap drops very suddenly across the insulator-metal transition 9 , which we find to occur at 28.   Interplay between electronic and lattice effects under pressure In order to better understand the band gap trend and insulator-metal transition, we performed complementary infrared and Raman scattering spectroscopies of MnPS 3 under compression. These data allow us to examine and test the role of the lattice across the (i) sliding and (ii) insulator-metal transitions and, at the same time, (iii) reveal the development of metallicity 9-11 . We find two very different but highly inter-related effects. The sliding transition determines how, when, and why the band gap collapses by establishing the space group and interlayer stacking sequence from which the insulator-metal transition takes place.
We begin by examining the Raman scattering response of MnPS 3 under compression. Evidence for sliding is indirect because the localized phonon modes are nearly decoupled from layer sliding. In other words, the phonons are governed by intra-slab interactions rather than inter-slab proximity effects. As a result, traditional peak coalescence due to restoration of the three-fold axes of rotation 47 is replaced by subtle crossover features in the phonon spectra. These small but important frequency shifts occur between 8 and 10 GPa [ Fig. 3a], in agreement with our theoretical calculations that show how gradual layer sliding is made manifest in the Raman response. Full details are given in the Supplementary Materials. Interestingly, the band gap vs. pressure trend is relatively linear in this regime [ Fig. 2c]-an indication that the electronic properties of MnPS 3 are decoupled from the sliding transition as well. This is because the charge transfer excitations that define the gap are local (rather than long-range) in nature and therefore mostly unaffected by the relative positioning of the two-dimensional chalcogenide layers. Nonetheless, the sliding transition renormalizes the critical pressure for band gap closure as discussed below.
Next, we consider the spectroscopic properties of MnPS 3 across the insulator-metal transition 9 . It is important to realize that a true metal will sport free carriers and a Drude response (along with strongly screened phonons), a weak metal will show an overdamped response, and a semiconductor will reveal strong phonons riding on a low, flat electronic background. A pressuredriven insulator-to-metal transition ought, therefore, to unveil the development of a Drude response with well-screened phonons. The infrared response of MnPS 3 is displayed in Fig. 3b, c. At ambient pressure, the reflectance is low and flat, with a prominent P-S stretching mode near 580 cm −1 . The dashed black line guides the eye, omitting the well-known signature of the diamond anvils. These features are very consistent until the level starts to rise slightly near 26 GPa. A metallic Drude response that completely screens the aforementioned vibrational mode develops quite suddenly in our hands at 28.2 GPa. Figure 3c highlights the simultaneous disappearance of the infrared-active P-S stretching mode in the high-pressure phase, consistent with the development of metallicity. The full trend is shown in Supplementary Materials. Based upon these data, we can add several more points to the band gap vs. pressure plot in Fig. 2c. Two of the points have large asymmetric error bars denoting both the size and direction of the positional uncertainty. The asymmetry is because we can estimate only lower limits of the band gap at 23.8 GPa and 25.2 GPa. At the other two pressures (28.2 and 30.5 GPa), the band gap has collapsed to zero, so these values are precise.
We therefore see that there are two aspects to the story of force-induced color change in MnPS 3 . The first is piezochromism itself. The second is the series of underlying structural distortions that eventually trigger the insulator-metal transition. This is pertinent to the story of piezochromism because it is when the band gap plunges to zero across the insulator-metal transition that deterministic control of piezochromism ends. In other words, the insulator-metal transition defines the upper limit of control.
Expedited gap closure due to the sliding transition In order to clarify the role of the interlayer structure in determining the rate of band gap closure, we performed firstprinciples density functional theory (DFT) and dynamical meanfield theory (DMFT) calculations for three different structural models: (i) the monoclinic C2/m structure at ambient conditions with a staggered phosphorous-dimer arrangement across the layers [ Fig. 4a], (ii) the intermediate-pressure structure after the sliding transition with an aligned phosphorous-dimer configuration [ Fig. 4b], and (iii) the high-pressure structure, similar to the aligned P-dimer phase in terms of stacking but with an aligned phosphorous-chain structure across the layers [Fig. 4c]. The lattice was fully relaxed in each case to minimize energy with the given structural (symmetry and volume) constraints. An enthalpy comparison from DFT + U calculations reveals that the aligned phosphorous-dimer structure is almost as stable as the staggered P-dimer structure even at ambient conditions. It becomes the ground state above ≈10 GPa (see Supplementary Materials). We expect the sliding transition to occur across a fairly broad pressure range as evidenced by the gradual change in the Raman spectra of MnPS 3 as well as the X-ray diffraction in FePS 3 10 , but for simplicity we chose the staggered and aligned phosphorousdimer and chain structures as extremal cases for this analysis.
In the ambient to small pressure range, most of the charge excitations take place within individual MnPS 3 layers. The absence of any sudden change in the optical band gap as a function of pressure below 20 GPa is thus attributed to the local nature of the charge transfer. As pressure is enhanced, the interlayer distance decreases and the system starts to recognize the two different layer stackings. Because of the one-dimensional (dimerized) chainlike structure of phosphorous along the layer-normal direction in the aligned P-dimer structure [ Fig. 4b], the band gap is more susceptible to pressure compared to that deriving from a staggered phosphorous-dimer structure. Eventually, collapse of the Mott-character (i.e., disappearance of the imaginary selfenergy peak at zero energy) in the aligned P-dimer structure occurs near 45 GPa. It is accompanied by a sudden reduction of the c-axis spacing and an abrupt jump in the phosphorous-dimer distance, which induces the one-dimensional chain-like character of phosphorous centers along the layer-normal direction [ Fig. 4c]. Figure 4d, e show the spectral functions A(k, ω) and projected density of states A(ω) for the aligned phosphorous-dimer state at 40.3 GPa and aligned phosphorous-chain state at 45.6 GPa, respectively. While the aligned P-dimer phase maintains Mottinsulating character [ Fig. 4d], robust metallicity is observed in the aligned P-chain structure [Fig. 4e]. The appearance of dispersive band character along the layer-normal direction (Γ-Z line) near the Fermi level in Fig. 4d is another feature signaling the transition from a quasi-two-dimensional Mott insulating to threedimensional metallic phase in the aligned phosphorous-chain structure of MnPS 3 .
The symmetry lowering across the insulator-metal transition deserves additional comment. Our calculations reveal that the phosphorous-dimer-to-chain transition (P31m to C2/m) takes place with a spin-state transition and Mott-type metallization. The collapse of the high-spin (S = 5/2) character leads to partial occupancy of the Mn t 2g orbital, which breaks the three-fold symmetry in each MnPS 3 layer due to the tendency towards Mn-Mn covalency (see Supplementary Materials for further information). This physical picture is different than in FePS 3 10 . Here, the high-pressure metallic phase has a d 6 (Fe 2+ ) low-spin configuration and, as a consequence, prefers restoration of the three-fold symmetry.
The precise value of the charge gap, as well as the type of structural distortion, that is predicted to take place across the insulator-metal transition is highly sensitive to our choice of starting structure as shown by the evolution of charge gaps of the two different stacking sequences as a function of pressure [ Fig. 4f]. Use of an aligned rather than staggered phosphorous-dimer structure reduces the critical pressure from 64 GPa 11 to~45 GPa. In view of the small energy differences between phases, we believe we are justified in identifying this with the insulator-metal transition. In addition to being much closer to the experimental value of the critical pressure, this model takes layer sliding into account 10 . As the pressure-induced Mott transition occurs simultaneously with an abrupt separation of phosphorous dimers and restoration of the phosphorous-chain structure normal to the Mn layers in the aligned phosphorous-dimer structure, it is clear that layer stacking order and interlayer overlap between phosphorous centers are playing a crucial role in MnPS 3 under compression. Thus, we find a clear distinction between conventional layered transition metal chalcogenides and phosphorus trisulfides, which surely deserves further investigation.
Lastly, we comment on the difference between the measured optical gap and calculated electronic gap [Figs 2b and 4f]. The measured optical gap is larger than the calculated electronic gap by ≈0.6 eV at ambient pressure. On the other hand, the simulated optical conductivity σ 1 (ω) from the same DMFT calculations [ Fig.  4g] reveals an optical gap of ≈3 eV. Despite the slightly larger value of the calculated optical gap compared to the experimentally estimated gap, the rate of gap closure vs. pressure is~0.5 eV per 10 GPa, in very good agreement with our measurements. Unlike the electronic gap, the optical gap is mostly unaffected by layer sliding. Likewise, the calculated optical conductivities of the SPD and APD structures are relatively insensitive to layer sliding. Analysis of the spectral functions reveals that the optical gap originates primarily from transitions between d-p-hybridized states at Mn sites within the same MnPS 3 plane, whereas the electronic gap is determined by the sulfur p-bands, which become dispersive under pressure because of the inter-plane overlap between sulfur p-orbitals located in adjacent layers. This difference between the electronic and optical gaps along with the insensitivity of optical gap to structural change emanates from the quasi-two-dimensional character of MnPS 3 -perhaps opening the door to independent control via pressure and/or epitaxial strain.

Structure-property relations in piezochromic materials
In order to better articulate strategies for the development of piezochromism, we compare the overall pressure scale for forceactivated color change in MnPS 3 with that in related materials. It is well-known that chalcogenides are relatively soft and sport large volume collapses under pressure 48 . These and other van der Waals materials are therefore reasonable platforms to search for piezochromic effects. The nature and size of the band gap is also important. It should not be too low or too high. 2H-MoS 2 , for instance, has a 1.2 eV indirect band gap that is in the near infrared region even before compression, and it closes near 50 GPa 49,50 . As another example, the layered semiconductor CrSiTe 3 displays a 0.4 eV indirect gap and a 1.2 eV direct gap 51 , so it will suffer from a similar lack of dynamic range. Turning to the lead halide perovskites, systems like CH 3 NH 3 PbI 3 are known to sport highly tunable electronic structures. The size of the gap at ambient conditions is on the order of 1.6 eV, which is below the visible range, and it closes in a non-linear manner-resulting in a challenge for property control 52 . The Pb-free halide double perovskites, on the other hand, exhibit band gaps in the visible range and are therefore more promising piezochromics 53 . Compression also closes the 2.7 eV optical gap in BiFeO 3 at a rate of −12.2 meV/GPa-with eventual metallization 54,55 . As 2 S 3 is another good example, with a 2.7 eV gap that closes rapidly 56 . What makes MnPS 3 particularly attractive is that it has a direct band gap in the visible range 57,58 . With a −50 meV/GPa shift of the gap under compression, the Mn compound is both agile and linearly responsive-until metallicity develops at 28.2 GPa. Similar work on the Ni and Fe analogs will allow the development of structure-property relations. Finally, we point out that the majority of currently known piezochromics are donor-acceptor complexes, polymers, molecular systems, and liquid crystals [25][26][27][28][29][30][31][32][33][34][35][36] . The development of this functionality in chalcogenides is therefore significant and potentially useful.
We combined diamond anvil cell techniques, optical spectroscopies, and first-principles electronic structure calculations to reveal piezochromism in the transition metal phosphorus trisulfide MnPS 3 . Under compression, the charge gap red-shifts across the visible and into the near infrared at a rate of −50 meV/GPa, plunging to zero at the insulator-metal transition-the upper limit of control. The mechanism at 28.2 GPa therefore appears to proceed as a structural distortion that triggers (i) metalization and (ii) the low-spin-state. In addition to accelerating the discovery and fundamental understanding of stress-activated color changes in complex van der Waals materials, this striking effect is reversible and occurs at room temperature, which may pave the way for interesting applications, including opto-electronics, sensors, and low power memory devices 6,[44][45][46] . Coverage of the full visible range and boosting sensitivity while maintaining linearity of control will advance these goals.

METHODS
Crystal growth and loading the diamond anvil cell MnPS 3 single crystals were prepared by chemical vapor transport techniques as described previously 59 . Polycrystalline material was loaded into a symmetric diamond anvil cell along with an annealed ruby ball. Care was taken to optimize the optical density in order to reveal the excitations of interest. KBr or vacuum grease were used as pressure mediums depending on the measurement. This assured a quasi-hydrostatic environment for the sample. Fluorescence from the ruby ball was used to determine pressure 60 . Various diamond anvil cells, each equipped with different sized diamond culets, were employed depending upon the needed pressure range and whether low fluorescence or Type II diamonds were required for Raman scattering or infrared spectroscopy, respectively.

Spectroscopic measurements
Optical measurements were performed using a Perkin Elmer Lambda-900 grating spectrometer between 1 and 6 eV with 3 nm resolution. Absorbance was calculated as αðEÞ ¼ Àln ðT ðEÞÞ, where T ðEÞ is the measured transmittance. The diamond anvil cell was carefully positioned in the beam, and pressure was increased systematically. Compression was reversible within our sensitivity. We complemented the optical properties work with both synchrotron based infrared spectroscopy (50-8000 cm −1 ; 2 or 4 cm −1 resolution; both transmittance and reflectance geometries) and Raman scattering (λ excit = 532 nm; ≈1 mW power; 30 s integration, averaged three times) under pressure. These experiments were performed using the 22-IR-1 beamline at the National Synchrotron Light Source II at Brookhaven National Laboratory. All data were collected at room temperature.

First-principles calculations
We employed state-of-the-art embedded dynamical mean-field theory (eDMFT) combined with density functional theory (DFT), which implements forces on atoms and allows relaxation of internal atomic coordinates 61 . For the optimization of the unit cell size and shape, we performed density functional theory calculations augmented by the on-site Coulomb repulsion U (DFT + U) 62 . The Vienna ab-initio Simulation Package (Vasp) N.C. Harms et al. was employed for the DFT + U calculations to optimize the cell shape and lattice parameters 63,64 , after which eDMFT optimizations of internal atomic coordinates were performed 11,61 . A continuous-time quantum Monte Carlo method in the hybridization-expansion limit was used to solve the auxiliary quantum impurity problem 65 , where the full 5 d-orbitals of Mn 2+ were chosen as our correlated subspace in a single-site DMFT approximation. Additional computational details are available in the Supplementary Materials and in ref. 11 .

DATA AVAILABILITY
The data sets generated and/or analyzed during the present study are available from the corresponding author on reasonable request.

CODE AVAILABILITY
The