Mode‐Selective Spin–Phonon Coupling in van der Waals Antiferromagnets

2D magnetic materials offer the opportunity to study and manipulate emergent collective excitations. Among these, spin–phonon coupling is one of the most important interactions correlating charge, spin and lattice vibrations. Understanding and controlling this coupling is important for spintronics applications, control of magnons and phonon by THz radiation, and for strain‐driven magnetoelastic applications. Here, a resonant mode‐selective spin–phonon coupling in several magnetic 2D metal thiophosphates (NiPS3, FePS3, CoPS3 and MnPS3) through multi‐excitation and temperature‐dependent Raman scattering measurements is uncovered. The phonon mode, which is a Raman‐active out‐of‐plane vibrational mode (∼250 cm−1 or 7.5 THz), exhibits an asymmetric Fano lineshape where its asymmetry is proportional to the spin–phonon coupling. The measurements reveal the coupling to be the highest in NiPS3, followed by FePS3 and CoPS3, and least in MnPS3. These differences are attributed to the metal–sulfur interatomic distances, which are the lowest in NiPS3, followed by CoPS3, FePS3 and MnPS3. Finally, the spin–phonon coupling is also observed in exfoliated materials, with a slight reduction between 20 and 30% in the thinnest flakes compared to the bulk crystals.


Introduction
3][4] Especially exciting are the observations that the magnetic properties may persist down to the mono-or few-layer limit in many of DOI: 10.1002/apxr.202300153 the materials. [5]This could enable new functionalities through the integration of new device architectures by artificially stacking magnetic 2D materials into heterostructures. [6]Advances in 2D magnetic materials can thus lead to atomically thin magneto-optic and magnetoelectric devices for ultracompact spintronics devices such as spin valves, spin field-effect transistors, and magnetic tunnel junctions, as well as on-chip optical communications and quantum computing applications. [4,5,7]mong the several new 2D magnetic materials recently discovered the metal thio-and seleno-phosphate family (or ternary metal phosphorus chalcogenides with the general formula MPX 3 , where M = Ni, Fe, Co, Mn, V, and Cr; X = S, Se) are highly promising candidates for 2D magnetics applications.[15][16][17][18] These phenomena underpin the physics of emergent and future devices based on the MPX 3 materials, making it important to understand and control them. [19]hus far, magnon-phonon coupling in MPX 3 compounds has been observed both in the presence and absence of externally applied magnetic fields; this coupling typically occurs below T N where the spins are locked in.Below T N , the magnons have been observed to interact with Raman and infrared-active phonons with frequencies between 100 and 600 cm −1 (or ∼3-18 THz).These coupling and hybridization effects have been observed through Raman and infrared spectroscopy, [13][14][15]20] as well as THz pump-probe spectroscopy. [18]Temperature-dependent Raman spectroscopy measurements in particular have revealed insights into spin-phonon coupling in FePS 3 , FePSe 3 , NiPS 3 and MnPSe 3 through large changes in peak intensities, frequencies and widths upon cooling the material below T N .[21][22][23][24] Intriguingly, recent reports of THz frequency mode-selective spinphonon coupling [19,25] in FePS 3 and NiPS 3 highlight the possibility of generating coherent phonons coupled to magnetic spins in these materials.While magnons exist in the AFM state in the MPX 3 compounds, there are also observations of spin-lattice coupling in the room temperature paramagnetic state, [25][26][27] emphasizing the complex interplay between lattice vibrational modes and spins in materials with different spin orders. Lasty, we note that in addition to the MPX 3 compounds, spin-phonon coupling has also been observed recently through Raman spectroscopy measurements in other 2D magnetic materials such as Cr 2 Ge 2 Te 6 , CrBr 3 , and CrSBr.[28] Here, we study bulk and exfoliated crystals of several magnetic MPS 3 compounds with different spin orders (NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 ), as well as two nonmagnetic compounds (CdPS 3 and ZnPS 3 ).We use resonance and non-resonance excitation energies to collect and analyze Raman spectra across a range of temperatures above and below T N .Our studies uncover coupling between spins and an out-of-plane phonon mode around 250 cm −1 (≈7.5 THz) in the magnetic MPS 3 compounds.In the paramagnetic state above T N, the spin-phonon coupling is manifested through peak asymmetry due to Fano resonance as well as quasielastic scattering due to spin density fluctuations.Below T N , the coupling results in significantly enhanced peak intensities as well as redshifted frequencies.We find the spin-phonon coupling to be the highest for NiPS 3 , followed by CoPS 3 and FePS 3 , and the least in MnPS 3 .The differences among the magnetic MPS 3 compounds are attributed to structural dissimilarities; in particular, to the distances between the metal and sulfur atoms, which are the least in NiPS 3 and highest in MnPS 3 . Our reslts reveal a universal trend, and suggest the potential for structural strain, i.e., chemical or mechanical pressure, to tune the spinphonon coupling in the layered MPS 3 materials.

Results
The MPS 3 compounds are isostructural layered materials wherein the metal ions and phosphorus doublets are arranged in a honeycomb lattice, all enclosed in octahedra formed by sulfur atoms (the structure can also be thought of as M 2 P 2 S 6 , where each [P 2 S 6 ] 4− unit contains two metal M 2+ ions).The magnetic spin order in the AFM state below T N in each of the MPS 3 compounds is different (shown schematically in Figure 1a), with spins coupled ferromagnetically between two of the three nearest neighbors within a layer in NiPS 3 and CoPS 3, forming ferromagnetic linear chains.These chains are coupled ferromagneti-cally between layers.The in-plane spin arrangement in FePS 3 is similar to that of NiPS 3 and CoPS 3 except the spins are aligned out-of-plane.The linear ferromagnetic chains in FePS 3 are antiferromagnetically coupled between layers.This arrangement forms a magnetic superstructure, doubling the magnetic primitive cell and results in the appearance of several new peaks in its low-temperature Raman spectrum due to zone folding. [29]The spins in MnPS 3 are also aligned out-of-plane and canted; however, the spins alternate up or down between the Mn atoms in the hexagonal lattice and are coupled ferromagnetically between layers.The spin structures lead to differing types of AFM behavior in the three materials, with Ising-type magnetism in FePS 3 , Heisenberg-type in MnPS 3 and zigzag-type antiferromagnetism in NiPS 3 and CoPS 3 . [30,31]Recent studies have reported that the magnetic behavior survives down to the monolayer in FePS 3 [32]   and CoPS 3 , [33] and down to the bilayer in NiPS 3 [27] and MnPS 3 . [34]he Néel temperatures of these materials vary, with T N ≈ 155, 123, 118 and 70 K for bulk NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 , respectively. [30]npolarized room temperature multi-excitation Raman spectra (collected using 1.58, 1.96, 2.41 and 2.54 eV laser excitations) from the bulk single crystals of NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 are shown in Figure 1b-e, respectively.In addition to the magnetic materials, we also include Raman spectra from two nonmagnetic MPS 3 compounds, ZnPS 3 and CdPS 3 (Figure 1f,g) where Zn 2+ and Cd 2+ represent closed-shell systems.The Raman spectra from the MPS 3 compounds exhibit several vibrational modes that are, in general, common to all 2D metal thiophosphates.37][38][39] Interestingly, in all of the spectra from the AFM MPS 3 compounds, we observe a clear excitation energy-dependent intensity for one peak in particular; its frequency is around 250 cm −1 (indicated by the black arrows in Figure 1b-e).The frequency of this peak varies slightly depending on the material, and is ≈254, 247, 244 and 245 cm −1 (or between 7.3 and 7.6 THz) at room temperature for NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 , respectively.Hereafter, we refer to this peak as the 250 cm −1 Raman mode for simplicity.Its excitation energy-dependent intensity is the strongest for NiPS 3 , with the maximum intensity for 1.96 eV (633 nm) excitation and minimum (almost negligible) for 2.54 eV (488 nm) excitation.On the other hand, for the non-magnetic MPS 3 compounds (CdPS 3 and ZnPS 3 ), we don't see a strong excitation energy-dependence for any of the Raman peaks.The 250 cm −1 mode is attributed to out-of-plane (A g ) vibrations of the S and P atoms in the S-bounded octahedra, as revealed by polarized Raman measurements (Figure S1, Supporting Information).The atomic displacements of this phonon mode are shown in the schematic in the inset of Figure 1h.Interestingly, while the 250 cm −1 mode is highly polarized in NiPS 3 , CoPS 3 and FePS 3 , it is depolarized in MnPS 3 , ZnPS 3 and CdPS 3 (Figures S1 and S2, Supporting Information).
To depict the excitation energy-dependent intensities more clearly, we plot the ratio of intensities of the 250 to the 380 cm −1 mode (PS 3 stretching mode) in Figure 1h.For a given material, the intensity of the PS 3 stretching mode does not vary significantly between laser excitations, thus justifying our choice of using this peak intensity for normalizing the intensities of the 250 cm −1 modes.The normalized intensities in Figure 1h show a clear excitation energy dependence, especially for the magnetic MPS 3 compounds.The intensity of the 250 cm −1 mode is the highest for 1.96 eV (633 nm) excitation for NiPS 3 , and CoPS 3 , for 1.58 eV (785 nm) excitation in the case of FePS 3 and in MnPS 3 the intensity is the highest for 2.54 eV excitation energy.For the non-magnetic CdPS 3 and ZnPS 3 , the 250 cm −1 mode intensity is mostly independent of laser excitation energy within our measured range.
This dependence of the 250 cm −1 mode intensity on the excitation energy suggests a resonance enhancement effect, which has been observed previously for FePS 3 and MnPS 3 . [40]Furthermore, considering that, among all the M elements, Fe, Ni, Co and Mn have unfilled d orbitals while Cd and Zn have fully filled d orbitals, our observation also suggests a strong link between the excitation energy and d orbital transitions in these cations.Reflectance curves collected from the bulk crystals and Tauc plot analysis (Figures S3 and S4, Supporting Information) reveals optical bandgaps for NiPS 3 , FePS 3 , CoPS 3 , MnPS 3 , CdPS 3 and ZnPS 3 to be 2.02, 1.45, 1.96, 2.92, 3.06, and 2.95 eV, respectively.[43] The close match of the excitation energy providing the highest intensity for the 250 cm −1 peak (Figure 1h) and the bandgap energies strongly suggests resonance enhancement due to an electronic transition in these compounds.We note that in the case of MnPS 3 , our highest excitation energy (2.54 eV) is lower than its bandgap (2.9 eV).However, the intensity of the 250 cm −1 mode in MnPS 3 progressively increases with excitation energy and is the highest for 2.54 eV, corresponding to the weaker transition we observed.Since MnPS 3 has a stronger transition at 2.92, we hypothesize that the intensity of the 250 cm −1 mode would continue to increase with higher excitation energies.We also note that in the cases of CdPS 3 and ZnPS 3 , our highest excitation energy (2.54 eV) is lower than their observed transitions (2.95 and 3.06 eV, respectively).For these materials, the 250 cm −1 intensity does not depend strongly on the excitation energy.
The resonance enhancement of the 250 cm −1 mode intensity only in the magnetic materials also suggests a correlation between the phonon mode and the magnetic/spin structures associated with the unfilled d orbitals.Indeed, a closer look at the 250 cm −1 mode in these compounds reveals an asymmetric lineshape, as can be seen in the spectra in Figure 2a.This asymmetry occurs due to quantum interference between a discrete excitation (in this case the phonon mode) and an electronic continuum and is called the Fano resonance. [44]Figure 2a shows that the Fano resonance due to electron-phonon coupling is the highest in NiPS 3 and that the peak asymmetry decreases significantly for the nonmagnetic CdPS 3 and ZnPS 3 .Fano resonances in NiPS 3 have been observed previously for two phonon modes ˜175 and 560 cm −1 , and attributed to electron-phonon and magnon-phonon coupling, respectively. [25,27]Interestingly, the Fano resonance in the 560 cm −1 becomes stronger upon cooling below T N , whereas the resonance in the 175 cm −1 mode only appears in the high temperature paramagnetic state.Based on the prior observations and the results presented in Figures 1h and 2a, we contend that the Fano resonances in the 250 cm −1 modes in the magnetic MPS 3 compounds occur due to coupling between the out-of-plane vibrational mode and spins associated with the unfilled d electron continua of the magnetic metal ions (Ni 2+ , Fe 2+ , Co 2+ and Mn 2+ ).
The temperature-dependence of the 250 cm −1 mode provides a clearer picture into the spin-phonon coupling.First, we fit the asymmetric Raman peaks to the well-known Breit-Wigner- , where  0 , Γ, and q are the phonon mode frequency, peak width and asymmetry parameter, respectively. [44]The reciprocal of this last term, 1/q is the Fano parameter, which represents the degree of asymmetry and thus the strength of the spin-phonon coupling.When 1/q is equal to zero, the peak becomes symmetric with a Lorentizian lineshape.We note that in our case the 250 cm −1 phonon modes have asymmetric tails on their high frequency sides, making 1/q positive, resulting from destructive interference of phonon mode with the d electron continuum of the metal ions.Figure 2b shows the temperature dependence of the the Fano parameters (we plot the absolute values 1/|q| in Figure 2b), which exhibit a clear decrease on cooling and a discontinuity around T N .We see this trend for NiPS 3 , CoPS 3 and FePS 3 and the decrease in the Fano parameter (electron-phonon coupling) across the AFM transition temperature indicates a significant effect of spin ordering on the 250 cm −1 phonon mode.47] Upon excitation with the Raman laser, the crystal field splitting results in optically excited, Raman-allowed intraband transitions among the d electron states in the conduction band, and the interference between the 250 cm −1 phonon mode and these transitions is responsible for the asymmetric Fano peak lineshape.With a decrease in temperature comes a reduction in the population of excited states, lowering the number of Raman-allowed transitions.This leads to a decrease in the quantum interference between the d electron continuum and the 250 cm −1 phonon mode.Below the transition temperature, the Fano parameters level off due to spin ordering.Such a decrease in the Fano parameter across a magnetic transition temperature has been seen previously in NiPS 3 [25,27] and further experimental and thoeretical studies may help understand the temperature-dependent quantum interference effects for the 250 cm −1 and other vibrational modes in the magnetic MPS 3 compounds.
Secondly, we analyze the temperature-dependent 250 cm −1 peak frequencies and intensities, and show them in Figure 3.One of the signatures of spin-phonon coupling is the observation of discontinuities in peak frequencies and intensities across T N . [48]ndeed, we observe these discontinuities in the 250 cm −1 peak frequencies for NiPS 3 , FePS 3, CoPS 3 and MnPS 3 (Figure 3a), which exhibit a notable deviation from the expected anharmonic temperature dependence (shown by the black curves in Figure 3a) and redshift to varying degrees at temperatures below T N .On the other hand, their intensities increase sharply upon cooling below T N (Figure 3b).The sharp increase in peak intensity has been observed previously for NiPS 3 and FePS 3 [23,49] and is attributed to an increase in the spin-dependent contribution to the Raman intensity, as predicted by Suzuki and Kamimura, [50] and discussed in greater detail later on.The increase in intenity is the highest for NiPS 3 and lowest for MnPS 3 (Figure S5, Supporting Information), suggesting that the spin-phonon coupling is the highest in NiPS 3 for the 250 cm −1 mode.This trend is similar to that of the Fano resonance, which is the highest in NiPS 3 and least in MnPS 3 , indicating that the spin-phonon coupling below T N and the electron-phonon coupling (Fano resonance) at room temperature share a common origin.Further evidence for the effect of the d electron continua in the AFM MPS 3 compounds on the Raman spectra comes from the measurement of quasi-elastic scattering (QES), which is characterized by a broadened central peak (≈0 cm −1 ) with a Lorentzian or Gaussian lineshape.In magnetic systems, QES occurs due to fluctuations of the energy density of the spins and is observable in the orbitally disordered paramagnetic state at temperatures well above T N . [51]Its intensity decreases with temperature due to a gradual ordering of spins upon cooling, and eventually resulting in a minimum in the AFM spin-ordered phase below T N .Figures 4a-c show the room temprature QES peak in our materials, obtained with unpolarized 1.58, 1.96 and 2.41 eV excitations, respectively.In order to plot the QES peak, we use the reduced Raman intensity (), which is obtained by normalizing the experimentally measured spectral intensity by [n(, T)+1], where n(, T) is the Bose thermal factor [1 − exp(− ℏ k B T )] −1 . [27,29]The increasing background intensities below 100 cm −1 are clearly visible on both the Stokes and anti-Stokes sides of the Raman spectra in Figure 4a-c.The QES peak intensity is also higher for NiPS 3 , FePS 3 and CoPS 3 compared to the rest of the materials.To quantify the differences between the QES areas for each material and to see their dependence on the laser excitation energy, we calculate the areas of the QES peaks (integrated intensity between −100 and 100 cm −1 ) for all the spectra and plot them in Figure 4d.Remarkably, the excitation energy-dependent trends for the QES areas follow the excitation energy-dependent intensities of the 250 cm −1 mode (Figure 1h) very closely.In general, the QES areas are the highest for NiPS 3 among all these compounds.The QES areas are also the highest for 1.96 eV excitation for NiPS 3 and CoPS 3 , 1.58 eV for FePS 3 and highest for 2.54 eV in the case of MnPS 3 .For both the non-magnetic materials, the QES area does not exhibit a strong excitation energy dependence.Thus, for the magnetic MPS 3 compounds, the intensities of the 250 cm −1 phonon mode and the QES areas are maximized for a particular excitation energy -1.96 eV for NiPS 3 and CoPS 3 , 1.58 eV for FePS 3 , and 2.54 eV for MnPS 3 .The temperature-dependence of the QES areas for the magnetic MPS 3 compounds also follows a similar trend as that of the Fano parameters -a general decrease upon cooling with a sharp downturn around T N (Figure S6, Supporting Information) due to spin ordering.We observe this for all of the magnetic MPS 3 compounds and our trends are similar to previously published results in NiPS 3 and FePS 3 . [26,27,29]Taken together the trends in temperature-dependent Fano parameters, peak intensities, and QES areas (Figure 1h, Figure S5, Supporting Information, and Figure 4d, respectively) suggest a strong correlation between the 250 cm −1 phonon mode and spin density fluctuations.Thus, the resonantly enhanced 250 cm −1 mode couples to the orbitally disordered and fluctuating d electron spins of the metal ions in the magnetic MPS 3 compounds in the paramagnetic at room temperature, and this spin-phonon coupling increases strongly below T N with the ordering of AFM spins.
Finally, we examine these effects as a function of layer thickness in the MPS 3 compounds.Mechanically exfoliated crystals (onto Pt-coated Si/SiO 2 substrates) exhibit the same excitation energy-dependence for the 250 cm −1 mode as observed in the bulk crystals (Figure S7, Supporting Information shows multiexcitation Raman spectra from 9 and 16 nm thick NiPS 3 ).Moreover, the peaks retain the Fano lineshapes in the exfoliated flakes; the Fano parameters for NiPS 3 , FePS 3 and CoPS 3 are shown as a function of flake thickness in Figure 5. Considering the error bars, the parameters do not exhibit a strong trend with thickness, although there might be a minor decrease between 20 and 30% in peak asymmetry with thickness.This would indicate a reduction of electron-phonon coupling with thickness, which has been previously observed in NiPS 3 for the high-frequency stretching mode ∼560 cm −1 . [27]Nonetheless, the data in Figure 5 indicate that, overall, the electron-phonon coupling and arguably, spinphonon coupling, could be present in the ultrathin limit.

Discussion
The mechanism of the mode-selective spin-dependent Raman scattering in the MPS 3 compounds is based on the model that was first described by Suzuki and Kamimura [50] and is shown schematically in Figure 6a.The scattering process takes place according to the following steps: 1) a d electron in the magnetic M ion at the i-site (M i ) is excited to the conduction band upon absorption of an incident photon; 2) a d electron from the nearest- neighbor ion at the j-site (M j ) transfers to the i-site via the intermediate non-magnetic [P 2 S 6 ] 4− cluster, resulting in the generation of a phonon; 3) the virtually excited d-electron in the conduction band recombines with the magnetic ion at the j-site, and the system returns to the ground state with the emission of the scattered photon.The use of resonance excitation in the case of NiPS 3 , CoPS 3 and FePS 3 results in a real excitation of the electron in the M i atom to the conduction band.The orbital splitting and overlap between the metal 3d and sulfur 3p orbitals also leads to the effective transfer of the d-electrons between the nearest neighbor ions, resulting in the observed increases (decreases) in peak intensities (frequencies) below T N (Figure 3).This scattering mechanism is also valid for the known MPSe 3 compounds, although further studies are needed to see whether there is any mode-selective spin-phonon coupling in the selenides.
Next, to show the variations in the degree of spin-phonon coupling among the MPS 3 compounds, we plot the Fano parameters (1/|q|, left axis) and QES areas (right axis) for all of our materials in Figure 6b (bottom).Here we plot the maximum QES areas, which correspond to the 1.58 eV excitation for FePS 3 , 1.96 eV for NiPS 3 and CoPS 3 , and 2.41 eV for MnPS 3 .While there are subtle differences between the two datasets presented in 6b, overall, the correspondence between the Fano parameters, QES areas, and the enhanced peak intensities below T N (Figure S5, Supporting Information), shows that the mode-selective spin-phonon coupling is the highest for NiPS 3 followed by CoPS 3 , FePS 3 and MnPS 3 .The corresponding values for the non-magnetic ZnPS 3 and CdPS 3 are two to three orders of magnitude lower than the parameter for NiPS 3 .
We attribute the differences in the spin-phonon coupling among these four magnetic materials to the dissimilarities in their crystal structures, in particular to their M-S interatomic distances.For a given MPS 3 compound, the S 6 octahedra are slightly distorted, resulting in unequal M-S interatomic distances.In Figure 6b (top) we also show the average M-S distances for the MPS 3 compounds (values taken from previously published reports; refs.[21, 52-60] with the error bars accounting for the spread in values.Figure 6b shows that the M-S distance is the least in NiPS 3 (2.501Å), followed by CoPS 3 (2.51Å), FePS 3 (2.544Å) and MnPS 3 (2.597Å).The M-S distance is the highest for CdPS 3 (2.668Å).The trend in the M-S distances is directly related to the metal cation radius, with Ni 2+ being the smallest and Mn 2+ the largest among the magnetic cations (Figure S8a, Supporting Information), and consequently these distances also lead to concomitant trends in sizes of the corresponding unit cells (Figure S8b, Supporting Information).The closer proximity of the smaller Ni 2+ ion to its surrounding S atoms thus enables the most efficient Raman scattering process as described above, and results in the highest spin-phonon coupling in NiPS 3 .Conversely, the larger Mn-S distance reduces the spin-phonon coupling in MnPS 3 , with CoPS 3 and FePS 3 falling in between the Ni and Mn-based materials.The variations in the M-S distances and unit cell sizes could also account for the high degree of polarization for the 250 cm −1 mode observed in NiPS 3 , CoPS 3 and FePS 3 compared to the rest of the compounds (Figure S2, Supporting Information).Overall, the results presented in Figure 6 highlight the potential for manipulating the MPS 3 unit cells, thereby tuning the spin-phonon coupling through the application of external strain or pressure, or through chemical doping/in-plane heterostructure formation. [61,62]

Conclusions
Through multi-excitation and temperature-dependent Raman spectroscopy measurements on magnetic (NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 ) and non-magnetic (CdPS 3 , ZnPS 3 ) MPS 3 compounds, we have uncovered spin-phonon coupling for an outof-plane (A g symmetry) vibrational mode that occurs ˜250 cm −1 (7.5 THz).A number of conclusions can be drawn from our experimental results - Our observations of mode-selective spin-phonon coupling in the magnetic MPS 3 compounds show the promise for future quantum applications based on field-dependent coherent phonon generation and control, as well as the potential for tuning the spin-phonon coupling through doping and strain.

Experimental Section
Crystal Synthesis: The MPS 3 compounds (M = Mn, Fe, Co, Ni, Zn, Cd) were synthesized via conventional vapor transport methods. [9]Briefly, M foil (Alfa Aesar Puratronic, 99.999%) or powder M foil (Alfa Aesar Puratronic, 99.999%, reduced in H 2 ), P chunks (Alfa Aesar Puratronic, 99.999+%), and S pieces (Alfa Aesar Puratronic, 99.999%) were combined together in a near-stoichiometric ratio (10% excess P was used) in an evacuated quartz ampoule (2 mm wall thickness, 22 mm OD, 10 cm in length) together with ≈100 mg I 2 crystals (Alfa Aesar, 99.8%).The sealed ampoule in a single-zone furnace was placed, heated to 700-750 °C (depending on the material, ref. [9]) over a period of 20 h, held at that temperature for 100 h, and cooled over a period of 20 h.The resulting crystals were maximum 5 mm x 5 mm in area and ≈200 μm in thickness.Sample compositions were determined by subjecting at least three distinct single-crystal specimens of each batch to multiple-spot scanning electron microscopy/energy-dispersive X-ray spectroscopy (SEM/EDS) analysis (9−12 spots total per batch) using a Thermo Scientific UltraDry EDS spectrometer joined with a JEOL JSM-6060 SEM.The compositions were stoichiometric, within error.
Reflectance Measurements: Reflectance spectra (between 200 and 1100 nm) were collected with a Craic microspectrophotometer.Measurements were performed by placing bulk crystals on silicon substrates and by focusing the excitation source (Xe lamp) through a 74x objective lens.The rectangular spot size was set to 10 × 10 μm and background spectra were collected from the silicon substrate prior to the sample spectra.Reflectance spectra were collected on 40 spots over a few crystals then averaged to ensure the reflectance spectrum was representative of the bulk crystal.The averaged reflectance spectrum was used to create a Tauc plot and extract the direct or indirect band gap from the x-intercept of the linear fit (in Origin Pro).
Raman Spectroscopy: Multiexcitation Raman spectra (using 488, 514.5, 633 and 785 nm excitation wavelengths) were collected using a Renishaw inVia Raman spectrometer.The excitation laser was focused onto bulk and exfoliated crystals using 50 or 100x objective lenses and spectra were collected by setting the laser power between 100 and 500 μW to prevent heating from the laser.Temperature-dependent Raman spectra (between 60 and 300 K) from bulk crystals were collected using an Advanced Research Systems closed cycle He cryostat.For these measurements, bulk crystals were placed onto a Cu sample holder and a long working distance 50x objective lens was used to focus the excitation laser (785 or 633 nm) on the crystals for spectral collection.The QES measurements were performed by inserting notch filters into the excitation path.For the 633 and 514.5 nm excitations, we used Eclipse filters with a cutoff ≈10 cm −1 and for the 785 nm excitation, an Ondax/Coherent THz probe with a cutoff ≈5 cm −1 .All spectra were spline baseline-corrected and fit to Voigt peaks using Igor Pro.
Mechanical Exfoliation: Mechanical exfoliation of the 2D crystals was carried out using a modified "Scotch Tape" methodology on Si/SiO 2 substrates with 285 nm of thermally grown oxide, with an additional coating of 5 nm Ti/40 nm Pt.The additional Pt layer was used to increase the efficiency of exfoliation because of enhanced metal-chalcogen interactions at the interface.The substrates were cleaned using an oxygen plasma cleaner under vacuum for 30 min prior to exfoliation.A bulk 2D crystal was placed onto scotch tape and cleaved several times to expose a fresh surface.A PDMS stamp was then pressed onto the exfoliated crystals on the tape to transfer exfoliated flakes to the PDMS stamp.Then the stamp was pressed firmly on the substrate with approximately 100-150 N of force for 15 min.The stamp was then slowly peeled yielding the exfoliated flakes on the substrates, which were then cleaned by several rinses in acetone and isopropyl alcohol to remove any bulky residue.
Atomic Force Microscopy (AFM): AFM was performed on a Bruker Dimension Icon AFM equipped with Nanoscope V controller.All measurements were performed under ambient conditions using tapping mode.TESPA (Nanoworld) AFM tapping mode tips were used with a force constant of 42 N m -1 and a resonance frequency of 320 kHz.

Figure 1 .
Figure 1.Structure and multi-excitation Raman spectra from MPS 3 compounds.a) Magnetic spin structures in NiPS 3 , CoPS 3 , FePS 3 and MnPS 3 .Room temperature multi-excitation Raman spectra from bulk crystals of b) NiPS 3 , c) FePS 3 , d) CoPS 3 , e) MnPS 3 , f) CdPS 3 and g) ZnPS 3 .h) Normalized intensity of the 250 cm −1 out-of-plane vibrational mode in the MPS 3 compounds as a function of laser excitation energy.The atomic displacements for this mode are shown in the schematic in the inset.

Figure 2 .
Figure 2. Asymmetric Fano lineshapes in the out-of-plane phonon mode.a) Waterfall plot showing the asymmetry in the 250 cm −1 modes (collected with 1.96 eV/633 nm excitation), fit to a Breit-Wigner-Fano lineshape.The Fano lineshapes are indicative of spin-phonon coupling.b) Log-linear plot showing the temperature dependence of the Fano parameters for NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 .Their Néel temperatures are indicated by the vertical dashed lines.

Figure 3 .
Figure 3. Temperature dependence of the a) frequencies and b) intensities (normalized with respect to that of the 380 cm −1 peak) of the 250 cm −1 peaks in NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 .The spectra are collected with the 1.58 eV (785 nm) excitation and peaks fitted with BWF lineshapes as described in the main manuscript.

Figure 4 .
Figure 4. Quasielastic scattering in the MPS 3 compounds.Reduced Raman intensity normalized by the Bose thermal factor, showing quasielastic scattering from the MPX 3 compounds for a) 1.58 eV, b) 1.96 eV, and c) 2.41 eV excitation energies.d) Area of the QES peaks as a function of laser energy.

Figure 5 .
Figure 5. Thickness dependence of the Fano parameters.Top, middle, bottom: Fano parameters as a function of thickness in NiPS 3 , CoPS 3 and FePS 3 , respectively.The values from the bulk crystals are shown as horizontal dashed lines, with the shaded areas representing the experimental errors.

Figure 6 .
Figure 6.Spin-phonon coupling in the MPS 3 compounds.a) Bottom: Fano parameters (left axis) and QES areas (right axis) for the MPS 3 compounds.Top: Metal-sulfur (M-S) bond distances for the MPS 3 compounds.The spin-phonon coupling is the highest (lowest) in NiPS 3 (MnPS 3 ) and corresponds to the lowest (highest) M-S distance.b) Mechanism of spin-dependent Raman scattering.

1 .
The out-of-plane 250 cm −1 mode is resonantly enhanced in the magnetic MPS 3 compounds for laser energies close to a d-d electronic transition.2. At room temperature, the unfilled d orbitals in the magnetic MPS 3 compounds (NiPS 3 , FePS 3 , CoPS 3 and MnPS 3 ) lead to significant spin density fluctuations as well as coupling with an out-of-plane Raman-active phonon mode ˜250 cm −1 .This can be seen in QES as well as peak asymmetry due to Fano resonance.3. The QES areas and Fano resonances reduce sharply across the AFM transition temperatures owing to emergent spin ordering and band renormalization.4.At temperatures below T N , rapid increase in peak intensitiesand discontinuities in peak frequencies occur due to spinphonon coupling, which is the strongest for NiPS 3 , followed by CoPS 3 and FePS 3 , and is the least for MnPS 3 .Concurrently, the room temperature Fano parameters and the QES areas follow the same trend.5.The differences in spin-phonon coupling for the 250 cm −1 mode between the magnetic MPS 3 compounds are attributed to the differences in structure, particularly the M-S interatomic distances, which are the least (highest) in NiPS 3 (MnPS 3 ).