Tuning Magnetic and Optical Properties in MnxZn1-xPS3 Single Crystals by the Alloying Composition

The exploration of two-dimensional (2D) antiferromagnetic (AFM) materials has shown great promise and interest in tuning the magnetic and electronic properties as well as studying magneto-optical effects. The current work investigates the control of magneto-optical interactions in alloyed MnxZn1-xPS3 lamellar semiconductor single crystals, with the Mn/Zn ratio regulating the coupling strength. Magnetic susceptibility results show a retention of AFM order followed by a decrease in N\'eel temperatures down to ~ 40% Mn concentration, below which a paramagnetic behavior is observed. Absorption measurements reveal an increase in bandgap energy with higher Zn(II) concentration, and the presence of Mn(II) d-d transition below the absorption edge. DFT+U approach qualitatively explained the origin and the position of the experimentally observed mid band-gap states in pure MnPS3, and corresponding peaks visible in the alloyed systems MnxZn1-xPS3. Accordingly, emission at 1.3 eV in all alloyed compounds results from recombination from a 4T1g Mn(II) excited state to a hybrid p-d state at the valence band. Most significant, temperature-dependent photoluminescence (PL) intensity trends demonstrate strong magneto-optical coupling in compositions with x>0.65. This study underscores the potential of tailored alloy compositions as a means to control magnetic and optical properties in 2D materials, paving the way for advances in spin-based technologies.


Introduction
The renewed interest in two-dimensional (2D) layered materials inspired by the discovery of graphene, 1 has opened a new paradigm in science and technology. 2 These materials consist of nearly atomistic layers held together by weak van der Waals (vdW) interactions, enabling the isolation of individual atomic layers. 3[6] Within these materials, the unpaired spins of adjacent magnetic ions are mutually coupled to form a ferromagnetic (FM) or antiferromagnetic (AFM) arrangement below the Curie (TC) or the Néel (TN) temperature, respectively.2][13][14][15][16] A classical family of 2D AFM compounds are the transition metal phosphorus trichalcogenides, represented by the chemical formula MPX3 (M= first-row transition metals, P=phosphorus, X=S, Se).In these compounds, a single layer consists of a network of shared-edge [MX6] 2+ and [P2X6] 4- octahedral units (in a ratio of 2:1).Metal ions across the layer are arranged in a honeycomb array with P2 located at the hexagon centers (Figure 1(a)).This metal framework facilitates AFM coupling between metal ions, aligning their spins either perpendicular (Ising or anisotropic Heisenberg) or parallel (XY) to the lamellar planes. 17,18The long-range magnetism in MPX3 compounds primarily arises from exchange interactions between the unpaired spins of nearest neighbors (NNs) metal ions.Such exchange interactions enable the formation of AFM-Néel (e.g.,  MnPS3), 19 AFM-zigzag (e.g., FePS3 , NiPS3) 18,19 and AFM-stripy magnetic configurations, as illustrated in

Figure 1(b).
The spin-exchange interactions in MPX3 materials are described by a simple Heisenberg Hamiltonian (Eq.1), typically involving interactions up to the third NN: 6,[20][21][22] (Eq.1) In this equation, i and j represent the metal sites, while J1, J2, and J3 are the exchange coupling constants between the first, second, and third NNs, respectively, as denoted in the AFM-Néel configuration in Figure 1(b)).Si,j denotes the spin operator at site i,j.Note that for systems involving crystalline anisotropy, dipolar interactions, or Zeeman coupling, the Hamiltonian should incorporate additional terms to fully describe the magnetic behavior. 6,20,235][26][27][28][29][30][31] For instance, Raman spectroscopy has uncovered spin-phonon coupling below the Néel temperature in FePS3 and MnPS3, [31][32][33] and magnon-phonon hybridization in MnPSe3. 34Excitonmagnon coupling has been observed in bulk MnPS3, 35 and a linear optical emission in FePS3 and NiPS3, related to the AFM-zigzag arrangement 26 or directionality, 36 have also been reported.In addition, recent DFT-based calculations unveiled that in MPX3 systems, the polarization type light coupled to optical transitions is dependent on the AFM spin arrangement. 37,38Pump-probe spectroscopy has detected a slowdown in spin dynamics near the Néel temperature of FePS3. 39More recently, a PL study on MnPS3 has identified a near-infrared (NIR) transition correlated with the Néel ordering. 30spite these initial observations regarding AFM MPX3 compounds, a fundamental understanding of the correlation between long-range spin-exchange interactions and optical properties has remained elusive.To address this question, this work implemented a dilution of the magnetic ions within the metal honeycomb lattice with diamagnetic constituents, aiming to modulate the strength of the first NN exchange coupling and to further examine whether the AFM configuration is preserved via distant interactions.The materials under investigation include MnxZn1-xPS3 alloyed compounds, where a MnPS3 matrix host accommodates variable amounts of diamagnetic Zn(II) ions.MnPS3 is an ideal model system due to its negligible spin-orbit coupling, and being a direct bandgap semiconductor. 40 addition, Mn(II) ions possess a ground state spin of 5/2 and an AFM-Néel arrangement below 78 K, 41 with the spins oriented nearly perpendicular to the honeycomb plane (with slight tilt of ~8˚). 42The choice of Mn and Zn, giving their similar ionic radii, minimizes internal strains and aggregations.As an added value, this study uncover the potential of variable alloy composition as a control knob for the magnetic configuration (more details in the results section).
This study explores the intricate interplay between optics and magnetism in bulk 2D MnxZn1-xPS3 alloyed compounds (0.37<x1) by comparing magnetic susceptibility with absorption, variable temperature steady-state PL, and transient-PL measurements.The optical measurements uncover the role of Mn(II) d-orbitals in the optical transitions, which serve as footmarks for drastic changes upon the change in composition.These optical observations, in agreement with the magnetic susceptibility data, reveal a reduction in TN as x decreases, thus supporting a correlation between the long-range magnetic order and optical properties.Furthermore, the study shows a retention of the AFM characteristic down to a composition of x=0.4.Finally, experimental findings were corroborated by DFT+U calculations, while taking a brute force approach to consider various magnetic phases in MnxZn1-xPS3 systems.The developed magnetic model offers insights into the magnetic ground state of the alloys, exchange parameters up to third NN, and the Néel temperature for each composition, in agreement with experimental results.

Results and Discussion
Synthesis and characterization of MnxZn1-xPS3 crystals.Bulk single crystals of MnxZn1-xPS3 were synthesized using a vapor-transport method, starting with stoichiometric amounts of the respective elements, as detailed in Ref. 43  compounds.An extensive Raman study on this samples was recently published in Ref. 41 .A homogeneous distribution of the elements was further supported by theoretical calculations of the bond distances at low temperatures within a unit cell (SI, Table S2).In MPS3 materials, the layer skeleton is largely dictated by the bipyramid [P2S6] 4-unit size, where the metal ions with smaller ionic radii compared to the P-P bond (rMn(II) = 0.83 Å, rZn(II) = 0.74 Å, P-P = 2.22 Å for MnPS3), exhibit partial freedom within the [MS6] 2+ unit.Table S2 reveals a minor reduction (less than 1%) in the unit cell size with increasing Zn content, which corresponds to a slight decrease in the bipyramid [P2S6] 4-unit size.
These theoretical evaluations suggest a reduced potential for aggregation, strain or vacancies in the as-grown bulk single crystals, although not entirely eliminating them.The regime between 300K to 120K corresponds to a paramagnetic phase, while the interval from 120K to TN is characterized as a frustrated magnetic stage, 44 which persists until the spins are locked into an ordered AFM-Néel configuration at TN.

Magnetic properties of bulk
Although the AFM nature remains at temperatures below TN, a decline in the χ⊥ intensity is noticeable, presumably due to the canting of spins toward the a-b plane. 45,46e χ⊥(T) trends of the Mn0.88 and Mn0.77 samples share similarities to pristine MnPS3, including a decrease in susceptibility below TN.Nevertheless, a noticeable shift in their TN to lower temperatures is evident with a dependence on the Mn fractions (justified in the simulations below) accompanied by a blurred frustration region.This plot reveals a linear relationship, in agreement with the anticipated trend after gradually incorporating Zn(II) into the host crystals. 47,48Ultimately, the AFM magnetic order eV (for MnPS3) and 2.95 eV (for Mn0.37), along with several well-defined sub-bandgap peaks, denoted as Ei.Noting that pristine ZnPS3 possesses a bandgap of 3.5 eV, 49 thus explaining the band-edge shift toward higher energy in Mn0.37.The Ei peaks were fitted by Gaussian functions (the fit and the used parameters are provided in Figure S3 and Table S3, respectively), with maximal energies consistent with those reported in the literature. 50These Ei peaks are attributed to the spin and parity forbidden d-d transitions of a localized Mn(II) ion at a octahedral site, from the ground state, 6 A1g, to three different excited states: 4 T1g, 4 T2g, and ( 4 Eg, 4 A1g), where the latter contains two degenerate levels. 50e energies of the 3d atomic-like Mn(II) excited states are in good agreement with those previously reported for Mn-doped semiconductors. 51In the present case, the third transition, E3 ( 6 A1g→( 4 Eg,   (a) (c) near-infrared regime with the increase of Zn(II) content (see inset).The remarkable red shift of 30 meV is close to the energy shift observed in the absorption E1 peak upon diamagnetic doping, confirming that the emission originates from the transition between the Mn(II) 4 T1g excited state and the hybrid p-d state in the VB (from now on referred to as 4 T1g→ 6 A1g(VB)).The total PL Stokes shift of ~600 meV in the emission spectra with respect to E1 is attributed to the low dielectric screening in thin semiconductors. 37,52It is important to pay attention that excitation with sub-bandgap energy showed a significantly weaker emission band (SI, Figure S4), implying that the PL emission is sensitized via an absorption above the band-edge, followed by a single or a cascade of relaxation processes into the Mn(II) excited states.S4).The long component dominates the decay in all samples.However, its contribution decreases with the decrease of the Mn(II) content.Essentially, PL decay times at the µsec range support the occurrence of a 4 T1g→ 6 A1g(VB) transition characterized by a partially allowed nature.
This contrasts with the typical msec decay in an atomistic Mn(II) 4 T1g→ 6 A1g transition. 51The discrepancy is related to the fact that the Mn(II) 6 A1g ground state is involved in p-d hybridization at the edge of the VB. 40The faster component in the decay curve is more likely associated with a nonradiative recombination process. 53gure 5(a,c) depicts the electronic structures of pure MnPS3 and ZnPS3 bulk crystals, respectively.
These were calculated using the DFT+U (PBE+U) and meta-GGA (EXC=mBJ) exchange-correlation functionals as described in the Methods.Note that U=1.8 eV was applied to Mn 3d states based on previously published ARPES measurements, 54 (a,c)) closely matches the experimental band gaps differences observed in these bulk materials measured at low temperatures (3.5 eV -3 eV = 0.5 eV). 49The choice of the onset of the absorption edge is further strengthened by the selection rules favoring transitions between different types of orbitals (Δl= ±1).Additionally, the agreement between the theoretical Ei values and the experimental Ei peaks, which are located below the absorption edge (Figure 4(a)), confirms the chosen onset of the absorption edge.Hence, the Ei peaks are attributed to all direct transitions occurring between the bands VB1 → CB1 (E1) and VB2 → CB1 (E2) at each of kpoints, resulting in an energy window equals to 0.5 eV (the blue region) visible in the projected density of states (PDOS) (Figure 5(a), right).The E3 peak can be attributed to the transition from VB1 to the conduction bands marked in red in region IV (yellow region).Importantly, the former energy window (0.5 eV) reflects the energy difference between the peaks E2 and E1 and aligns well with the energy difference of the experimental peaks E2 -E1 = 2.5 -1.9 = 0.6 eV.Moreover, the energy itself matches.
That is, assuming that the E1 transition occurs from VB1 to CB1 at K high symmetry point (see Figure 5(a)), its energy equals 1.9 eV, consistent with the maximum peak position of the experimental value (E1 = 1.9 eV).Based on the band structure of MnPS3, ZnPS3 and the crystal field theory of metal ion with electronic configuration 3d 5 in octahedral geometry with ground state ( 6 A1g) and excited states ( 4 T1g, 4 T2g, 4 Eg) (for more details see Figure 3.9 in Ref. 55 ), a schematic diagram illustrating an oversimplified picture of atomic 3d Mn 2+ states embedded in the p states of P and S is constructed in  Note that all the PDOS are aligned in respect to the onset of absorption edge (neglecting the excitonic effects).The p states of P are present in the entire region of the plotted CB and below the top of region I in the VB, and due to its small contribution, they are not separately plotted.All bands are occupied up to Efermi level marked by the grey dotted line.The abbreviation "Abs.Edge" denotes the absorption edge.In the case of the PDOS of ZnPS3, the PBE approach with a rigid shift to match the band gap obtained in the mBJ approach was used.
shift in energy, followed by a decline in the intensity close to the Néel temperature (dashed line in  when the latter exposed a weak AFM behavior for Mn0.50, albeit a loss of AFM order for Mn0.37 (Figure 3).It is worth noting that temperature-dependent PL measurements were performed at two distinct locations on the crystals to assess the repeatability of the results.The data from both measurements exhibit consistent trends in intensity variation with temperature and yield identical knee temperatures (Figure S6).
The FWHM of the PL emission's dependence on temperature is another way to follow the magnetic influence on optical events.Here, Γ 0 is the broadening at 0 K,   represents the broadening produced by acoustic phonons and   denotes the broadening produced by optical phonons with energy   .The values used in the simulations were based on a recent Raman spectroscopy study on similar MnxZn1-xPS3 crystals. 43For a starting point, to minimize the number of variables in the simulations, The LO phonon energy,   , was matched to the energy of the Raman mode P3 (155 cm -1 for MnPS3), due to its involvement with the Mn 2+ motion 60,61 and to a magnetic ordering. 31,43,62The fit and variables are presented in the SI, S6, exposing the following trends: (i) the values of   show a gradual change from the Mn-rich compositions to those enriched with Zn.Specifically, for Mn0.88 and Mn0.77 there is a substantial agreement between the used LO frequencies and the P3 vibrational mode of MnPS3.

Figure S8, and Table
Nonetheless, for Mn0.65 down to Mn0.37, the best fit values of   were smaller, gradually shifting towards lower energies, eventually matching the P3 mode of ZnPS3 (130 cm -1 ).(ii) The LO phonon coupling term,   , decreases gradually, from the Mn-rich (115 meV) to the Zn-rich (50 meV), and (iii) the coupling of the photogenerated carriers and acoustic phonons,   , is negligible.The high correlation observed between the P3 vibrational mode and the photogenerated carriers in samples with x > 0.65 is in agreement with the integrated PL intensity results, demonstrating a coupling to the Néel temperature for x > 0.65.Therefore, it becomes evident that the optical events are strongly influenced by the spin-phonon coupling, the Mn content, and its magnetic arrangement.while Mn0.50 shows AFM behavior, its weak magneto-optical coupling is evident, probably due to the negligible exchange interactions as well as spin-phonon coupling.
The distinct behavior of the Mn0.50 sample was also distinguished while following the polarization of light in MnxZn1-xPS3 crystals.Representative polar plots of a few different crystals (recorded at 5K) are shown in Figure S9.Unlike other samples that showed a lack of polarization, the Mn0.50 sample exhibited elliptical polarization, which decreases near its Néel temperature of ~ 12 K.Specifically, the polarization along the main ellipsoid axis coincides with a crystallographic direction.DFT+U calculations (discussed in length in the following section) verify a magnetic phase transition in the Mn0.50 sample from AFM-Néel to AFM-stripy.Moreover, these calculations reveal the presence of nearly four degenerate AFM-stripy phases within a unit cell.This can lead to a selective linear polarization along a preferred orientation, resembling to the linear polarization previously observed in NiPS3 and FePS3, albeit along a zigzag direction. 26,36Nevertheless, the stochastic nature of Zn-Mn alloying in the Mn0.50 sample likely results in the coexistence of stripy and Néel configurations, leading to the observed elliptical pattern.The mechanism guiding oscillating dipoles by a magnetic directionality is an intriguing topic that would be further elaborated elsewhere.

DFT calculations of MnxZn1-xPS3.
The magnetic state of the alloyed compounds was elucidated using DFT+U calculations.An average magnetic phase model was implemented to consider various magnetic configurations (AFM-Néel, AFM-zigzag, AFM-stripy, FM) within the MnxZn1-xPS3 alloyed compounds.
While this analysis is applicable across the entire range of x, the focus was primarily on specific values (x = 1.00, 0.75, and 0.50) for efficiency.A comprehensive description of the magnetic phases and corresponding calculation details can be found in the methods section.
The analysis assumed a random distribution of Zn cations within the honeycomb lattice.DFT+U calculations demonstrated that the clustering of Zn cations is not energetically favored (as illustrated in the SI, Figure S10), confirming the homogeneity of Zn distribution and supporting the reported EDX measurements (Figure 2).In addition, the average exchange energy of all magnetic configurations was considered to determine the exchange interactions ( 1 ,  2 , and  3 ) and Néel temperatures of the alloyed systems.Note that these results are valid for both bulk and monolayers, as interlayer interactions were shown to have minimal effect on the magnetic arrangement. 63e pristine MnPS3 compound was used to calibrate the DFT model, including the computation of DFT+U energies for the four magnetic configurations outlined in Figure 1(b), as detailed in the Methods below.The exchange interactions were then derived using Eq.E1 (see Methods).5][66] Note that positive values of J indicate AFM interactions, while negative J designates FM interactions.The TN was determined using Eq.E2 and found to be 114.3K for the pristine MnPS3.The observed deviation from the experimental value is attributed to a limitation of the mean-field approximation, often overestimating this temperature by at least 20%. 20change coefficients and Néel temperatures for each concentration are presented in Table 1 and For x=0.75 compound, DFT results show that all the magnetic phases that exhibit AFM-Néel arrangement have the lowest energy, with mutual differences lower than 0.1 meV.Conversely, the energy difference between Néel and other magnetic configurations is substantially higher (>3 meV).For Mn0.50, the analysis uncovered six magnetic phases with three FM and three AFM arrangements (Figure M2).Remarkably, all three AFM structures seem to have an AFM-stripy magnetic pattern, implying that the MnxZn1-xPS3 system undergoes a dilution-dependent magnetic phase transition around x=0.50.This phase transition aligns with the observed polarization in the PL of the Mn0.50 compound (Figure S9).Polarization can be expected for ferromagnetically coupled spin chains, where a strong coupling between the spin vector and the electric dipole oscillator was previously found. 27e results indicate a preference for AFM-stripy configurations over the FM phases as the magnetic ground state, with an energy difference of more than 10 meV.Note that additional magnetic arrangements were found by doubling the rectangular unit cell of the x=0.50 compound (SI, Figure S11).Nevertheless, these arrangements are significantly higher in energy.
As presented in Table 1, there is a monotonic decline in the first and second exchange interactions with decreasing Mn content.The monotonic decrease in J1 and J2 is expected due to their strong dependency on the distance between Mn-Mn.However, an increase in J3 is observed at x=0.50, likely associated with the Néel to stripy magnetic phase transition.Note that the observed weak magnetooptical coupling in the x=0.50 compound could be ascribed to the small value of J1.
To further validate the averaged magnetic phase model, the TN values for the various compounds were calculated using equations provided in the Methods and plotted in Figure 6(c) (orange triangles).Note that the calculated Néel temperatures were normalized to the TN of MnPS3 extracted from the SQUID measurements (79 K).As anticipated, the calculated TN demonstrates a gradual linear decrease with the increasing concentration of Zn(II), consistent with the TN extracted from the SQUID measurements.This confirms the reliability of the utilized average phases technique as a practical and effective approximation method to comprehensively characterize the magnetic behaviors of the MnxZn1-xPS3 alloyed compounds.

Conclusions
In conclusion, this work has demonstrated the tunability of the magneto-optical coupling in single crystals with the composition MnxZn1-xPS3.A vapor transport synthesis method provides the alloyed MnxZn1-xPS3, covering compositions from 0.37 ≤ x ≤ 1, encompassing the full spectrum of magnetic characters from paramagnetic attributes (x = 0.37) to the characteristic features of magnetic AFM-Néel materials (x = 1).A careful analysis of both absorption and photoluminescence (steady state-and transient-PL) of the alloyed crystals has revealed a distinct emission mechanism stemming from the 4 T1g→ 6 A1g of the Mn(II) ion, which is partially allowed due to the hybridization of the S(p) and Mn(d) orbitals in the VB.The elucidation of the observed d-d transitions below the absorption edge relied on the assumption that the onset of the absorption edge emerging from deeper VB states in MnPS3 based on DFT+U approach and previously published ARPES measurements, with the latter providing accurate positioning of the d-states within the PDOS.An origin of these peaks, visible in the pure and alloys systems, can be understood in terms of an oversimplified atomic picture of the 3d Mn states

Methods
Materials.Bulk single crystals of MnxZn1-xPS3 (0.25 ≤ x ≤ 1) were grown via the vapor sublimation synthesis.Briefly, stoichiometric amounts of Mn, red phosphorus, S8, and Zn were ground in a mortar and pestle into a homogeneous mixture.The powder was transferred to a quartz tube and sealed under vacuum.Then, the tube was calcined in a gradient two-zone furnace for a week, where the hot (substrate zone) and cold (product zone) areas were set to 650˚C and 600˚C, respectively.After a week, the bulk MnxZn1-xPS3 single crystals were collected from the cold zone.
PL measurements.PL measurements were performed using a fiber-based confocal microscope embedded in a cryogenic system (attoDRY1000 closed cycle cryostat), with a heater capable of changing the temperature of the sample between 5 K -300 K.The temperature was controlled by the Lake Shore PID system.The sample was excited by a 405/450 nm laser diode, and the emission was detected by the FERGIE spectrograph.On the optical head, a 473 nm long-pass dichroic mirror was used to transmit the laser to the sample while filtering it from the emission.An additional 800 nm long-pass filter was installed on the emission path to filter the laser completely.The lifetime measurements were acquired using a 450 nm pulse laser with a pulse duration of 70 ps.The transient PL was collected by a superconducting nanowire single photon (SNSPD) detector coupled to a PicoHarp300 time-correlated single photon counter (TCSP).SQUID.SQUID measurements were performed in the Quantum Matter Research (QMR) center at the Technion Institute using a SQUID magnetometer Quantum Design MPMS3, which provides a sensitivity of ≤10 -7 emu.The magnetic susceptibilities were measured under an external magnetic field of 1000 Oe (0.1 Tesla), parallel or perpendicular to the lamellar planes of the crystals.
Electron microscopy.High-resolution scanning electron microscope (HR-SEM) images were acquired with Zeiss Ultra-Plus FEG-SEM.Energy Dispersive X-ray (EDX) spectra were gathered using Quanta 200 FEI E-SEM.Both measurements were conducted under an accelerating voltage of 20 kV.
The EDX spectra were meticulously acquired to perform a quantitative assessment of the composition and to estimate the atomic ratios of [Mn]/[Zn] in the alloyed samples of MnxZn1−xPS3.
Magnetic configurations of MnxZn1-xPS3.The average magnetic phase analysis of the MnxZn1-xPS3 systems was performed to investigate the influence of Zn alloying on the template MnPS3 compound.This approach involves using the magnetic configurations of the original MnPS3 matrix with the rectangular unit cell (Figure 1(b)), substituting Mn with Zn based on the parameter x, and accounting for all non-equivalent phases.In this way, the unperturbed MnPS3 compound serves as a reference in the calculations to calibrate the model.For each alloying concentration, the smallest supercell preserving the AFM arrangement was selected.This methodology transforms disordered systems into ordered models (supercells) by considering all possible non-equivalent magnetic arrangements within the employed supercell.Furthermore, for each alloying concentration, the lateral lattice parameters were optimized, keeping the position of the ions fixed.Pure MnPS3 (x=1.00).The exchange interactions in the isotropic compound can be derived from three linear equations, dependent on the DFT total energies of the meta-stable magnetic configurations, as shown in Eq.E1. (Eq.E1) Where   ,  é ,   , and   are the DFT total energies of the MnPS3 magnetic configurations, and S is the spin magnetic moment.
Hence, the Néel temperature can be deduced from the magnetic configuration with the lowest energy, corresponding to the AFM-Néel arrangement, as demonstrated in Eq.E2: 67 (Eq.E2) Where   is the Boltzmann constant.
x=0.75.As previously mentioned, Zn atoms are randomly distributed within the honeycomb matrix.
However, in an AFM environment, different Zn positions within the lattice generate different exchange energies between the Mn atoms.Therefore, it is crucial to consider the average effect of all Zn displacements in the AFM crystal.To encompass all the magnetic phases with a 3:1 Mn to Zn ratio while maintaining zero net magnetization, a 2x1 rectangular unit cell template was used, where two atoms of Mn were replaced with Zn, as depicted in Figure M1.This yielded 11 non-degenerate virtual magnetic arrangements.Among these, the FM, AFM-Néel, and AFM-zigzag configurations contributed three magnetic arrangements each, while the AFM-stripy pattern contributed two.By averaging the exchange energy over a single magnetic cell, the mean exchange energy of a specific magnetic cell arrangement was obtained.The resulting exchange terms are then formulated as follows: (Eq.E3) Note that the coefficients of the DFT energies depend on the number of magnetic arrangements at each configuration (Néel, stripy, zigzag, FM).The magnetic ground state of the Mn0.75 compound was determined to be AFM-Néel.Consequently, the average Néel exchange energy was calculated according to the following equation: (Eq.E4)   ̅ = ( + 1) 3  (− 20 9 ⁄  1 + 4 2 − 7 3 ⁄  3 ) Where the (− 20 9 ⁄  1 + 4 2 − 7 3 ⁄  3 ) term is the mean exchange energy of the Néel phases.An example of the calculation scheme for Mn0.75Zn0.25PS3 is provided in the SI section 11.3.Where   ̅̅̅̅̅ is the average DFT energy of the three FM arrangements.Importantly, the minor energy differences between the AFM-stripy phases result in coexisting magnetic phases at finite temperatures, making it challenging to determine which exchange energy should be considered to extract TN.Therefore, the average exchange energy of the AFM-stripy magnetic phases was utilized,  240Ry for the plane wave kinetic energy of the wavefunctions and charge density, respectively.We consider a mesh of 42 special k points in the irreducible wedge of the first Brillouin zone, corresponding to a grid of 10×8×1 in the Monkhorst Pack scheme.All calculations were spin-polarized.
To account for the localization of the d orbital, we include the Hubbard potential (DFT +U), setting U to 3eV to achieve reasonable convergence of the Heisenberg parameters. 64For structural optimization, we used ion relaxation posterior to a minimized Birch-Murnaghan plot, keeping the ratio of the a/b lattice parameters constant, as expected for the highly isotropic MnPS3. 40,68This approach should allow complete structural optimization of the MnPS3 monolayers while preserving the symmetry of the crystal.All calculations refer to a monolayer slab with a vacuum length of 20Å.The density of states (DOS) have been calculated using VASP software. 69The alloy has been considered within a supercell consisting of 4-fold primitive hexagonal unit cells.For each of the fractional concentrations (0.25, 0.50, 0.75), particular structural configurations have been considered.In order to improve the band gaps obtained within PBE exchange correlational functional, the modified Becke-Johnson (mBJ) potential 70 has been employed for ZnPS3. 71The convergence criteria for the energy and force were set to 10 −7 eV and 10 −3 eV/˚A, respectively.A semi-empirical Grimme method 72 with a D3 parametrization (DFT-D3) was adopted 73 to account for dispersive forces.

Figure 1 .
Figure 1.(a) Illustration of an MPX3 layer.The blue, purple and yellow balls represent the metal, phosphorus and chalcogen ions, respectively.(b) Magnetic configurations: FM, AFM-Néel, AFM-zigzag, and AFM-stripy.Spin up and down are represented by blue and grey balls, respectively.Rectangular unit cell is indicated by black dashed lines.The antiferromagnetic Néel configuration highlights the exchange coupling of the first three nearest neighbors.

Figure 2 .
Figures 2(a) and (b) exhibit HR-SEM images of the MnPS3 and Mn0.77 crystals, respectively, confirming their high crystallinity, stacking arrangement, and well-defined surface morphology.The pink squares MnxZn1-xPS3.The impact of the diamagnetic ion on the magnetic properties of MnxZn1-xPS3 was exploited by examining the magnetic susceptibility (χ) versus temperature, while investigating single crystals with different compositions.The experiments involved the use of a superconducting quantum interference device (SQUID) operating at temperatures ranging between 4K to 300K and under a weak external magnetic field (1 kOe) oriented parallel (‖) or perpendicular (Ʇ) to the a-b plane of the crystals.Note that MnPS3 possesses an AFM-Néel configuration with an easy magnetic vector oriented along the tilted c-crystallographic axis, viz., would have proportionate projections along the two monitored directions.

Figure 3 (
Figure 3(a) shows temperature-dependent susceptibility plots under a perpendicular magnetic field (χ⊥) for samples indicated by the legend.The complementary data recorded under parallel magnetic field (χ∥) are displayed at the SI, Figure S2(a).For the pristine MnPS3, a decrease in temperature elevates the χ⊥ intensity up to ~120K, after which it stabilizes until reaching the Néel temperature at TN = 79.2±2.4K (black arrow in Figure 3(a)).The regime between 300K to 120K corresponds to a

Figure 3 (
Figure 3(a) provides insights into the magnetic behavior of the Mn0.50 and Mn0.37 samples.The χ⊥(T) trend of the Mn0.50 crystal veils a fine structure detail, but a plot of dχ/dT (inset in Figure 3(b))displays a discernible hump associated with an AFM-Néel point, around ~12 K, along with a contribution of para-magnetism.The χ⊥(T) trend of the Mn0.37 sample exhibits a total loss of AFM character and is compatible with a paramagnetic behavior (following the Curie-Weiss law).Overall, the TN values extracted from the SQUID measurements and their dependence on the Mn content are plotted in Figure3(b).This plot reveals a linear relationship, in agreement with the anticipated trend

Figure 3 .
Figure 3. (a) perpendicular magnetic susceptibility of the alloyed crystals under a magnetic field of 1 kOe.(b) The Néel temperature of the alloyed crystals, derived from the derivative of the parallel magnetic susceptibility with temperature.Inset: the derivative of the susceptibility of the Mn0.50 sample.

4 A1g)
), is hidden by the room temperature absorption edge of MnPS3, yet it is visible in the Mn0.37 crystal spectrum.Upon incorporating Zn(II) into the lattice, both E1 and E2 bands in the Mn0.37 spectrum are shifted towards lower energies by 40 meV and 80 meV, respectively.Notably, the intensities of the Ei transitions in Figure4(a) are relatively strong with respect to the band-edge scale, reflecting a partially allowed transition as a result of p-d hybridization in the valence band (VB).40The involvement of d-orbitals in the absorption spectra and the p-d hybridization in the VB are further verified by DFT+U calculations, as will be discussed below.

Figure 4 (
Figure 4(b) depicts a set of PL spectra of bulk MnxZn1-xPS3 single crystals acquired at 5K.The samples were excited using a 405 nm continuous-wave (CW) laser.The PL spectra comprise a single broad band with a full-width-at-half-maximum (FWHM) of about 140 meV, which gradually shifts towards the

Figure 4 .
Figure 4. (a) Absorption spectra with spectral deconvolution of MnPS3 and Mn0.37 recorded at room temperature.(b) PL spectra of MnxZn1-xPS3 obtained at a temperature of 5 K, while exciting with a CW 405 nm laser.Inset: the position of the PL peak as a function of the Mn(II) content, derived from a Gaussian fit.(c) PL decay curves of MnxZn1-xPS3 recorded at a temperature of 5 K while exciting with a pulsed laser of 450 nm wavelength.The best fit is depicted by the dashed black line.

Figure 4 (
Figure 4(c) presents a set of PL-decay curves for the samples listed in the legend.These curves were best fitted by bi-exponential functions (black dashed lines), revealing two different decay times for each sample, ranging from 96 to 169 μsec for the longer component and 3 to 3.5 μsec for the shorter component (SI, TableS4).The long component dominates the decay in all samples.However, its ensuring the correct position of the 3d states within the valence bands relative to the valence band maximum (VBM).It is assumed that the absorption onset in MnPS3 originates from valence bands deeper than the top of the VB.Namely, the fundamental absorption edge (neglecting excitons) occurs between the top of the green region (consisting of p states) in Figure 5(a) to the bottom of the CB (marked in red), resulting in a fundamental electronic band gap of Egap MnPS3 =2.7 eV.While the electronic band gaps calculated by these approaches still underestimate the actual values, the calculated difference between ZnPS3 and MnPS3 band gaps (Egap ZnPS3 -Egap MnPS3 = 3.2 eV -2.7 eV = 0.5 eV) (see Figures 5

Figure 5 (
Figure 5(b).This diagram indicates possible optical transitions related to d-d transitions.Particularly, within the crystal field approach in octahedral coordination, the E1, E2, and E3 transitions correspond to the electronic transitions 6 A1g→ 4 T1g, 6 A1g→ 4 T2g, 6 A1g→ 4 Eg, respectively.Note that the relative positions of the eg and t2g states are schematically depicted in Figure 5(b) based on the main contributions of the 3d states visible in the PDOS of MnPS3.Future investigations may employ alternative methods such as Maximally Localized Wannier Functions to provide crystal field and exchange splitting parameters.Figure 5(d) displays the PDOS of the studied alloys.The PDOS plots uncover a dominance of Mn d-orbitals at the CB, and hybridization between Mn(d) and S(p) orbitals (blue region) at the VBM.More specifically, the Mn 3d states generate tails close to the band-edges, acting as band-gap traps, in contrast to the electronic PDOS of pure ZnPS3.Note that the Ei peaks attributed to the Mn(II) d-d transitions are visible in all alloys with any concentration of Mn atoms within the fundamental electronic band gap, except for pure ZnPS3.It is important to note the mixed

Figure 5 .
Figure 5. Electronic structure for the (a) MnPS3 and (c) ZnPS3 bulk materials.(b) Schematic diagram of optical transitions in MnxZn1-xPS3 crystals, showing an oversimplified picture of atomic 3d states of Mn 2+ in an octahedral crystal field with t2g states (triple horizontal lines) and eg states (double horizontal lines) partially embedded in the p states of S and P atoms.(d) Projected density of states (PDOS) of MnxZn1-xPS3 crystals with different Mncontent (x).Note that all the PDOS are aligned in respect to the onset of absorption edge (neglecting the excitonic effects).The p states of P are present in the entire region of the plotted CB and below the top of region I in the VB, and due to its small contribution, they are not separately plotted.All bands are occupied up to Efermi level marked by the grey dotted line.The abbreviation "Abs.Edge" denotes the absorption edge.In the case of the PDOS of ZnPS3, the PBE approach with a rigid shift to match the band gap obtained in the mBJ approach was used.

Figure 6 (
Figure 6(a)).A corresponding integrated PL intensity versus temperature plot is shown in the inset, extracted from fitting the PL bands by a mono-Gaussian function (SI, FigureS5(a)).The increase in intensity up to 50 K, as depicted in Figure6(a), stems from thermal excitation of the 4 T1g state,56,57 followed by a complete quenching of the emission when approaching 120 K.Note that the blue shift in the PL energy (FigureS5(b)) with increasing temperature was observed previously in Mn 2+ -doped nanocrystals,57,58 and attributed to the decrease in crystal field and the thermal activation of phonons.Additionally, slightly above 50 K, a knee point in the inset plot designates the start of the intensity drop.This point, labeled hereon as TK (the knee temperature), was determined through the derivative of the curve (SI, FigureS5(c)) to be 72.4±6.2K for MnPS3.The quenching of the intensity above TK is ascribed to the activation of a non-radiative process facilitated by phonons, thus following an Arrhenius relation as shown by the red line in the inset (more information is provided in section 8 of the SI).The temperature-dependent integrated PL intensity profiles of the alloyed crystals are depicted in Figure 6(b), where the TK points were extracted in a similar manner as for the MnPS3 and are marked by the black arrows.Figure 6(c) represents the dependence of the TK values versus the

Figure 6 (
c) represents the dependence of the TK values versus the fraction of Mn (x) by the green circles.These are compared with the TN points extracted from the magnetic susceptibility (blue squares), along with a linear fit (red dashed line).Interestingly, the green symbols closely coincide with TN down to x ~ 0.65.However, they strongly deviate from the red line for x < 0.65.The observation in Figure6(c) shows a strong correlation with the SQUID measurements,

Figure 6 ( 59 (
d) depicts a set of FMHM(T) plots for various compositions of MnxZn1-xPS3 crystals.The trend of these curves is dictated by electron-phonon interactions, described by the relation given in Eq. 2:

Figure 6 .
Figure 6.(a) A color map displaying the temperature-dependent PL of MnPS3 under 405 nm laser excitation.inset: the temperature dependent of the PL integrated intensity of MnPS3.(b) Temperature-dependent of the integrated PL intensity of the alloyed crystals.(c) Comparison of the Néel temperatures of the alloyed compounds derived from SQUID measurements (blue squares), the knee temperature obtained from the TD-PL measurements (green circles), and the Néel temperatures calculated from DFT simulations (orange triangles).A linear fit for the Néel temperature (extracted from SQUID) is provided (dashed red line) to guide the eye.(d) Temperature-dependent FWHM of the PL emission of the alloyed crystals.
intensity uncovered a correlation to the magnetic properties, showing a drop in the intensity near the crystal's Néel temperature.This correlation has been detected down to x=0.65 and was attributed to the persistence of spin-phonon coupling down to this concentration.Finally, the magnetic results were verified by DFT+U calculations based on an averaged phase model, allowing the extraction of the magnetic arrangements, spin-exchange parameters and the Néel temperatures of the alloyed compounds.Particularly, DFT calculations revealed a magnetic phase transition from AFM-Néel to AFM-stripy for the compound x=0.5.The present comprehensive work sheds light on the correlation between the optical and magnetic properties of bulk MnxZn1-xPS3 crystals, providing an understanding of the underlying physical phenomena leading to the connection between the magnetic and optical properties in the investigated AFM materials.
For the calculations of the MnxZn1-xPS3 ground states, ab initio calculations were performed using the PBE (Perdew-Burke-Ernzerhof) generalized gradient exchange-correlation functional with PAW (projected augmented wave) pseudopotentials as implemented in the open-source Quantum Espresso package.All calculations were performed on a plane wave basis with a cutoff of 40Ry and

Table 1 .
Exchange parameters of the MnxZ1-xPS3 compounds obtained from DFT+U calculations.p states coming from the S and P orbitals.Most notably, temperature-dependent PL