Emergent Altermagnetism and Topological Response In Janus MnPSX Monolayers

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Guerrero-Sanchez, R. Ponce-Perez, D.M. Hoat, R. Gonzalez-Hernandez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7964011/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Mar, 2026 Read the published version in Scientific Reports → Version 1 posted 13 You are reading this latest preprint version Abstract Through a comprehensive computational study, we demonstrate that g -type altermagnetism can be effectively engineered in Janus MnPS₃ monolayer via chalcogen substitution. Replacing one sulfur layer with O, Se, or Te breaks inversion symmetry and induces a charge density asymmetry, lifting Kramers degeneracy and resulting in a momentum-dependent spin splitting characteristic of altermagnetic materials. The magnitude of this splitting is governed by the interplay of electronegativity and atomic radius, with oxygen substitution yielding the largest effect due to its strong Mn–O and P–O bonds driven by high electronegativity and small atomic size. Remarkably, the structural asymmetry and charge redistribution also facilitate a topological response, leading to the emergence of a topological phase with nontrivial quantum spin Hall order. Our findings reveal a new pathway to tailor altermagnetism and topological properties in 2D materials through charge density engineering, opening exciting prospects for spintronic and quantum topological applications in layered magnetic systems. Physical sciences/Materials science Physical sciences/Physics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction For many years, materials have been categorized into four main types: Nonmagnetic, ferromagnetic, ferrimagnetic, and antiferromagnetic. Recently, a new fundamental phase has been discovered in both theoretical and experimental ways; this is the well-known Altermagnetism 1 , 2 , 3 . This latest phase is characterized by being a collinear and fully compensated magnetic order, which exhibits a momentum-dependent spin splitting in its band dispersions. This spin splitting appears even in the absence of spin-orbit coupling 4 , 5 . Altermagnets combine zero net magnetization with an alternating spin polarization in reciprocal space, a fingerprint that can be easily identified via symmetry analysis and first-principles band-structure calculations. In an experimental context, this is achieved through angle-resolved photoemission spectroscopy 6 , nanoscale domain imaging 7 , and X-Ray magnetic circular dichroism 8 . The theoretical foundations of altermagnets are still under study, and the research community is continuing to extend its understanding of this emerging magnetic phase 9 , 10 . Recent studies have predicted a variety of phenomena stabilized by altermagnetic spin symmetries, including the realization of Weyl node-metals 11 , topological Hamiltonian models 12 , chiral magnons 13 , 14 , spin-splitter effects 15 , and spin-current 16 and spin-photocurrents 17 generation. So altermagnetism is making a bridge between electronic, optical, and magnetic responses, previously unimagined for conventional magnets. In recent reviews, it is emphasized that altermagnets facilitate the introduction of new functionalities in spintronics devices 18 , 19 , 20 , 21 . Most discoveries of altermagnetism have focused on bulk systems, with experimental evidence already reported in MnTe and CrSb 22 , 23 , 24 , 25 , 26 , 27 , 28 . In MnTe, maps of the local altermagnetic vector were imaged by combining X-ray magnetic circular dichroism, magnetic linear dichroism, and photoemission electron microscopy 6 . In CrSb, the band splitting near the Fermi energy was observed using spin-integrated soft X-ray angular resolved photoemission spectroscopy together with band structure calculations 7 . Although bulk properties are highly applicable in several fields, the advantage of reducing dimensionality, which often induces symmetry breaking, orbital rearrangements, and potential anisotropic charge densities, may be key in reshaping alternant magnetism and its applications in devices down to the nanoscale. Regarding 2D altermagnets, spin-group theory has been used to classify their distinct families 29 , while the stacking of monolayers is also a matter of interest for generating altermagnetism 30 . Additionally, several monolayer candidates have been proposed using high-throughput screening calculations, including those with large spin splitting, such as RuF 4 , VF 4 , AgF 2 , and OsF 4 31 . Another interesting 2D altermagnet is the MnS 2 monolayer with a pentagonal structure, which exhibits not only this, but also a topological character 32 . An alternative route to induce altermagnetism in 2D is by generating out-of-plane asymmetry, which introduces intrinsic charge-density polarization. A recent prediction of Janus Cr 2 SeO monolayer is an example of that, in which the structural polarity couples altermagnetism with ferroelectricity and piezovalley effects 33 . Those findings suggest that charge-density asymmetry is a structural driver of altermagnetism. Considering the potential impact of Janus phase formation, we turned our attention to the transition metal phosphorus trichalcogenide MPX 3 structure, where M is a transition metal and X is S, Se, or O 34 . The S- and Se-based structures could be easily exfoliated from the bulk and hold promising antiferromagnetic arrangements. In this work, we focus on engineering the MnPS₃ monolayer to induce its Janus phases through selective substitution with O, Se, and Te, aiming to uncover robust altermagnetic behavior in compounds such as MnPS 1.5 O 1.5 , MnPS 1.5 Se 1.5 , and MnPS 1.5 Te 1.5 . Our results reveal that charge-density asymmetry serves as an effective mechanism to control nonrelativistic spin splitting in 2D altermagnets 35 . Remarkably, the induced structural polarity and charge redistribution also give rise to a topological response, leading to the emergence of a nontrivial quantum spin Hall phase in MnPS 1.5 O 1.5 and MnPS 1.5 Te 1.5 . Results Structural stability. To begin with this analysis, we first determine the structure of this well-known 2D material, MnPS 3 . MnPS 3 exhibits an antiferromagnetic Néel-type magnetic arrangement in a trigonal \(\:P\stackrel{-}{3}1m\) (162) space group, which holds inversion symmetry 35 . The calculated lattice parameter is a = 6.02 Å, which agrees well with previous values reported in the literature 36 . In this structure, previously exfoliated and characterized as a collinear antiferromagnet material 37 , 38 , the Mn 2+ cations form a honeycomb-like lattice with P-P dimers and those are coordinated with three S atoms in a P 2 S 6 bipyramid 39 (Fig. 1 ). Our calculated P-S, P-P, and Mn-S bond distances are 2.08 Å, 2.26 Å, and 2.60 Å, respectively (Table 1 ). Previous phonon dispersion calculations have also shown that the MnPS 3 structure can remain stable in an antiferromagnetic phase, as it does not exhibit any signs of negative frequencies 40 . Considering this, we then proceed to engineer the MnPS 3 monolayer to generate its Janus counterpart using O, Se, and Te. The possible structures are MnPS 1.5 O 1.5 (MnPSO), MnPS 1.5 Se 1.5 (MnPSe), and MnPS 1.5 Te 1.5 (MnPSTe) as shown in Fig. 2 (a-c) . We then fully relaxed the Janus counterparts, keeping the vacuum space fixed until an optimized structure was achieved. The obtained lattice parameters in the trigonal space group are 5.56 Å, 6.22 Å, and 6.73 Å for MnPSO, MnPSSe, and MnPSTe, respectively, while the main distances are depicted in Table 1 . From Table 1 , we can observe how the structure of MnPS 3 changes as one of the S layers is substituted with a chalcogen, following a clear trend. The trend reflects an interesting relationship between the structural parameters and the electronegativity of chalcogens (Fig. 2 d) and atomic size ( Figure S1 ). In terms of electronegativity, it follows the order O > S > Se > Te, while in atomic radius, O < S < Se < Te. In the first case, upon introducing O, the lattice parameter contracts by 7.64%, as the strong Mn-O and P-O bonds dominate the structure, which is evident in the reduction of the P-P distance from 2.26 Å to 2.17 Å. Table 1 Optimized lattice parameters in and distances (in Å) of the pristine and Janus systems. The structural trends shown here are consistent with the variations in lattice constant illustrated in Fig. 2 . Monolayer a (Å) d P−S (Å)/ d P−X (Å) d P−P (Å) d Mn−S /d Mn−X (Å) MnPS 3 6.02 2.08 2.26 2.60 MnPSO 5.56 1.96/1.86 2.17 2.63/2.15 MnPSSe 6.22 2.13/2.18 2.25 2.63/2.74 MnPSTe 6.73 2.21/2.36 2.22 2.66/2.94 In contrast, when replacing S with Se and Te, which are larger than S, they weaken the local bonding and induce an expansion in the lattice parameter and bond distances; the expansion percentages are 3.32% and 11.79%, respectively (Fig. 2 d), indicating bond elongation in Mn-X and P-X. Either O or Se and Te induce an apparent asymmetry, with one side contracted by stronger or more covalent bonding (O) and the other expanded due to weaker bond formation resulting from less electronegative species (Se or Te). This asymmetry may impact the electronic characteristics of the materials, as we will see in the coming sections. In the second case, the lattice parameter contracts for O, which has a smaller atomic radius, and expands for Se and Te. As electronegativity increases and atomic radius decreases, the structure tends to contract; otherwise, if electronegativity is lower and atomic radius increases, the structure tends to expand. The thermal stability of the structures is investigated using AIMD simulations over a temperature range from 100 to 300 K. Figure 3 shows the temperature at which the structures are stable. Notice that the MnPS 3 and the Janus MnPS 1.5 Se 1.5 monolayers remain stable up to room temperature. The inset of the figure shows the atomistic representation of both compounds after AIMD simulations, where it is clearly noticed that non-broken bonds are present. On the other hand, the MnPS 1.5 O 1.5 and MnPS 1.5 Te 1.5 monolayers are stable up to 100 K. However, slight structural distortions are observed in both cases. Despite these distortions, no bond breaking occurs, confirming their structural stability. The thermal stability of MnPS 1.5 O 1.5 and MnPS 1.5 Te 1.5 was further assessed through ab initio molecular dynamics simulations at 200 and 300 K for 10 ps, revealing only minor distortions within each temperature range. Structurally, the monolayer change is related to the difference in electronegativity between S and O. While in the case of MnPS 1.5 Te 1.5 , the instability of the system comes from the difference in atomic radius between S and Te. The slight distortion in both monolayers is due to the significant difference in electronegativity between S and O (0.86) and S and Te (0.48). For more details on the thermal stability plots and structures, see Figures S2-S5 in the Supplementary Information (SI). Considering that MnPS 3 is stable up to room temperature and also dynamically stable 40 . We proceed further to determine the formation energies of the Janus structures. The formation energy is suitable in our case since the MnPS 3 , MnPS 1.5 O 1.5 , MnPS 1.5 Se 1.5 , and MnPS 1.5 Te 1.5 monolayers have different atomic species rather than varying numbers of atoms. Therefore, the formation energy of the Janus monolayers was computed assuming thermodynamic equilibrium between the system and the elemental reservoir of each atomic species 41 . Under equilibrium, \(\:{\mu\:}_{i}\) is the energy per atom that can be exchanged between the monolayer and the reservoir, so its value is restricted to preclude phase separation or precipitation. The formation energy has the following form, $$\:{E}_{f}={E}_{Janus}-{E}_{{MnPS}_{3}}-{\mu\:}_{S}{n}_{S}-{\mu\:}_{Se}{n}_{Se}-{\mu\:}_{Te}{n}_{Te}-{\mu\:}_{O}{n}_{O}$$ where \(\:{E}_{Janus}\) and \(\:{E}_{{MnPS}_{3}}\) stand for the total energies of the Janus and pristine monolayers. At the same time, n i defines the number of atoms (n i >0 when adding atoms and n i <0 when removing atoms), and \(\:{\mu\:}_{i}\) its respective chemical potential. We used the chemical potential of S since it is the one that changes in all cases. Then it is bounded by the stability of the MnPS 3 and its elemental bulk phase, such that \(\:{\mu\:}_{s}^{bulk}-\raisebox{1ex}{${{\Delta\:}\text{H}}_{f}$}\!\left/\:\!\raisebox{-1ex}{$3$}\right.\le\:{\mu\:}_{S}\le\:{\mu\:}_{S}^{bulk}\) , with \(\:{{\Delta\:}\text{H}}_{f}=\) -5.96 eV per formula unit. The left part of the range represents S-poor conditions while the right part S-rich conditions. In all cases, we keep O, Se, and Te rich conditions ( \(\:{\mu\:}_{i}={\mu\:}_{i}^{bulk}\) ). Table 2 Formation energies in (eV/Å 2 ) of the MnPS 1.5 O 1.5 , MnPS 1.5 Se 1.5 , and MnPS 1.5 Te 1.5 , taking as reference the MnPS 3 monolayer. Monolayer MnPS 3 MnPS 1.5 O 1.5 MnPS 1.5 Se 1.5 MnPS 1.5 Te 1.5 S-rich 0 -0.18 0.09 0.20 S-poor 0 -0.24 0.03 0.13 The thermodynamic stability of the Janus MnPS 3 − x Y x (Y = O, Se, Te) monolayers was evaluated through their formation energies under S-rich and S-poor conditions, taking pristine MnPS₃ as the reference state. The results, summarized in Table 2 , reveal that all substituted systems exhibit either negative or slightly positive formation energies, confirming that the chalcogen replacement is thermodynamically accessible within the considered chemical potential range. Among them, MnPS 1.5 O 1.5 is clearly the most favorable configuration, with negative formation energies in all growth regimes. This behavior aligns directly with the electronegativity of O since it generates stronger Mn-O bonds compared with Mn-S. In contrast, MnPS 1.5 Se 1.5 and MnPS 1.5 Te 1.5 exhibit small positive formation energies under S-poor conditions, suggesting that their incorporation requires additional energy and may occur under non-equilibrium conditions. Overall, the stability follows the same sequence as electronegativity (O > S > Se > Te) and the expected decrease in bond strength with the increasing chalcogen atomic radius. The results presented here suggest that the Janus MnPS 1.5 O 1.5 monolayer is the most stable and experimentally achievable; however, the other monolayers can still be induced with external stimuli such as kinetic control during synthesis. Electronic structure. The pristine MnPS₃ monolayer crystallizes in a trigonal lattice described by the magnetic space group P-3’1m (#162.75). In this structure, Mn atoms occupy Wyckoff 2d sites, forming a honeycomb lattice with antiparallel out-of-plane magnetic moments, stabilizing a collinear Néel antiferromagnetic order. Importantly, this configuration preserves the combined spatial-inversion and time-reversal (PT) symmetry, despite the breaking of conventional time-reversal symmetry. The symmetry group includes a threefold rotation C₃ around the z-axis and antiunitary operations such as PT and mirror–time-reversal combinations (M x T) 35 . This PT symmetry ensures that every k-point in the 2D Brillouin zone is invariant under PT, which enforces Kramers degeneracy of the bands throughout the BZ as (PT)²=−1, with and without spin-orbit coupling. Consequently, spin band degeneracy is preserved in the pristine MnPS₃ phase, as evidenced by the electronic band structure shown in Fig. 4 a, which exhibits semiconducting behavior with a direct band gap of approximately 2.13 eV. The electronic structures of the Janus MnPS 3 − x Y x (Y = O, Se, Te) monolayers were analyzed along the conventional Γ–M–K–Γ paths, commonly used for hexagonal lattices. Along these directions, the energy bands remain degenerate, even in presence of structural asymmetry. To probe the possible emergence of altermagnetism induced by the charge density asymmetry generated by the Janus structures, we computed the band structures along the \(\:{{\Gamma\:}}_{2}\) -KM2- \(\:{{\Gamma\:}}_{1}\) path, where KM2 is located between M and K high symmetry points, \(\:{{\Gamma\:}}_{2}\) and \(\:{{\Gamma\:}}_{1}\) two different points in the Brillouin zone (see Fig. 5 ). In Fig. 4 b, we present the band structure of the Janus MnPS 1.5 O 1.5 ; here, the substitution of one S layer with O produces short and strong P-O and Mn-O bonds in contrast to P-S and Mn-S bonds (see Table 1 ). This contraction in the structure (7.6%) was mainly caused by the electronegativity difference (0.86) and the small atomic radius of O, which maximizes electronic asymmetry and results in the largest momentum-dependent spin splitting around the KM2 point. In the case of MnPS 1.5 Se 1.5 , Se has an electronegativity value that is almost identical to that of S, with a difference of only 0.03. Due to the radius difference, the lattice expands by 3.3%. In this case, there is a slight structural asymmetry, with larger P-Se and Mn-Se bonds, but electronically similar to P-S and Mn-S, which generates weak symmetry breaking, as shown in Fig. 4 c. Consequently, the observed altermagnetic splitting is small. In the case of MnPSTe, the electronegativity difference is smaller than that of S and O, being 0.48. Also, the covalent radius of Te is the largest of all studied species, which is manifested in the very long P-Te and Mn-Te bonds, resulting in the most significant lattice expansion (11.79%). The combination of electronegativity difference and covalent radius induces an asymmetry significant enough to generate the momentum-dependent spin separation. Janus monolayers follow a clear trend: MnPS 1.5 O 1.5 generates an electronegativity and atomic radius difference-controlled altermagnetism, MnPS 1.5 Se 1.5 provides a more structural effect due to the minimal perturbation induced by the electronegativity difference, and finally, in the MnPS 1.5 Te 1.5 monolayer, the effect appears due to both electronegativity difference and structural asymmetry, which is less marked than in MnPS 1.5 O 1.5 because the difference in electronegativity is more meaningful than the size difference. These distinctions are reflected in the varying magnitudes of spin splitting shown in Fig. 4 . Upon formation of the Janus MnPS 3 − x Y x (Y = O, Se, Te) monolayer, the lattice symmetry is reduced to a noncentrosymmetric magnetic space group P31m (#157.53). This reduction results in the loss of PT symmetry, lifting the Kramers degeneracy observed in the pristine structure. As a result, momentum-dependent spin splitting emerges throughout the BZ, characterized by a sign-alternating pattern, an unmistakable signature of altermagnetism. This behavior is illustrated in Fig. 5 , which displays the spin-resolved Fermi surface contours, obtained from nonrelativistic calculations, below the Fermi level for MnPSO, MnPSSe, and MnPSeTe monolayers. The spin symmetry analysis, considering the decoupled spin and lattice degrees of freedom, reveals that the remaining mirror symmetry combined with spin inversion [C 2 || M x ] connects the opposite Mn sublattices in real space. When coupled with the threefold rotational symmetry (C 3 ), this combination gives rise to an altermagnetic spin pattern in reciprocal space 35 . This is explicitly represented by the spin splitting model in Fig. 5 a. These symmetries imply that spin splitting manifests along generic paths in the Brillouin zone ( u,v,0 ), particularly large along the Γ–KM2 (where KM2 is between M and K) direction, consistent with the results for the Janus MnPS 3 − x Y x monolayers in Fig. 5 (b-d) . Conversely, along high-symmetry directions such as Γ–M and Γ–K, mirror symmetries protect nodal line degeneracies, preserving energy crossings in these specific directions (see the dotted lines in Figs. 5 (b-d)). Notably, the Janus MnPS 3 − x Y x monolayers satisfy the symmetry requirements to be classified as an altermagnet 42 , with the spin space group P 1 3 1 1 − 1 m ∞m 1, which implies g -wave type altermagnetism 2 , 3 . Figure 5 b shows that the magnitude of spin splitting is greatest in MnPS 1.5 O 1.5 , while in the Se- and Te-based Janus compounds (Figs. 5 (c-d) ), the splitting is weaker but preserves the same alternating symmetry. Specific bond contractions, such as the shortening of P–O and Mn–O bonds in MnPSO, enhance local electronic asymmetry by increasing electronegativity differences and strengthening covalent interactions. This increased asymmetry breaks inversion-time-reversal symmetry and lifts Kramers degeneracy, leading to pronounced momentum-dependent spin texture. Conversely, bond expansions observed in MnPSSe and MnPSTe reduce electronic asymmetry, resulting in weaker spin splitting and more uniform spin textures. These findings indicate that the electronegativity of the substituting elements primarily governs the magnitude of the altermagnetic response, while the underlying nonrelativistic mechanisms remain unchanged. Topological properties. Finally, the incorporation of spin–orbit coupling (SOC) into the Janus MnPX 1.5 Y 1.5 monolayers induces subtle changes in their electronic structures, as depicted in Fig. 6 . In this figure, the color scale represents the p -chalcogen orbital contribution to the electronic bands for MnPS 1.5 O 1.5 and MnPS 1.5 Te 1.5 materials. Notably, the characteristic spin splitting persists, confirming its nonrelativistic origin associated with the altermagnetic state. In the case of MnPS 1.5 O 1.5 , SOC opens a finite topological band gap of approximately 0.03 eV at the Γ point. As seen in Fig. 6 a, the orbital-resolved bands exhibit pronounced p –S hybridization, indicating that the SOC-induced mixing between Mn– d and chalcogen– p orbitals drive a band inversion around Γ, signaling a possible topological transition. This behavior is supported by the spin Hall conductivity (SHC) as a function of the Fermi level, where a pronounced peak emerges within the band gap, an indication of strong spin Berry curvature accumulation and surface conducting states, typical of a topological insulator phase. The calculated ℤ₂=1 invariant confirms the emergence of an altermagnetic topological insulating state in the MnPS 1.5 O 1.5 monolayer. A similar topological response is observed in the MnPS 1.5 Te 1.5 monolayer, where SOC slightly reduces the band gap from 0.12 eV to 0.10 eV. The system preserves its nonrelativistic spin splitting, evidencing the persistence of altermagnetic order, while exhibiting a nearly quantized SHC of approximately e/4π within the band gap, as shown in Fig. 6 b. This plateau-like behavior signals a topologically nontrivial state, further confirmed by the calculated ℤ₂=1 index. Conversely, MnPS 1.5 Se 1.5 and pristine MnPS 3 do not exhibit band inversion in their band structures, maintaining a trivial band topology with suppressed SHC near the Fermi level (see Figures S6 and S7 ). Nevertheless, the emergence of nontrivial topology in the Janus counterparts, originating from a topologically trivial compound, is a significant result. This demonstrates that structural polarity and chalcogen composition jointly tune both the altermagnetic and topological properties in Janus MnPS₃-derived systems. Discussion This study demonstrates that Janus MnPX 1.5 Y 1.5 monolayers represent a previously unexplored class of two-dimensional materials in which altermagnetism and topology coexist and are tunable through chemical asymmetry. By systematically varying the chalcogen composition, we reveal how structural polarity and charge-density imbalance lift the Kramers degeneracy and generate momentum-dependent spin splitting without requiring relativistic effects, establishing a nonrelativistic route to spin-polarized phenomena in 2D magnets. The emergence of topological phases upon inclusion of spin–orbit coupling in MnPSO and MnPSTe further underscores the interplay between symmetry breaking, local bonding, and relativistic interactions, providing a unified framework for engineering spin–topological coupling at the atomic scale. These findings not only broaden the fundamental understanding of symmetry-driven magnetism but also highlight Janus altermagnets as promising candidates for next-generation spintronic and topological devices, where controllable charge asymmetry can be harnessed to design multifunctional quantum materials. Methods By spin-polarized first-principles calculations, we investigated the altermagnetic properties of the MnPS 3 − x Y x (Y = O, Se, Te) Janus monolayers. Calculations were performed in the density functional theory framework as implemented in the Vienna ab initio Simulation Package (VASP) 43 , 44 , 45 . The exchange-correlation functional is treated according to the gradient generalized approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) parametrization 46 . The electron-ion interactions are modeled using the projected augmented wave (PAW) method 47 with an energy cutoff of 460 eV. To treat the highly correlated Mn-d electrons, we employ the Hubbard correction according to the methodology proposed by Dudarev et al 48 with U = 4 eV. The thermal stability of the structures is investigated by ab initio molecular dynamics (AIMD) calculations. The AIMD simulations were carried out using the Nose-Hoover thermostat 49 in an NVT ensemble at various temperatures (from 100 to 300 K), with a time step of 1 fs and a simulation duration of 10,000 time steps. Maximally localized Wannier functions were constructed using the wannier90 code 50 to obtain accurate tight-binding Hamiltonians for the Janus MnPX 1.5 Y 1.5 monolayers. The initial projections included Mn–d and chalcogen–p orbitals on both spin channels, totaling 68 Wannier functions. The wannier hamiltonians were used to compute the Z2 index and the spin Hall conductivity (SHC) via the Kubo–Berry formalism on dense 240×240×1 with the wanniertools code 51 . Declarations Data availability All data supporting the findings of this study are included in the article. The atomistic positions file is available from the corresponding author upon reasonable request. Acknowledgements J.G.-S., discloses support for the research of this work from DGAPA-UNAM projects IG101124 and IA100226. Calculations were performed in the DGTIC-UNAM Supercomputing Center projects LANCAD-UNAM-DGTIC-422 and LANCAD-UNAM-DGTIC-368. R.G.-H. thank the continuous support of the Alexander Von Humboldt Foundation, Germany. Funding statement This work was supported by the DGAPA-UNAM (grant numbers IG101124 and IA100226) and by the DGTIC-UNAM (grant numbers LANCAD-UNAM-DGTIC-422 and LANCAD-UNAM-DGTIC-368). Contributions J.G.-S., R.P.P., D.M.H., and R.G.-H. performed the calculations and contributed to the organization of the article. R.G.-H. and J.G.-S. proposed the study. All authors contributed to the first draft and reviewed it. 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09:29:30","extension":"html","order_by":17,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":114559,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/2b4d03a500a499ba9b3c66e1.html"},{"id":95620030,"identity":"5da42caf-00d6-409d-ab7d-672267f2e0b5","added_by":"auto","created_at":"2025-11-11 09:29:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":133245,"visible":true,"origin":"","legend":"\u003cp\u003eAtomistic structure of the MnPS₃ monolayer. The left panel shows the top view, while the right panel presents the side view, with the crystallographic axes indicated.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/10a5af6150ff192991e0b198.png"},{"id":95620031,"identity":"3450baa2-c810-4620-bb0e-42203006be3e","added_by":"auto","created_at":"2025-11-11 09:29:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":229307,"visible":true,"origin":"","legend":"\u003cp\u003eAtomistic relaxed structures of (a) MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e (MnPSO), (b) MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e (MnPSSe), and (c) MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e (MnPSTe) monolayers. Each panel shows the top and side views, highlighting the structural asymmetry induced by chalcogen substitution. (d) Lattice parameter variation as a function of the incorporated chalcogen’s electronegativity, showing a clear lattice contraction with increasing electronegativity.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/a4971e93f71b3adceeb76634.png"},{"id":95620032,"identity":"9c0efd49-5b66-49e5-b70e-0f4eab5f4ba6","added_by":"auto","created_at":"2025-11-11 09:29:29","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":200777,"visible":true,"origin":"","legend":"\u003cp\u003eAIMD simulations for the pristine MnPS\u003csub\u003e3\u003c/sub\u003e and MnPS\u003csub\u003e3-x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e (Y = O, Se, Te) monolayers. The top views of each structure after thermal evolution are shown, confirming high-temperature stability for all cases, particularly for MnPSSe and MnPS₃, which preserve their structural up to 300 K.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/41f9b2036ec7e5207a73b12b.png"},{"id":95657424,"identity":"d532d634-6666-4ac3-9bb4-6b98c7da53e0","added_by":"auto","created_at":"2025-11-11 16:20:47","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":165689,"visible":true,"origin":"","legend":"\u003cp\u003eNonrelativistic band structure in the \u0026nbsp;Γ\u003csub\u003e2\u003c/sub\u003e-KM2- Γ\u003csub\u003e1\u003c/sub\u003e\u0026nbsp;path of the a) Pristine MnPS3 monolayer, b) Janus MnPS1.5O1.5, c) Janus MnPS1.5Se1.5, and d) Janus MnPS1.5Te1.5. Here, KM₂ denotes an intermediate point between the K and M high-symmetry points, while Γ₁ and Γ₂ correspond to different Γ points in the Brillouin zone. Red and blue lines indicate majority and minority spin channels, respectively. The Fermi level is set to zero energy, and the orange line marks the energy level of the first spin splitting used for the Fermi surface analysis.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/2dc74187a6d9ee342bfa63ce.png"},{"id":95656309,"identity":"1198ee49-7089-4c3c-86f1-27ae50fc421d","added_by":"auto","created_at":"2025-11-11 16:18:24","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":182369,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic of the spin splitting in the 2D Brillouin zone of the Janus MnPS\u003csub\u003e3-x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e monolayers, highlighting the high-symmetry points Γ, K, and M, as well as the intermediate point KM2. The dashed line indicates the combined symmetry operation [C\u003csub\u003e2\u003c/sub\u003e∣∣M\u003csub\u003ex\u003c/sub\u003e], (b–d) Spin-resolved Fermi surface contours obtained from nonrelativistic calculations at 0.3, 0.2 and 0.5 eV below the Fermi level for MnPSO, MnPSSe, and MnPSeTe, respectively. These energies correspond to the first spin-split valence bands highlighted in the orange line in Figure 4. Red and blue lines denote opposite spin polarizations, while the dotted lines denote the spin-degenerate Γ–M–K path. The alternating sign of the spin splitting reflects the g-type altermagnetic behavior.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/e2fa04bf59ba1f53fc05ba0c.png"},{"id":95620034,"identity":"fd1da532-f5c5-4899-8387-97c0ab137201","added_by":"auto","created_at":"2025-11-11 09:29:29","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":135536,"visible":true,"origin":"","legend":"\u003cp\u003eSpin–orbit–coupling band structures and spin Hall conductivity (SHC) of Janus MnPS3-xYx monolayers. Panels (a) and (b) show the band structure (left) and the SHC spectra (right) for MnPS1.5O1.5 and MnPS1.5Te1.5, respectively. The color scale represents the orbital projection onto the chalcogen p-states. SOC opens a topological gap in MnPS1.5O1.5, which is reflected in the SHC peak inside the band gap energy.\u0026nbsp;\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/2ab9b9dcc3cf759ea2c6153a.png"},{"id":104740067,"identity":"3dc7a77f-6c7e-4720-96df-564b25b3b771","added_by":"auto","created_at":"2026-03-16 16:14:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1564070,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/dd267489-c6d0-4d65-ae3c-2ebf9f36121a.pdf"},{"id":95658104,"identity":"50fb82e7-dc02-41f5-956b-52f6c5856a54","added_by":"auto","created_at":"2025-11-11 16:22:55","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2772277,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryCollectionAM18oct25.docx","url":"https://assets-eu.researchsquare.com/files/rs-7964011/v1/ef696829cd3fb1cefbf4357c.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Emergent Altermagnetism and Topological Response In Janus MnPSX Monolayers","fulltext":[{"header":"Introduction","content":"\u003cp\u003eFor many years, materials have been categorized into four main types: Nonmagnetic, ferromagnetic, ferrimagnetic, and antiferromagnetic. Recently, a new fundamental phase has been discovered in both theoretical and experimental ways; this is the well-known Altermagnetism\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. This latest phase is characterized by being a collinear and fully compensated magnetic order, which exhibits a momentum-dependent spin splitting in its band dispersions. This spin splitting appears even in the absence of spin-orbit coupling\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Altermagnets combine zero net magnetization with an alternating spin polarization in reciprocal space, a fingerprint that can be easily identified via symmetry analysis and first-principles band-structure calculations. In an experimental context, this is achieved through angle-resolved photoemission spectroscopy\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, nanoscale domain imaging\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e, and X-Ray magnetic circular dichroism\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe theoretical foundations of altermagnets are still under study, and the research community is continuing to extend its understanding of this emerging magnetic phase\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Recent studies have predicted a variety of phenomena stabilized by altermagnetic spin symmetries, including the realization of Weyl node-metals\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, topological Hamiltonian models\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e, chiral magnons\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, spin-splitter effects\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, and spin-current\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e and spin-photocurrents\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e generation. So altermagnetism is making a bridge between electronic, optical, and magnetic responses, previously unimagined for conventional magnets. In recent reviews, it is emphasized that altermagnets facilitate the introduction of new functionalities in spintronics devices\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eMost discoveries of altermagnetism have focused on bulk systems, with experimental evidence already reported in MnTe and CrSb\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e,\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. In MnTe, maps of the local altermagnetic vector were imaged by combining X-ray magnetic circular dichroism, magnetic linear dichroism, and photoemission electron microscopy\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. In CrSb, the band splitting near the Fermi energy was observed using spin-integrated soft X-ray angular resolved photoemission spectroscopy together with band structure calculations\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e. Although bulk properties are highly applicable in several fields, the advantage of reducing dimensionality, which often induces symmetry breaking, orbital rearrangements, and potential anisotropic charge densities, may be key in reshaping alternant magnetism and its applications in devices down to the nanoscale.\u003c/p\u003e\u003cp\u003eRegarding 2D altermagnets, spin-group theory has been used to classify their distinct families\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e, while the stacking of monolayers is also a matter of interest for generating altermagnetism\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Additionally, several monolayer candidates have been proposed using high-throughput screening calculations, including those with large spin splitting, such as RuF\u003csub\u003e4\u003c/sub\u003e, VF\u003csub\u003e4\u003c/sub\u003e, AgF\u003csub\u003e2\u003c/sub\u003e, and OsF\u003csub\u003e4\u003c/sub\u003e\u003csup\u003e31\u003c/sup\u003e. Another interesting 2D altermagnet is the MnS\u003csub\u003e2\u003c/sub\u003e monolayer with a pentagonal structure, which exhibits not only this, but also a topological character\u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. An alternative route to induce altermagnetism in 2D is by generating out-of-plane asymmetry, which introduces intrinsic charge-density polarization. A recent prediction of Janus Cr\u003csub\u003e2\u003c/sub\u003eSeO monolayer is an example of that, in which the structural polarity couples altermagnetism with ferroelectricity and piezovalley effects\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. Those findings suggest that charge-density asymmetry is a structural driver of altermagnetism. Considering the potential impact of Janus phase formation, we turned our attention to the transition metal phosphorus trichalcogenide MPX\u003csub\u003e3\u003c/sub\u003e structure, where M is a transition metal and X is S, Se, or O\u003csup\u003e34\u003c/sup\u003e. The S- and Se-based structures could be easily exfoliated from the bulk and hold promising antiferromagnetic arrangements. In this work, we focus on engineering the MnPS₃ monolayer to induce its Janus phases through selective substitution with O, Se, and Te, aiming to uncover robust altermagnetic behavior in compounds such as MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e, MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e, and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e. Our results reveal that charge-density asymmetry serves as an effective mechanism to control nonrelativistic spin splitting in 2D altermagnets\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. Remarkably, the induced structural polarity and charge redistribution also give rise to a topological response, leading to the emergence of a nontrivial quantum spin Hall phase in MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cem\u003eStructural stability.\u003c/em\u003e To begin with this analysis, we first determine the structure of this well-known 2D material, MnPS\u003csub\u003e3\u003c/sub\u003e. MnPS\u003csub\u003e3\u003c/sub\u003e exhibits an antiferromagnetic N\u0026eacute;el-type magnetic arrangement in a trigonal \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:P\\stackrel{-}{3}1m\\)\u003c/span\u003e\u003c/span\u003e (162) space group, which holds inversion symmetry\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. The calculated lattice parameter is a\u0026thinsp;=\u0026thinsp;6.02 \u0026Aring;, which agrees well with previous values reported in the literature\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. In this structure, previously exfoliated and characterized as a collinear antiferromagnet material\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e,\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e, the Mn\u003csup\u003e2+\u003c/sup\u003e cations form a honeycomb-like lattice with P-P dimers and those are coordinated with three S atoms in a P\u003csub\u003e2\u003c/sub\u003eS\u003csub\u003e6\u003c/sub\u003e bipyramid\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Our calculated P-S, P-P, and Mn-S bond distances are 2.08 \u0026Aring;, 2.26 \u0026Aring;, and 2.60 \u0026Aring;, respectively (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003ePrevious phonon dispersion calculations have also shown that the MnPS\u003csub\u003e3\u003c/sub\u003e structure can remain stable in an antiferromagnetic phase, as it does not exhibit any signs of negative frequencies\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. Considering this, we then proceed to engineer the MnPS\u003csub\u003e3\u003c/sub\u003e monolayer to generate its Janus counterpart using O, Se, and Te. The possible structures are MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e (MnPSO), MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e (MnPSe), and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e (MnPSTe) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003cb\u003e(a-c)\u003c/b\u003e.\u003c/p\u003e\u003cp\u003eWe then fully relaxed the Janus counterparts, keeping the vacuum space fixed until an optimized structure was achieved. The obtained lattice parameters in the trigonal space group are 5.56 \u0026Aring;, 6.22 \u0026Aring;, and 6.73 \u0026Aring; for MnPSO, MnPSSe, and MnPSTe, respectively, while the main distances are depicted in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFrom Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, we can observe how the structure of MnPS\u003csub\u003e3\u003c/sub\u003e changes as one of the S layers is substituted with a chalcogen, following a clear trend. The trend reflects an interesting relationship between the structural parameters and the electronegativity of chalcogens (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed) and atomic size (\u003cb\u003eFigure \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e\u003c/b\u003e). In terms of electronegativity, it follows the order O\u0026thinsp;\u0026gt;\u0026thinsp;S\u0026thinsp;\u0026gt;\u0026thinsp;Se\u0026thinsp;\u0026gt;\u0026thinsp;Te, while in atomic radius, O\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;Se\u0026thinsp;\u0026lt;\u0026thinsp;Te. In the first case, upon introducing O, the lattice parameter contracts by 7.64%, as the strong Mn-O and P-O bonds dominate the structure, which is evident in the reduction of the P-P distance from 2.26 \u0026Aring; to 2.17 \u0026Aring;.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eOptimized lattice parameters in and distances (in \u0026Aring;) of the pristine and Janus systems. The structural trends shown here are consistent with the variations in lattice constant illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMonolayer\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ea (\u0026Aring;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ed\u003csub\u003eP\u0026minus;S\u003c/sub\u003e (\u0026Aring;)/ d\u003csub\u003eP\u0026minus;X\u003c/sub\u003e (\u0026Aring;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ed\u003csub\u003eP\u0026minus;P\u003c/sub\u003e (\u0026Aring;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ed\u003csub\u003eMn\u0026minus;S\u003c/sub\u003e/d\u003csub\u003eMn\u0026minus;X\u003c/sub\u003e (\u0026Aring;)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMnPS\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.60\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMnPSO\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.96/1.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.63/2.15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMnPSSe\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.13/2.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.63/2.74\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMnPSTe\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e6.73\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.21/2.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e2.66/2.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIn contrast, when replacing S with Se and Te, which are larger than S, they weaken the local bonding and induce an expansion in the lattice parameter and bond distances; the expansion percentages are 3.32% and 11.79%, respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed), indicating bond elongation in Mn-X and P-X. Either O or Se and Te induce an apparent asymmetry, with one side contracted by stronger or more covalent bonding (O) and the other expanded due to weaker bond formation resulting from less electronegative species (Se or Te). This asymmetry may impact the electronic characteristics of the materials, as we will see in the coming sections. In the second case, the lattice parameter contracts for O, which has a smaller atomic radius, and expands for Se and Te. As electronegativity increases and atomic radius decreases, the structure tends to contract; otherwise, if electronegativity is lower and atomic radius increases, the structure tends to expand.\u003c/p\u003e\u003cp\u003eThe thermal stability of the structures is investigated using AIMD simulations over a temperature range from 100 to 300 K. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the temperature at which the structures are stable. Notice that the MnPS\u003csub\u003e3\u003c/sub\u003e and the Janus MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e monolayers remain stable up to room temperature. The inset of the figure shows the atomistic representation of both compounds after AIMD simulations, where it is clearly noticed that non-broken bonds are present. On the other hand, the MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e monolayers are stable up to 100 K. However, slight structural distortions are observed in both cases. Despite these distortions, no bond breaking occurs, confirming their structural stability. The thermal stability of MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e was further assessed through ab initio molecular dynamics simulations at 200 and 300 K for 10 ps, revealing only minor distortions within each temperature range. Structurally, the monolayer change is related to the difference in electronegativity between S and O. While in the case of MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e, the instability of the system comes from the difference in atomic radius between S and Te. The slight distortion in both monolayers is due to the significant difference in electronegativity between S and O (0.86) and S and Te (0.48). For more details on the thermal stability plots and structures, see \u003cb\u003eFigures S2-S5\u003c/b\u003e in the Supplementary Information (SI).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eConsidering that MnPS\u003csub\u003e3\u003c/sub\u003e is stable up to room temperature and also dynamically stable\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. We proceed further to determine the formation energies of the Janus structures. The formation energy is suitable in our case since the MnPS\u003csub\u003e3\u003c/sub\u003e, MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e, MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e, and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e monolayers have different atomic species rather than varying numbers of atoms. Therefore, the formation energy of the Janus monolayers was computed assuming thermodynamic equilibrium between the system and the elemental reservoir of each atomic species\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. Under equilibrium, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the energy per atom that can be exchanged between the monolayer and the reservoir, so its value is restricted to preclude phase separation or precipitation. The formation energy has the following form,\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{E}_{f}={E}_{Janus}-{E}_{{MnPS}_{3}}-{\\mu\\:}_{S}{n}_{S}-{\\mu\\:}_{Se}{n}_{Se}-{\\mu\\:}_{Te}{n}_{Te}-{\\mu\\:}_{O}{n}_{O}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{Janus}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{E}_{{MnPS}_{3}}\\)\u003c/span\u003e\u003c/span\u003e stand for the total energies of the Janus and pristine monolayers. At the same time, n\u003csub\u003ei\u003c/sub\u003e defines the number of atoms (n\u003csub\u003ei\u003c/sub\u003e\u0026gt;0 when adding atoms and n\u003csub\u003ei\u003c/sub\u003e\u0026lt;0 when removing atoms), and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{i}\\)\u003c/span\u003e\u003c/span\u003e its respective chemical potential. We used the chemical potential of S since it is the one that changes in all cases. Then it is bounded by the stability of the MnPS\u003csub\u003e3\u003c/sub\u003e and its elemental bulk phase, such that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{s}^{bulk}-\\raisebox{1ex}{${{\\Delta\\:}\\text{H}}_{f}$}\\!\\left/\\:\\!\\raisebox{-1ex}{$3$}\\right.\\le\\:{\\mu\\:}_{S}\\le\\:{\\mu\\:}_{S}^{bulk}\\)\u003c/span\u003e\u003c/span\u003e, with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Delta\\:}\\text{H}}_{f}=\\)\u003c/span\u003e\u003c/span\u003e-5.96 eV per formula unit. The left part of the range represents S-poor conditions while the right part S-rich conditions. In all cases, we keep O, Se, and Te rich conditions (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\mu\\:}_{i}={\\mu\\:}_{i}^{bulk}\\)\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eFormation energies in (eV/\u0026Aring;\u003csup\u003e2\u003c/sup\u003e) of the MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e, MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e, and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e, taking as reference the MnPS\u003csub\u003e3\u003c/sub\u003e monolayer.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMonolayer\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMnPS\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eS-rich\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.20\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eS-poor\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe thermodynamic stability of the Janus MnPS\u003csub\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e (Y\u0026thinsp;=\u0026thinsp;O, Se, Te) monolayers was evaluated through their formation energies under S-rich and S-poor conditions, taking pristine MnPS₃ as the reference state. The results, summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, reveal that all substituted systems exhibit either negative or slightly positive formation energies, confirming that the chalcogen replacement is thermodynamically accessible within the considered chemical potential range. Among them, MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e is clearly the most favorable configuration, with negative formation energies in all growth regimes. This behavior aligns directly with the electronegativity of O since it generates stronger Mn-O bonds compared with Mn-S. In contrast, MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e exhibit small positive formation energies under S-poor conditions, suggesting that their incorporation requires additional energy and may occur under non-equilibrium conditions. Overall, the stability follows the same sequence as electronegativity (O\u0026thinsp;\u0026gt;\u0026thinsp;S\u0026thinsp;\u0026gt;\u0026thinsp;Se\u0026thinsp;\u0026gt;\u0026thinsp;Te) and the expected decrease in bond strength with the increasing chalcogen atomic radius. The results presented here suggest that the Janus MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e monolayer is the most stable and experimentally achievable; however, the other monolayers can still be induced with external stimuli such as kinetic control during synthesis.\u003c/p\u003e\u003cp\u003e\u003cem\u003eElectronic structure.\u003c/em\u003e The pristine MnPS₃ monolayer crystallizes in a trigonal lattice described by the magnetic space group P-3\u0026rsquo;1m (#162.75). In this structure, Mn atoms occupy Wyckoff 2d sites, forming a honeycomb lattice with antiparallel out-of-plane magnetic moments, stabilizing a collinear N\u0026eacute;el antiferromagnetic order. Importantly, this configuration preserves the combined spatial-inversion and time-reversal (PT) symmetry, despite the breaking of conventional time-reversal symmetry. The symmetry group includes a threefold rotation C₃ around the z-axis and antiunitary operations such as PT and mirror\u0026ndash;time-reversal combinations (M\u003csub\u003ex\u003c/sub\u003eT)\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. This PT symmetry ensures that every k-point in the 2D Brillouin zone is invariant under PT, which enforces Kramers degeneracy of the bands throughout the BZ as (PT)\u0026sup2;=\u0026minus;1, with and without spin-orbit coupling. Consequently, spin band degeneracy is preserved in the pristine MnPS₃ phase, as evidenced by the electronic band structure shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea, which exhibits semiconducting behavior with a direct band gap of approximately 2.13 eV.\u003c/p\u003e\u003cp\u003eThe electronic structures of the Janus MnPS\u003csub\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e (Y\u0026thinsp;=\u0026thinsp;O, Se, Te) monolayers were analyzed along the conventional Γ\u0026ndash;M\u0026ndash;K\u0026ndash;Γ paths, commonly used for hexagonal lattices. Along these directions, the energy bands remain degenerate, even in presence of structural asymmetry. To probe the possible emergence of altermagnetism induced by the charge density asymmetry generated by the Janus structures, we computed the band structures along the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Gamma\\:}}_{2}\\)\u003c/span\u003e\u003c/span\u003e-KM2-\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Gamma\\:}}_{1}\\)\u003c/span\u003e\u003c/span\u003e path, where KM2 is located between M and K high symmetry points, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Gamma\\:}}_{2}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\Gamma\\:}}_{1}\\)\u003c/span\u003e\u003c/span\u003e two different points in the Brillouin zone (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb, we present the band structure of the Janus MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e; here, the substitution of one S layer with O produces short and strong P-O and Mn-O bonds in contrast to P-S and Mn-S bonds (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). This contraction in the structure (7.6%) was mainly caused by the electronegativity difference (0.86) and the small atomic radius of O, which maximizes electronic asymmetry and results in the largest momentum-dependent spin splitting around the KM2 point. In the case of MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e, Se has an electronegativity value that is almost identical to that of S, with a difference of only 0.03. Due to the radius difference, the lattice expands by 3.3%. In this case, there is a slight structural asymmetry, with larger P-Se and Mn-Se bonds, but electronically similar to P-S and Mn-S, which generates weak symmetry breaking, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec. Consequently, the observed altermagnetic splitting is small. In the case of MnPSTe, the electronegativity difference is smaller than that of S and O, being 0.48. Also, the covalent radius of Te is the largest of all studied species, which is manifested in the very long P-Te and Mn-Te bonds, resulting in the most significant lattice expansion (11.79%). The combination of electronegativity difference and covalent radius induces an asymmetry significant enough to generate the momentum-dependent spin separation.\u003c/p\u003e\u003cp\u003eJanus monolayers follow a clear trend: MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e generates an electronegativity and atomic radius difference-controlled altermagnetism, MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e provides a more structural effect due to the minimal perturbation induced by the electronegativity difference, and finally, in the MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e monolayer, the effect appears due to both electronegativity difference and structural asymmetry, which is less marked than in MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e because the difference in electronegativity is more meaningful than the size difference. These distinctions are reflected in the varying magnitudes of spin splitting shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eUpon formation of the Janus MnPS\u003csub\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e (Y\u0026thinsp;=\u0026thinsp;O, Se, Te) monolayer, the lattice symmetry is reduced to a noncentrosymmetric magnetic space group P31m (#157.53). This reduction results in the loss of PT symmetry, lifting the Kramers degeneracy observed in the pristine structure. As a result, momentum-dependent spin splitting emerges throughout the BZ, characterized by a sign-alternating pattern, an unmistakable signature of altermagnetism. This behavior is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, which displays the spin-resolved Fermi surface contours, obtained from nonrelativistic calculations, below the Fermi level for MnPSO, MnPSSe, and MnPSeTe monolayers.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe spin symmetry analysis, considering the decoupled spin and lattice degrees of freedom, reveals that the remaining mirror symmetry combined with spin inversion [C\u003csub\u003e2\u003c/sub\u003e || M\u003csub\u003ex\u003c/sub\u003e] connects the opposite Mn sublattices in real space. When coupled with the threefold rotational symmetry (C\u003csub\u003e3\u003c/sub\u003e), this combination gives rise to an altermagnetic spin pattern in reciprocal space\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. This is explicitly represented by the spin splitting model in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea. These symmetries imply that spin splitting manifests along generic paths in the Brillouin zone (\u003cem\u003eu,v,0\u003c/em\u003e), particularly large along the Γ\u0026ndash;KM2 (where KM2 is between M and K) direction, consistent with the results for the Janus MnPS\u003csub\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e monolayers in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u003cb\u003e(b-d)\u003c/b\u003e. Conversely, along high-symmetry directions such as Γ\u0026ndash;M and Γ\u0026ndash;K, mirror symmetries protect nodal line degeneracies, preserving energy crossings in these specific directions (see the dotted lines in Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b-d)). Notably, the Janus MnPS\u003csub\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e monolayers satisfy the symmetry requirements to be classified as an altermagnet\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e, with the spin space group P\u003csup\u003e1\u003c/sup\u003e3\u003csup\u003e1\u003c/sup\u003e1\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003em\u003csup\u003e\u0026infin;m\u003c/sup\u003e1, which implies \u003cem\u003eg\u003c/em\u003e-wave type altermagnetism\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eb shows that the magnitude of spin splitting is greatest in MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e, while in the Se- and Te-based Janus compounds (Figs.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e\u003cb\u003e(c-d)\u003c/b\u003e), the splitting is weaker but preserves the same alternating symmetry. Specific bond contractions, such as the shortening of P\u0026ndash;O and Mn\u0026ndash;O bonds in MnPSO, enhance local electronic asymmetry by increasing electronegativity differences and strengthening covalent interactions. This increased asymmetry breaks inversion-time-reversal symmetry and lifts Kramers degeneracy, leading to pronounced momentum-dependent spin texture. Conversely, bond expansions observed in MnPSSe and MnPSTe reduce electronic asymmetry, resulting in weaker spin splitting and more uniform spin textures. These findings indicate that the electronegativity of the substituting elements primarily governs the magnitude of the altermagnetic response, while the underlying nonrelativistic mechanisms remain unchanged.\u003c/p\u003e\u003cp\u003e\u003cem\u003eTopological properties.\u003c/em\u003e Finally, the incorporation of spin\u0026ndash;orbit coupling (SOC) into the Janus MnPX\u003csub\u003e1.5\u003c/sub\u003eY\u003csub\u003e1.5\u003c/sub\u003e monolayers induces subtle changes in their electronic structures, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. In this figure, the color scale represents the \u003cem\u003ep\u003c/em\u003e-chalcogen orbital contribution to the electronic bands for MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e and MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e materials. Notably, the characteristic spin splitting persists, confirming its nonrelativistic origin associated with the altermagnetic state. In the case of MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e, SOC opens a finite topological band gap of approximately 0.03 eV at the Γ point. As seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea, the orbital-resolved bands exhibit pronounced \u003cem\u003ep\u003c/em\u003e\u0026ndash;S hybridization, indicating that the SOC-induced mixing between Mn\u0026ndash;\u003cem\u003ed\u003c/em\u003e and chalcogen\u0026ndash;\u003cem\u003ep\u003c/em\u003e orbitals drive a band inversion around Γ, signaling a possible topological transition. This behavior is supported by the spin Hall conductivity (SHC) as a function of the Fermi level, where a pronounced peak emerges within the band gap, an indication of strong spin Berry curvature accumulation and surface conducting states, typical of a topological insulator phase. The calculated ℤ₂=1 invariant confirms the emergence of an altermagnetic topological insulating state in the MnPS\u003csub\u003e1.5\u003c/sub\u003eO\u003csub\u003e1.5\u003c/sub\u003e monolayer.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eA similar topological response is observed in the MnPS\u003csub\u003e1.5\u003c/sub\u003eTe\u003csub\u003e1.5\u003c/sub\u003e monolayer, where SOC slightly reduces the band gap from 0.12 eV to 0.10 eV. The system preserves its nonrelativistic spin splitting, evidencing the persistence of altermagnetic order, while exhibiting a nearly quantized SHC of approximately \u003cem\u003ee/4π\u003c/em\u003e within the band gap, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb. This plateau-like behavior signals a topologically nontrivial state, further confirmed by the calculated ℤ₂=1 index. Conversely, MnPS\u003csub\u003e1.5\u003c/sub\u003eSe\u003csub\u003e1.5\u003c/sub\u003e and pristine MnPS\u003csub\u003e3\u003c/sub\u003e do not exhibit band inversion in their band structures, maintaining a trivial band topology with suppressed SHC near the Fermi level (see \u003cb\u003eFigures S6 and S7\u003c/b\u003e). Nevertheless, the emergence of nontrivial topology in the Janus counterparts, originating from a topologically trivial compound, is a significant result. This demonstrates that structural polarity and chalcogen composition jointly tune both the altermagnetic and topological properties in Janus MnPS₃-derived systems.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study demonstrates that Janus MnPX\u003csub\u003e1.5\u003c/sub\u003eY\u003csub\u003e1.5\u003c/sub\u003e monolayers represent a previously unexplored class of two-dimensional materials in which altermagnetism and topology coexist and are tunable through chemical asymmetry. By systematically varying the chalcogen composition, we reveal how structural polarity and charge-density imbalance lift the Kramers degeneracy and generate momentum-dependent spin splitting without requiring relativistic effects, establishing a nonrelativistic route to spin-polarized phenomena in 2D magnets. The emergence of topological phases upon inclusion of spin\u0026ndash;orbit coupling in MnPSO and MnPSTe further underscores the interplay between symmetry breaking, local bonding, and relativistic interactions, providing a unified framework for engineering spin\u0026ndash;topological coupling at the atomic scale. These findings not only broaden the fundamental understanding of symmetry-driven magnetism but also highlight Janus altermagnets as promising candidates for next-generation spintronic and topological devices, where controllable charge asymmetry can be harnessed to design multifunctional quantum materials.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eBy spin-polarized first-principles calculations, we investigated the altermagnetic properties of the MnPS\u003csub\u003e3\u0026thinsp;\u0026minus;\u0026thinsp;x\u003c/sub\u003eY\u003csub\u003ex\u003c/sub\u003e (Y\u0026thinsp;=\u0026thinsp;O, Se, Te) Janus monolayers. Calculations were performed in the density functional theory framework as implemented in the Vienna ab initio Simulation Package (VASP)\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e,\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e. The exchange-correlation functional is treated according to the gradient generalized approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) parametrization\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. The electron-ion interactions are modeled using the projected augmented wave (PAW) method\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e with an energy cutoff of 460 eV. To treat the highly correlated Mn-d electrons, we employ the Hubbard correction according to the methodology proposed by Dudarev \u003cem\u003eet al\u003c/em\u003e\u003csup\u003e\u003cem\u003e48\u003c/em\u003e\u003c/sup\u003e with U\u0026thinsp;=\u0026thinsp;4 eV.\u003c/p\u003e\u003cp\u003eThe thermal stability of the structures is investigated by ab initio molecular dynamics (AIMD) calculations. The AIMD simulations were carried out using the Nose-Hoover thermostat\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e in an NVT ensemble at various temperatures (from 100 to 300 K), with a time step of 1 fs and a simulation duration of 10,000 time steps.\u003c/p\u003e\u003cp\u003eMaximally localized Wannier functions were constructed using the wannier90 code\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e to obtain accurate tight-binding Hamiltonians for the Janus MnPX\u003csub\u003e1.5\u003c/sub\u003eY\u003csub\u003e1.5\u003c/sub\u003e monolayers. The initial projections included Mn\u0026ndash;d and chalcogen\u0026ndash;p orbitals on both spin channels, totaling 68 Wannier functions. The wannier hamiltonians were used to compute the Z2 index and the spin Hall conductivity (SHC) via the Kubo\u0026ndash;Berry formalism on dense 240\u0026times;240\u0026times;1 with the wanniertools code\u003csup\u003e\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data supporting the findings of this study are included in the article. The atomistic positions file is available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eJ.G.-S., discloses support for the research of this work from DGAPA-UNAM projects IG101124 and IA100226. Calculations were performed in the DGTIC-UNAM Supercomputing Center projects LANCAD-UNAM-DGTIC-422 and LANCAD-UNAM-DGTIC-368. R.G.-H. thank the continuous support of the Alexander Von Humboldt Foundation, Germany.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the DGAPA-UNAM\u0026nbsp;(grant numbers IG101124 and IA100226)\u0026nbsp;and by the\u0026nbsp;DGTIC-UNAM (grant numbers LANCAD-UNAM-DGTIC-422 and LANCAD-UNAM-DGTIC-368).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eJ.G.-S., R.P.P., D.M.H., and R.G.-H. performed the calculations and contributed to the organization of the article. R.G.-H. and J.G.-S. proposed the study. All authors contributed to the first draft and reviewed it. R.G.-H. and J.G.-S. shaped the final version.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorresponding authors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrespondence to Rafael Gonzalez-Hernandez.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003e\u0026Scaron;mejkal, L., Gonz\u0026aacute;lez-Hern\u0026aacute;ndez, R., Jungwirth, T. \u0026amp; Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 6, eaa z8809 (2020).\u003c/li\u003e\n \u003cli\u003e\u0026Scaron;mejkal, L., Sinova, J. \u0026amp; Jungwirth. T. Beyond Conventional Ferromagnetism and Antiferromagnetism: A Phase with Nonrelativistic Spin and Crystal Rotation Symmetry. Phys. Rev. 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Commun.\u003c/em\u003e \u003cstrong\u003e224\u003c/strong\u003e, 405 (2018).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7964011/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7964011/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThrough a comprehensive computational study, we demonstrate that \u003cem\u003eg\u003c/em\u003e-type altermagnetism can be effectively engineered in Janus MnPS₃ monolayer via chalcogen substitution. Replacing one sulfur layer with O, Se, or Te breaks inversion symmetry and induces a charge density asymmetry, lifting Kramers degeneracy and resulting in a momentum-dependent spin splitting characteristic of altermagnetic materials. The magnitude of this splitting is governed by the interplay of electronegativity and atomic radius, with oxygen substitution yielding the largest effect due to its strong Mn\u0026ndash;O and P\u0026ndash;O bonds driven by high electronegativity and small atomic size. Remarkably, the structural asymmetry and charge redistribution also facilitate a topological response, leading to the emergence of a topological phase with nontrivial quantum spin Hall order. Our findings reveal a new pathway to tailor altermagnetism and topological properties in 2D materials through charge density engineering, opening exciting prospects for spintronic and quantum topological applications in layered magnetic systems.\u003c/p\u003e","manuscriptTitle":"Emergent Altermagnetism and Topological Response In Janus MnPSX Monolayers","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-11 09:29:25","doi":"10.21203/rs.3.rs-7964011/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-13T05:57:14+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-06T12:06:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"142385438178666068958948635246274658940","date":"2025-12-10T08:05:02+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-08T13:35:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"334738720158466796646710293132543392212","date":"2025-12-03T07:25:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"45731528060966631093674444894102476776","date":"2025-11-05T05:08:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"220124492296621000434839723085172259495","date":"2025-11-03T14:07:44+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"170048135618858691794783363258774492285","date":"2025-10-31T18:32:36+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-31T04:56:33+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-31T03:17:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-28T06:58:57+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-28T06:57:49+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-10-27T22:12:55+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"bfc43d78-69b4-49ac-a108-2bab5400a5d8","owner":[],"postedDate":"November 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":57456475,"name":"Physical sciences/Materials science"},{"id":57456476,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-03-16T16:10:28+00:00","versionOfRecord":{"articleIdentity":"rs-7964011","link":"https://doi.org/10.1038/s41598-026-38927-4","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-03-11 15:59:00","publishedOnDateReadable":"March 11th, 2026"},"versionCreatedAt":"2025-11-11 09:29:25","video":"","vorDoi":"10.1038/s41598-026-38927-4","vorDoiUrl":"https://doi.org/10.1038/s41598-026-38927-4","workflowStages":[]},"version":"v1","identity":"rs-7964011","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7964011","identity":"rs-7964011","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}