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 spectroscopy⁶, nanoscale domain imaging⁷, and X-Ray magnetic circular dichroism⁸.

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-metals¹¹, topological Hamiltonian models¹², chiral magnons^13,14, spin-splitter effects¹⁵, and spin-current¹⁶ and spin-photocurrents¹⁷ 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 microscopy⁶. 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 calculations⁷. 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 families²⁹, while the stacking of monolayers is also a matter of interest for generating altermagnetism³⁰. Additionally, several monolayer candidates have been proposed using high-throughput screening calculations, including those with large spin splitting, such as RuF₄, VF₄, AgF₂, and OsF₄³¹. Another interesting 2D altermagnet is the MnS₂ monolayer with a pentagonal structure, which exhibits not only this, but also a topological character³². 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 Cr₂SeO monolayer is an example of that, in which the structural polarity couples altermagnetism with ferroelectricity and piezovalley effects³³. 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 MPX₃ structure, where M is a transition metal and X is S, Se, or O³⁴. 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_1.5O_1.5, MnPS_1.5Se_1.5, and MnPS_1.5Te_1.5. Our results reveal that charge-density asymmetry serves as an effective mechanism to control nonrelativistic spin splitting in 2D altermagnets³⁵. 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_1.5O_1.5 and MnPS_1.5Te_1.5.

Structural stability. To begin with this analysis, we first determine the structure of this well-known 2D material, MnPS₃. MnPS₃ exhibits an antiferromagnetic Néel-type magnetic arrangement in a trigonal (162) space group, which holds inversion symmetry³⁵. The calculated lattice parameter is a = 6.02 Å, which agrees well with previous values reported in the literature³⁶. In this structure, previously exfoliated and characterized as a collinear antiferromagnet material^37,38, the Mn²⁺ cations form a honeycomb-like lattice with P-P dimers and those are coordinated with three S atoms in a P₂S₆ bipyramid³⁹ (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 MnPS₃ structure can remain stable in an antiferromagnetic phase, as it does not exhibit any signs of negative frequencies⁴⁰. Considering this, we then proceed to engineer the MnPS₃ monolayer to generate its Janus counterpart using O, Se, and Te. The possible structures are MnPS_1.5O_1.5 (MnPSO), MnPS_1.5Se_1.5 (MnPSe), and MnPS_1.5Te_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 MnPS₃ 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. 2d) 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.

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. 2d), 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 MnPS₃ and the Janus MnPS_1.5Se_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_1.5O_1.5 and MnPS_1.5Te_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_1.5O_1.5 and MnPS_1.5Te_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_1.5Te_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 MnPS₃ is stable up to room temperature and also dynamically stable⁴⁰. We proceed further to determine the formation energies of the Janus structures. The formation energy is suitable in our case since the MnPS₃, MnPS_1.5O_1.5, MnPS_1.5Se_1.5, and MnPS_1.5Te_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 species⁴¹. Under equilibrium, 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,

where and 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 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 MnPS₃ and its elemental bulk phase, such that , with -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 ().

The thermodynamic stability of the Janus MnPS_3 − xY_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_1.5O_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_1.5Se_1.5 and MnPS_1.5Te_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_1.5O_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_xT)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. 4a, which exhibits semiconducting behavior with a direct band gap of approximately 2.13 eV.

The electronic structures of the Janus MnPS_3 − xY_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 -KM2- path, where KM2 is located between M and K high symmetry points, and two different points in the Brillouin zone (see Fig. 5).

In Fig. 4b, we present the band structure of the Janus MnPS_1.5O_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_1.5Se_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. 4c. 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_1.5O_1.5 generates an electronegativity and atomic radius difference-controlled altermagnetism, MnPS_1.5Se_1.5 provides a more structural effect due to the minimal perturbation induced by the electronegativity difference, and finally, in the MnPS_1.5Te_1.5 monolayer, the effect appears due to both electronegativity difference and structural asymmetry, which is less marked than in MnPS_1.5O_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 − xY_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 [C₂ || M_x] connects the opposite Mn sublattices in real space. When coupled with the threefold rotational symmetry (C₃), this combination gives rise to an altermagnetic spin pattern in reciprocal space³⁵. This is explicitly represented by the spin splitting model in Fig. 5a. 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 − xY_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 − xY_x monolayers satisfy the symmetry requirements to be classified as an altermagnet⁴², with the spin space group P¹3¹1^− 1m^∞m1, which implies g-wave type altermagnetism^2,3.

Figure 5b shows that the magnitude of spin splitting is greatest in MnPS_1.5O_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_1.5Y_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_1.5O_1.5 and MnPS_1.5Te_1.5 materials. Notably, the characteristic spin splitting persists, confirming its nonrelativistic origin associated with the altermagnetic state. In the case of MnPS_1.5O_1.5, SOC opens a finite topological band gap of approximately 0.03 eV at the Γ point. As seen in Fig. 6a, 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_1.5O_1.5 monolayer.

A similar topological response is observed in the MnPS_1.5Te_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. 6b. This plateau-like behavior signals a topologically nontrivial state, further confirmed by the calculated ℤ₂=1 index. Conversely, MnPS_1.5Se_1.5 and pristine MnPS₃ 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.

This study demonstrates that Janus MnPX_1.5Y_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.

By spin-polarized first-principles calculations, we investigated the altermagnetic properties of the MnPS_3 − xY_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) parametrization⁴⁶. The electron-ion interactions are modeled using the projected augmented wave (PAW) method⁴⁷ 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 al⁴⁸ 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 thermostat⁴⁹ 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 code⁵⁰ to obtain accurate tight-binding Hamiltonians for the Janus MnPX_1.5Y_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 code⁵¹.

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.