Valley polarization, Rashba interaction, and weak altermagnetism in inversion-asymmetric MnPS$_\text{3}|$WS$_\text{2}$ van der Waals heterostructures

Nirmal Ganguli; Purba Dutta; Soumajyoti Bid

REVIEW 4 major objections 4 minor 59 references

Valley polarization, Rashba interaction, and weak altermagnetism in inversion-asymmetric MnPS$_\text{3}|$WS$_\text{2}$ van der Waals heterostructures

T0 review · 4 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read A single van der Waals interface between monolayer MnPS3 and WS2 is predicted to host altermagnetic spin splitting, Rashba spin splitting, and valley polarization at once, with electric field and strain as control knobs.

desk verdict The paper shows plausible DFT evidence for coexisting altermagnetic, Rashba, and valley effects in a MnPS3|WS2 stack, but it has an internal band-alignment contradiction, never states what is new versus prior work, and ignores ~3.8% built-in strain on WS2. read the letter →

arxiv 2607.16454 v1 pith:FDASE7AO submitted 2026-07-17 cond-mat.mtrl-sci cond-mat.mes-hallcond-mat.str-el

Purba Dutta , Soumajyoti Bid , Nirmal Ganguli This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hallcond-mat.str-el

keywords vanderWaalsheterostructureMnPS3WS2altermagnetismRashbaspinsplittingvalleypolarizationspin-valleylockingBerrycurvature

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper predicts that putting a single WS2 monolayer on a MnPS3 monolayer produces an inversion-asymmetric interface that simultaneously behaves as an altermagnet, a Rashba spin-split semiconductor, and a valley-polarized system. It claims a direct band gap near 1.65 eV, with the conduction and valence band edges in WS2 (type-I alignment), and that both an out-of-plane electric field and in-plane biaxial strain can switch the alignment between type-I and type-II while modulating the spin and valley splittings. If true, one material interface—not a stack of separately engineered layers—could serve as a tunable building block for spintronic and valleytronic devices. The result matters because altermagnetism, Rashba physics, and valleytronics are usually pursued in different materials.

What carries the argument

The argument rests on three effective Hamiltonians plus the symmetry analysis that justifies them. At the Q point, a two-band model with sixth-order momentum terms (k₊⁶ ± k₋⁶) produces the alternating spin splitting with six nodal lines that defines the i-wave altermagnet. At Γ, a linear Rashba Hamiltonian H = H₀ + α_R(k_x σ_y − k_y σ_x) fits the helical valence-band spin texture with α_R ≈ 0.4. At K/K̄, a k·p Hamiltonian with Dirac, mass, and spin-orbit terms—including a valley-Zeeman term—yields valley splitting and a spin- and valley-dependent Berry curvature. The symmetry backbone is the interface point group C₃: inversion is broken by the heterogeneous stacking while a threefold rotatio

What would settle it

Spin- and angle-resolved photoemission on a MnPS3|WS2 stack: the coexistence claim is refuted if no helical Rashba texture appears near Γ or if the bands near the Q point remain spin-degenerate instead of showing the predicted six sign-alternating nodal lines.

Watch

Extended reading notes

Core claim

The central claim is that the deliberate lack of inversion symmetry at the MnPS3|WS2 interface turns an ordinary antiferromagnetic/semiconductor bilayer into a single platform where three spin-orbit phenomena coexist. In the valence band near Γ the heterostructure shows a Rashba-type helical spin texture (Rashba coefficient α_R ≈ 0.4); in the conduction band the K and K̄ valleys split by about 2.5 meV for one stacking geometry, reaching up to 3.5 meV under an electric field of −0.18 V/Å; and away from high-symmetry points the otherwise degenerate opposite-spin bands split with a six-nodal-line pattern characteristic of i-wave altermagnetism. These effects are traced to the C₃ point group and

Load-bearing premise

The calculation models the interface by compressing a 2×2 WS2 sheet by about 3.8% so it fits the MnPS3 lattice and calls that the zero-strain starting point; if the real interface instead relaxes into a Moiré pattern, the predicted gap, the few-meV splittings, and the six nodal lines could all change.

Editorial extensions

If this is right

A single MnPS3|WS2 interface could provide altermagnetic, Rashba, and valley-selective spin-orbit functionality on one stack, removing the need to combine separate materials.
An electric field can reversibly switch the band alignment between type-I and type-II and drive the valley splitting through values up to about 3.5 meV, including sign changes near −0.18 V/Å.
In-plane biaxial strain tunes the gap, alignment, and Rashba splitting, with tensile strain strengthening the Rashba texture and strong compressive strain suppressing it.
The altermagnetic spin splitting is reported to persist over the studied electric-field range, indicating that the magnetic order and its associated band splitting survive the tuning.
The effective Hamiltonians imply finite, spin- and valley-dependent Berry curvature with opposite signs at K and K̄, so valley-contrasting transport and optical responses should be observable if the model is correct.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the zero-strain reference already compresses a free-standing 2×2 WS2 sheet by about 3.8% to match the MnPS3 lattice; a physical Moiré stack may show different gap and splitting magnitudes, so the quantitative predictions deserve retesting in a larger supercell.
Beyond the paper: if the altermagnetic and valley splittings share the same Mn-sublattice environment, reversing the electric-field polarity or switching the Néel vector could flip spin and valley contrasts together, offering a magnetoelectric memory readout.
Beyond the paper: the predicted few-meV valley splitting should be visible as a circular-polarization difference in exciton photoluminescence; a null result there would localize the failure in the commensurate-cell model rather than in the coexistence idea.
Beyond the paper: the fitted model parameters give an explicit map—Rashba coefficient and valley splitting versus field and strain—that could be tested independently by spin-resolved photoemission and Kerr rotation measurements.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's the two-minute version. The core observation—a single MnPS3|WS2 interface showing altermagnetic spin splitting, Rashba spin textures, and valley splitting in the same DFT bands—is plausible and directly evidenced in the band structures. But before you trust the numbers, know two things: the paper contradicts itself on the band alignment (type-I in the abstract/conclusion, type-II in Sec. III.A), and it never explains what's new relative to Ref [25], which already reported similar phenomena in MnPS3/TMDC heterostructures. Also, the "zero strain" cell pins WS2 to the MnPS3 lattice with about 3.8% compression, unacknowledged.

What is actually new is the quantitative detail for this specific interface: the Γ-point Rashba coefficient, the stacking-dependent 2.5 meV valley splitting for stacking I, the field-driven 3.5 meV splitting with sign reversal, and the strain/EEF-driven band-alignment switching. The DFT setup (PBE+U, vdW-corrected, three stackings) is standard, and the key observations—six nodal lines for i-wave altermagnetism, helical Rashba textures, stacking-selective valley splitting—are shown directly. The effective Hamiltonians are symmetry-guided and fitted to the DFT bands; that's fine for interpreting the bands, not independent confirmation.

The soft spots, in order of importance:

1. Band-alignment contradiction. Abstract and conclusions say type-I; Sec. III.A says type-II at zero field. The strain and field sections use both references. A reader cannot tell which is meant. Easy fix, but currently corrosive.

2. Built-in strain. The "zero-strain" reference already compresses WS2 by ~3.8% relative to its free-standing lattice. If the physical interface forms a moiré, the global C3 and 2' symmetries behind the altermagnetic and valley analysis are only local. The qualitative coexistence may survive, but the quantitative numbers (1.65 eV gap, 2.5/3.5 meV splittings, even the nodal-line pattern) belong to a specific strained commensurate stack. This should be stated and discussed.

3. Model circularity. The fitted model coefficients (α_R, the K/K̄ parameters) reproduce the DFT bands, and the altermagnetic λ and μ are not quoted. That's acceptable for interpretation, but the Berry curvature and spin-valley locking claims are not independent predictions. A minor issue.

4. Missing checks. No U-sensitivity, no input files. A referee will want at least one other U value and a statement that the qualitative results are robust.

Who gets value: people working on vdW spintronics, valleytronics, and altermagnetism. It deserves a serious referee because the coexistence claim is potentially important and the evidence is direct. I'd send it to peer review, but expect heavy revision: fix the alignment characterization, add an explicit delta vs Ref [25], acknowledge the strain reference, and add the basic convergence checks. If those are handled, it's publishable.

Referee Report

4 major / 4 minor

Summary. The paper reports DFT+U calculations of MnPS3|WS2 van der Waals heterostructures in three stacking configurations, using a 2×2 WS2 supercell placed on the MnPS3 lattice. The main claims are: a direct band gap of about 1.65 eV, an altermagnetic spin splitting without spin-orbit coupling along K1→K2 with a sixfold 'i-wave' nodal structure, Rashba-like helical spin textures at Γ, a stacking-dependent conduction-band valley splitting of 2.5 meV in configuration I, and electric-field/strain tunability including type-I/II band-alignment transitions and a maximum valley splitting of 3.5 meV at EEF = −0.18 V/Å. Symmetry-adapted effective Hamiltonians are introduced for the altermagnetic Q-point, the Rashba Γ-point, and the K/K̄ valleys, and a Berry-curvature expression is derived and used for model outputs.

Significance. If the results hold, the paper would provide a single native vdW interface in which altermagnetic order, Rashba spin splitting, spin-valley locking, and valley polarization coexist and respond to external field and strain — a genuinely attractive prospect for spintronic and valleytronic applications. The work has concrete strengths: direct DFT calculations are reported for multiple stackings; the altermagnetic splitting without SOI is presented in the dispersion and isoenergetic plots (Figs. 5, 6); the Rashba spin textures are explicitly shown (Fig. 8); and the analytic two-band Berry-curvature derivation is given in Appendices A and B. The manuscript is nevertheless not yet in publishable form because at least one central claim is internally inconsistent and the simulation-cell strain state is not disclosed.

major comments (4)

[Sec. III.A, Abstract, Sec. IV] The band alignment is stated to be type-II in Sec. III.A ('suggesting a direct band gap of ∼1.65 eV and type-II band alignment at the K and K̄ points'), while the Abstract and Sec. IV state type-I ('The band-edge states show type-I band alignment'). Section III.E and Fig. 14 also imply zero-field type-I. Since the electric-field/strain tuning of the type-I ↔ type-II transition is one of the paper's headline claims, the actual zero-field alignment must be established unambiguously and stated consistently throughout.
[Sec. II, Sec. III.D] The simulation cell pins a 2×2 WS2 supercell to the MnPS3 lattice constant a = 6.067 Å, whereas the optimized 2×2 WS2 cell is 2×3.154 = 6.308 Å. The ε = 0 reference is therefore already under about 3.8% biaxial compression. This is nowhere stated. The altermagnetic symmetry analysis in Sec. III.B relies on global C3 and magnetic little co-group 2′; all reported numbers (1.65 eV gap, 2.5/3.5 meV valley splittings, α_R ≈ 0.4, six nodal lines) are properties of this particular coherently strained commensurate stack. The authors should explicitly discuss whether this model represents the physical Moiré-forming interface, and what near-field and symmetry-lowering effects may do to the claimed coexistence. This is load-bearing for the Abstract's promise of a physical multifunctional interface.
[Secs. III.B.1, III.C.1–2] The effective Hamiltonians are central to the interpretation, but the altermagnetic coefficients λ and μ in Eqs. (2)–(3) are never quoted, so Fig. 6(c,d) cannot be reproduced or quantitatively connected to the DFT splitting. Similarly, the K/K̄ model parameters v_F, Δ, δ, λ_i, λ_u, λ_v are given in the Fig. 10 caption but no provenance (fitting procedure, error bars, or comparison with a direct DFT Berry-curvature calculation) is provided. The Berry curvature in Eq. (7)/Fig. 10 is thus model-derived from parameters fitted to the same DFT bands, not an independent DFT prediction. Please report all fitted parameters and, if the Berry-curvature claim is to be made for the material, compute it directly from the DFT wave functions or at least show that the model faithfully reproduces the DFT band structure and spin texture.
[Sec. III.E, Fig. 15] The field-dependent valley splitting is described as investigated 'in the type-II stacking configuration,' which is not defined: is this stacking configuration II, or the type-II band-alignment regime? The distinction matters because the zero-field 2.5 meV valley splitting was found only in stacking configuration I (Fig. 9), whereas Fig. 15 shows large splittings (up to 3.5 meV) at negative EEF. Please specify which stacking and which band-alignment state is used for the field sweep, and reconcile this with the earlier statement that configurations II and III show no appreciable zero-field valley splitting.

minor comments (4)

[Fig. 2 caption / Sec. III.A] The electrostatic potential is said to be 'illustrated in Fig. 2(d)' in the text, but the caption labels it as panel (g). Please correct the cross-reference.
[Abstract/IV vs III.D] Related to the type-I/type-II contradiction: the sentence in Sec. III.D, 'the band alignment changes from type II to type I' under compressive strain, plus the Abstract's type-I claim, make it unclear what the zero-strain, zero-field alignment actually is. A single explicit definition and one consistent usage would remove the ambiguity.
[Appendices A–B] Minor typographical issues exist (e.g., 'yeilds' in Appendix B). More substantively, the derivation would benefit from stating at the outset that H is restricted to a single spin/valley sector so that the 2×2 form is explicitly justified.
[Sec. III.B] The statement that Eq. (2) 'preserves the magnetic point-group symmetry' while the second term is 'antisymmetric' is terse; a short group-theory table for the 2′ little co-group representations would help the reader verify the i-wave assignment.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central coexistence claims are direct DFT results, and the fitted effective Hamiltonians are transparently used as explanatory models, not as independent predictions.

full rationale

The paper's central claims—the direct gap (~1.65 eV), valence-band Rashba splitting, 2.5 meV and 3.5 meV valley splittings, and the six nodal lines of i-wave altermagnetism—are all obtained from DFT band-structure calculations (Figs. 4–9, 15). The effective Hamiltonians are introduced after the DFT results as symmetry-constrained interpretations: Eq. (2) is said to 'reproduce' the DFT spin splitting, Eq. (4) has α_R explicitly 'determined by fitting' the DFT bands, and the K/K̄ model is introduced 'to elucidate the microscopic origin' of the spin-valley locking already seen in DFT. The Berry curvature of Fig. 10 is computed 'using the fitted parameters of the model Hamiltonian,' which is an interpretive repackaging rather than an independent prediction used to establish the abstract's main results. The self-citations (e.g., refs. 16, 23, 24, 46, 47) are contextual references for standard Rashba and altermagnetism formulations and do not carry a load-bearing uniqueness argument. The strain-reference issue (WS2 already compressed by ~3.8% at ε=0) is a modeling/representativeness concern that affects external validity, but it is not circular: no derived quantity is defined in terms of itself, and the calculations are not fitted to the conclusions they are used to support. Under the quoted-evidence standard, no specific reduction of a claimed result to its own input can be exhibited.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper's quantitative claims rest on one hand-chosen U value, a strain-mismatched supercell whose built-in strain is unacknowledged, and effective models whose coefficients are fitted to the DFT bands. The DFT band structures themselves are the primary evidence; the model 'derivations' add interpretation rather than independent confirmation.

free parameters (5)

Hubbard U_eff on Mn 3d = 5 eV
Chosen by hand in Sec. II (Dudarev +U). Controls the 1.65 eV gap, 4.59–4.61 μB moments, and the altermagnetic/valley splitting magnitudes. No U-sensitivity scan is reported.
Rashba coefficient α_R (Eq. 4) = ≈ 0.4 (units not stated)
Sec. III.C.1: 'we determine the Rashba coefficient α_R ≈ 0.4 by fitting the DFT-obtained bands to Eq. (4)'. Used to claim Rashba splitting at Γ; obtained by fit, not derivation.
K/K̄ model parameters (v_F, Δ, δ, λ_i, λ_u, λ_v) = v_F=1.23×10^5 m/s; Δ=−0.075 eV; δ=0.07 meV; λ_i=0.072 meV; λ_u=0.06 meV; λ_v=0.072 meV
Fig. 10 caption: Berry curvature 'computed using the fitted parameters of the model Hamiltonian'. Parameters are fit to the DFT band dispersion, so the spin-valley locking and Berry curvature conclusions are not independent of the DFT input.
Altermagnetic model coefficients λ and μ (Eqs. 2–3) = not stated
Sec. III.B.1: model is 'constrained by the magnetic point group 2′' and chosen to reproduce the DFT nodal structure (Fig. 6(c,d)); numerical values of λ and μ are never quoted.
Built-in WS2 strain in the heterostructure cell = ≈ −3.8% (compressive)
Sec. II: heterostructure uses the MnPS3 lattice constant a=6.067 Å with a 2×2 supercell of WS2 (free-standing 2×3.154=6.308 Å). WS2 is therefore compressed ~3.8% at 'zero strain' — an unacknowledged constraint on all zero-field results and on the strain reference ε=0.

assumptions (5)

domain assumption GGA-PBE + Hubbard U (U_eff=5 eV) with DFT-D2 corrections gives the ground-state electronic structure of the heterostructure.
Sec. II: used throughout; no functional or U-sensitivity benchmark is provided, and PBE+U is known to underestimate gaps and moments (the paper concedes the moment underestimation in Sec. III.A).
domain assumption The relaxed heterostructure preserves the C3 point group and the magnetic little co-group 2′ at the Q-point.
Sec. III.B: the altermagnetic classification and the six nodal lines depend on this symmetry reduction; the paper does not explicitly verify the space group of the relaxed structure.
ad hoc to paper A 2×2 WS2 supercell coherently strained to the MnPS3 lattice faithfully represents the physical interface.
Sec. II: the ~3.8% lattice mismatch is never mentioned; a Moiré or fully relaxed supercell could give different hybridization, gap, and splittings.
domain assumption The low-energy physics at K/K̄ is described by the two-band massive Dirac Hamiltonian (Eq. 5) with the fitted parameters.
Sec. III.C.2: standard k·p model; the spin- and valley-dependent Berry curvature follows from this model, not from an independent DFT Berry-curvature calculation.
standard math The i-wave altermagnetic Hamiltonian (Eqs. 2–3) contains the symmetry-allowed terms relevant around Q.
Sec. III.B.1: sixth-order harmonics are the lowest terms allowed by 2′ symmetry; the model reproduces the DFT nodal pattern, but coefficients are unconstrained by measurement.

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Cite this review

Pith. "Pith review of Valley polarization, Rashba interaction, and weak altermagnetism in inversion-asymmetric MnPS$_\text{3}|$WS$_\text{2}$ van der Waals heterostructures." pith.science (2026). https://pith.science/paper/FDASE7AO

@misc{pith2026260716454,
  author       = {Pith},
  title        = {Pith review of: Valley polarization, Rashba interaction, and weak altermagnetism in inversion-asymmetric MnPS$_\text3|$WS$_\text2$ van der Waals heterostructures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FDASE7AO}},
  note         = {Machine review of arXiv:2607.16454}
}

abstract

The deliberate breaking of inversion ($\mathcal{P}$) symmetry in antiferromagnets has recently emerged as an effective means to induce various features, such as the emergence of Berry curvature, spin-valley locking, magnetoelectric coupling, and the transition from conventional antiferromagnetism to altermagnetism. Conversely, in non-magnetic systems, inversion symmetry breaking in the presence of strong spin-orbit interaction (SOI) gives rise to momentum-dependent spin splitting via the Rashba effect, enabling tunable spin polarization through external electric fields. Motivated by recent advances in two-dimensional materials, we perform first-principles calculations based on density functional theory to investigate the van der Waals (vdW) heterostructure formed by a $\mathcal{P}$-symmetric MnPS$_3$ monolayer and a WS$_2$ monolayer. We demonstrate that the interface hosts a rich interplay of emergent phenomena, including an altermagnetic phase, Rashba spin splitting, spin-valley locking, and valley polarization. Our results demonstrate that the heterostructure exhibits semiconducting behavior with a direct band gap of approximately 1.65~eV and a type-I band alignment. Remarkably, the electronic structure and band alignment can be effectively tuned between type-I and type-II regimes via an external electric field and in-plane biaxial strain. Furthermore, field-induced modulation enables strong control over the altermagnetic phase and the valley splitting. These findings establish the proposed vdW heterostructure as a highly tunable platform with significant potential for spintronic and valleytronic applications.

Figures

Figures reproduced from arXiv: 2607.16454 by the authors.

**Figure 4.** FIG. 4. Panels (a), (b), and (c) show the spin-polarized band dispersion of the heterostructure, for the stacking configurations [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 6.** FIG. 6. Panels (a) and (b) show the spin-polarized 3D band [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

Figures from the paper (8 more)

**Figure 8.** Figure 8: FIG. 8. The spin-textures for the highest pair of valence bands [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 9.** Figure 9: FIG. 9. The band dispersion of MnPS [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

**Figure 10.** Figure 10: FIG. 10. The band splitting at the high-symmetry points [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

**Figure 11.** Figure 11: FIG. 11. In-plane biaxial strains are applied on the MnPS [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

**Figure 12.** Figure 12: FIG. 12. The spin-textures for the highest two valence bands [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]

**Figure 13.** Figure 13: FIG. 13. The electric field dependent band splitting of the [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]

**Figure 14.** Figure 14: FIG. 14. The variation of band alignment, interlayer distance, and electric field induced band splitting in the MnPS [PITH_FULL_IMAGE:figures/full_fig_p013_14.png]

**Figure 15.** Figure 15: FIG. 15. The variation of band dispersion near the valley points with the applied electric field in the momentum space and [PITH_FULL_IMAGE:figures/full_fig_p014_15.png]

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We employ density functional theory (DFT) using the vaspcode [35, 36], which utilizes a plane wave basis set along with the projector augmented wave (PA W) method [37]

axes; mirror symmetry across the [001], [110], [100], and [010] planes; three-fold rotational symmetry both anticlockwise and clockwise about the [001] axis; six-fold anticlockwise and clockwise rotational symmetry with its inversion about the [001] axis; and the identity oper...

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

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How- ever, once we move away from theK-point, a small but clear altermagnetic spin splitting appears along the path K1 →K 2 (see Fig

Effective two-band model Hamiltonian at theQ-point without SOI In the MnPS 3|WS2 heterostructure, the underlying magnetic symmetry keeps the bands spin-degenerate along certain directions in the Brillouin zone. How- ever, once we move away from theK-point, a small but clear altermagnetic spin splitting appears along the path K1 →K 2 (see Fig. 3(e) (inset)...

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Since our DFT calculations show negligible MAE, an out-of-plane easy-axis orientation is adopted for the investigation of valley features present in the band dispersion

⃗k·⃗ pmodel Hamiltonian atK/ ¯Kpoint with SOI Spin-valley locking and valley polarization are some of the most useful features of 2D materials and het- erostructures, with a variety of interesting outcomes and envisaged applications. Since our DFT calculations show negligible MAE, an out-of-plane easy-axis orientation is adopted for the investigation of v...

2019

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Effective two-band model Hamiltonian atΓpoint with SOI The MnPS 3|WS2 heterostructure exhibitsC 3 point group symmetry, lacking an inversion center. This ab- sence of inversion symmetry and SOI associated with W atoms, combined with a built-in electrostatic po- tential difference across the heterostructure, leads to momentum-dependent Rashba spin splittin...

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