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arxiv: 2604.21613 · v1 · submitted 2026-04-23 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

Emergence of a non-bulk hexagonal Fe₂S₂ single layer via phase transformation

Affan Safeer , Wejdan Beida , Felix Oberbauer , Nicolae Atodiresei , Gustav Bihlmayer , Max Wolfertz , Chiara Schlichte , Wouter Jolie
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Stefan Bl\"ugel Jeison Fischer Thomas Michely
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Pith reviewed 2026-05-09 21:17 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall
keywords 2D materialsiron sulfidephase transformationmackinawiteβ-CuI structuregraphene substratescanning tunneling microscopydensity functional theory
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The pith

A hexagonal Fe₂S₂ single layer with β-CuI structure forms by thermal transformation of mackinawite grown on graphene.

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

The paper shows that confining iron sulfide to a single atomic layer can stabilize a crystal structure that does not exist in bulk form. Starting from single-layer mackinawite on a graphene-covered iridium surface, heating triggers a change to a hexagonal lattice whose measured spacing and electronic features match the β-CuI arrangement, a buckled double honeycomb of FeS sheets. Experiments track the transformation in real time through scanning tunneling microscopy and low-energy electron diffraction, while calculations identify the structure and indicate that electron correlations and magnetism help hold it together. The work treats the new layer as an example of how reduced dimensionality alone can open access to otherwise inaccessible Fe-S phases.

Core claim

A previously unknown hexagonal Fe₂S₂ single layer with β-CuI structure, consisting of two vertically stacked and buckled FeS honeycomb lattices, appears through thermally driven phase transformation of single-layer mackinawite on graphene/Ir(111). In-situ STM and LEED document the shift from tetragonal to hexagonal order together with distinct morphological and electronic changes; first-principles calculations select the β-CuI geometry as the best match and find that on-site Coulomb repulsion plus magnetic order contribute to its stability. The initial preference for mackinawite nucleation is attributed to its low edge energy.

What carries the argument

The β-CuI structure, a buckled bilayer of FeS honeycombs whose lattice parameters and electronic signatures are matched by calculations that include on-site Coulomb interactions and magnetic order.

If this is right

  • Fe₂S₂ single layers become a platform for studying structural polymorphism in two dimensions.
  • Reduced dimensionality alone can stabilize crystal phases unavailable in three-dimensional bulk Fe-S compounds.
  • On-site Coulomb interactions and magnetic order are relevant to the energetic stability of the new 2D Fe-S layer.
  • Single-layer mackinawite nucleates in preference to other phases because of its low edge energy, even when it is not the lowest-energy structure overall.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same annealing-driven route could be tested on other transition-metal chalcogenide monolayers to generate additional non-bulk 2D phases.
  • Magnetic ordering in the β-CuI layer may produce distinct spin-dependent electronic properties that differ from bulk iron sulfides.
  • Changing the supporting substrate could shift the relative stability of mackinawite versus the hexagonal phase and thereby control which structure forms.

Load-bearing premise

The measured hexagonal lattice constants and electronic signatures correspond uniquely to the β-CuI arrangement rather than to any other possible Fe₂S₂ configuration or substrate-induced distortion.

What would settle it

An atomic-resolution STM image or LEED pattern recorded after annealing that shows lattice vectors or symmetry incompatible with the calculated β-CuI Fe₂S₂ parameters would disprove the structural assignment.

Figures

Figures reproduced from arXiv: 2604.21613 by Affan Safeer, Chiara Schlichte, Felix Oberbauer, Gustav Bihlmayer, Jeison Fischer, Max Wolfertz, Nicolae Atodiresei, Stefan Bl\"ugel, Thomas Michely, Wejdan Beida, Wouter Jolie.

Figure 1
Figure 1. Figure 1: Tetragonal single layer mackinawite (t-Fe [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Hexagonal single layer Fe2S2 in β-CuI-structure (h-Fe2S2). (a) Overview STM topograph after annealing sample in Figure 1a at 850 K (Vb = 1.8 V, It = 50 pA, 400 nm × 250 nm.) Inset in lower left corner is atomic resolution topograph (Vb = 100 mV, It = 2 nA, 4 nm × 4 nm.) of t-Fe2S2 (Vb = −100 mV, It = 1 nA, 5 nm × 5 nm). Unit cell is indicated by black rhombus. (b) STM line profile along blue line in (a). (… view at source ↗
Figure 3
Figure 3. Figure 3: STM annealing sequence of Fe2S2. After growth of Fe2S2 at 350 K the sample was annealed in subsequent steps of 300 s at the temperatures indicated in (a) to (f). In (a), all visible islands are t-Fe2S2. In (b) and (c) ’h’ highlights all h-Fe2S2 islands while in (d) ’t’ identifies remaining t-Fe2S2 islands. STM parameters: (a) Vb = 2.0 V, It = 50 pA; (b) Vb = 2.0 V, It = 50 pA; (c) Vb = 1.3 V, It = 70 pA; (… view at source ↗
Figure 4
Figure 4. Figure 4: LEED annealing sequence of Fe2S2. After the same annealing steps as in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Dependence of Fe2S2 structure on growth temperature. (a)-(c) Same amount of Fe deposited in identical S background pressure of 5 × 10−9 mbar at the temperatures indicated. The label ’h’ indicates areas of h-Fe2S2 while all other island areas are t-Fe2S2. STM parameters: (a) Vb = 0.9 V, It = 60 pA; (b) Vb = 1.1 V, It = 90 pA; (c) Vb = 1.5 V, It = 50 pA. All images 200 nm × 180 nm. STM data taken at 300 K [… view at source ↗
Figure 6
Figure 6. Figure 6: (a), (b) Total energy per Fe atom in (a) with respect to [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

Two-dimensional materials can stabilize crystal structures that are absent from their bulk counterparts, offering opportunities for materials design. Here, we report the synthesis of a previously unknown hexagonal Fe$_2$S$_2$ single layer with $\beta$-CuI structure, a buckled layer of two vertically stacked FeS honeycomb lattices, realized by thermally induced transformation of single layer mackinawite grown on graphene/Ir(111). In situ scanning tunneling microscopy and low-energy electron diffraction reveal a transition from a tetragonal to a hexagonal lattice accompanied by distinct morphological and electronic signatures. The hexagonal Fe$_2$S$_2$ forms reproducibly upon annealing and represents a new structural motif within the Fe-S material family. First-principles calculations identify the $\beta$-CuI structure as most consistent with experiment. The calculations suggest that on-site Coulomb interactions and magnetic order are relevant to understanding the stability of the new 2D Fe-S compound. The preferred nucleation of single-layer mackinawite, despite being energetically disfavored, is speculated to result from its low edge energy, analogous to the 3D case. Our results establish Fe$_2$S$_2$ as a platform for exploring structural polymorphism in two dimensions and demonstrate that reduced dimensionality can stabilize crystal structures not accessible in bulk materials.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript reports the synthesis of a previously unknown hexagonal Fe₂S₂ single layer with β-CuI structure (a buckled bilayer of two FeS honeycomb lattices) via thermally induced transformation of single-layer mackinawite grown on graphene/Ir(111). In-situ STM and LEED provide direct evidence of the tetragonal-to-hexagonal lattice transition with accompanying morphological and electronic changes; first-principles DFT calculations are used to identify the structure as most consistent with experiment and to highlight the role of on-site Coulomb interactions and magnetic order in its stability.

Significance. If the structural assignment holds, the work demonstrates that reduced dimensionality can stabilize non-bulk crystal structures in the Fe-S system, establishing a new platform for exploring polymorphism in 2D materials. The in-situ experimental evidence from STM and LEED is a clear strength, offering direct observation of the phase change without reliance on ex-situ transfer artifacts, while the computational component provides useful insight into electronic factors; reproducible nucleation of the mackinawite precursor is also noted as an interesting observation.

major comments (3)
  1. [DFT identification section] DFT identification section: the claim that the β-CuI structure is the unique match to the observed hexagonal lattice, morphology, and electronic signatures is not supported by an exhaustive enumeration of competing 2D Fe₂S₂ candidates (different buckling amplitudes, lateral shifts, vacancy orderings, or Fe/S ratios). Without this, the assignment remains sensitive to the specific choice of Hubbard U and spin polarization, as alternative motifs could reproduce the experimental lattice constant once parameters are tuned.
  2. [Computational methods and results] Computational methods and results: the stability analysis emphasizes that on-site Coulomb interactions and magnetic order are relevant, yet no sensitivity analysis or error bars on the Hubbard U parameter for Fe are provided to demonstrate how the energy ordering or structural preference changes with U (a free parameter in the calculations). This weakens the assertion that these factors are necessary rather than protocol-dependent.
  3. [LEED and STM results section] LEED and STM results section: while the tetragonal-to-hexagonal transition is observed, the manuscript lacks quantitative pattern simulation or intensity analysis of the LEED spots to rule out alternative hexagonal arrangements that might produce similar diffraction under the same substrate registry.
minor comments (3)
  1. [Discussion] The speculation in the discussion that preferred nucleation of single-layer mackinawite results from low edge energy (analogous to 3D) would benefit from a brief supporting calculation or additional reference to edge-energy studies in related 2D systems.
  2. [Figure captions] STM image figure captions should explicitly state bias voltages, tunneling currents, and scale bars to facilitate direct comparison with the DFT-simulated images.
  3. [Abstract and introduction] Notation consistency: the structure is referred to as both 'hexagonal Fe₂S₂' and 'β-CuI Fe₂S₂'; a single consistent descriptor in the abstract and early sections would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We have carefully considered each point and provide point-by-point responses below. Where appropriate, we have revised the manuscript to address the concerns raised.

read point-by-point responses

  1. Referee: [DFT identification section] DFT identification section: the claim that the β-CuI structure is the unique match to the observed hexagonal lattice, morphology, and electronic signatures is not supported by an exhaustive enumeration of competing 2D Fe₂S₂ candidates (different buckling amplitudes, lateral shifts, vacancy orderings, or Fe/S ratios). Without this, the assignment remains sensitive to the specific choice of Hubbard U and spin polarization, as alternative motifs could reproduce the experimental lattice constant once parameters are tuned.

    Authors: We agree that an exhaustive enumeration of all conceivable 2D Fe₂S₂ configurations would strengthen the structural assignment. While a fully exhaustive search is computationally prohibitive, we have now performed additional DFT calculations on several key alternative structures, including variations in buckling amplitude, lateral shifts between the two FeS layers, and selected vacancy orderings consistent with the observed stoichiometry. These results are added to the revised Supplementary Information and confirm that the β-CuI structure provides the best overall agreement with the experimental lattice constant, morphology, and electronic signatures. We have also clarified in the main text that our identification relies on the most plausible candidates dictated by the observed symmetry and Fe:S ratio rather than claiming uniqueness without qualification. revision: yes

  2. Referee: [Computational methods and results] Computational methods and results: the stability analysis emphasizes that on-site Coulomb interactions and magnetic order are relevant, yet no sensitivity analysis or error bars on the Hubbard U parameter for Fe are provided to demonstrate how the energy ordering or structural preference changes with U (a free parameter in the calculations). This weakens the assertion that these factors are necessary rather than protocol-dependent.

    Authors: We acknowledge the value of demonstrating robustness with respect to the Hubbard U parameter. In the revised manuscript, we have included a sensitivity analysis for U values ranging from 0 to 6 eV, showing the relative energies of the β-CuI structure compared to competing motifs. The energetic preference for the β-CuI structure and the stabilizing effect of magnetic order remain consistent across this range. We now report error bars derived from the variation with U and have updated the discussion to reflect that these factors are relevant within the tested parameter space. revision: yes

  3. Referee: [LEED and STM results section] LEED and STM results section: while the tetragonal-to-hexagonal transition is observed, the manuscript lacks quantitative pattern simulation or intensity analysis of the LEED spots to rule out alternative hexagonal arrangements that might produce similar diffraction under the same substrate registry.

    Authors: We agree that quantitative dynamical LEED simulations would offer additional rigor. However, such analysis requires specialized expertise and resources beyond the scope of the present study. In the revised manuscript, we have expanded the discussion of the LEED patterns with a more detailed qualitative comparison to the expected diffraction spots for the β-CuI structure under the graphene/Ir(111) registry. Combined with the atomic-resolution STM images and the distinct electronic signatures observed in tunneling spectroscopy, this multi-probe evidence continues to support the assigned structure while making the limitations of the diffraction data explicit. revision: partial

Circularity Check

0 steps flagged

No circularity; experimental synthesis and DFT identification are independent

full rationale

The paper's central claim rests on direct experimental observations via in situ STM and LEED of a tetragonal-to-hexagonal lattice transition upon annealing, with the new phase identified as β-CuI Fe₂S₂ by matching to first-principles calculations. No derivation step reduces the reported structure, stability, or nucleation preference to a self-definition, a fitted parameter renamed as a prediction, or a load-bearing self-citation chain. The DFT results are used for post-hoc consistency checking rather than constructing the experimental outcome by definition, and the speculation on edge-energy-driven nucleation is explicitly labeled as such without being used to derive the main result. This is a standard experimental-computational workflow that remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The stability conclusion depends on DFT with on-site Coulomb interactions and magnetic order whose specific parameter values are not detailed in the abstract; standard DFT approximations are invoked without independent verification of their applicability to this system.

free parameters (1)
  • Hubbard U parameter for Fe
    On-site Coulomb interactions are stated as relevant to stability; this is a typical adjustable parameter in DFT+U calculations whose value is chosen to match experiment or prior literature.
axioms (1)
  • domain assumption Standard approximations in density functional theory accurately capture the relative stability of Fe-S structures when augmented with Hubbard U and magnetic order.
    Invoked to identify the β-CuI structure as most consistent with experiment.

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