# Reactive molecular beam epitaxy growth of a 1T-FeS 2 single-layer-atomic structure, moiré, and decoupling via intercalation

Mahesh Krishna Prabhu, Philippe David, Valérie Guisset, Lucio Martinelli, Johann Coraux, Gilles Renaud

► To cite this version:

Mahesh Krishna Prabhu, Philippe David, Valérie Guisset, Lucio Martinelli, Johann Coraux, et al. Reactive molecular beam epitaxy growth of a 1T-FeS 2 single-layer-atomic structure, moiré, and decoupling via intercalation. ACS Nano, 2025, 19 (14), pp.13941-13951. 10.1021/acsnano.4c17873. hal-05015271

HAL Id: hal-05015271

https://hal.science/hal-05015271v1

Submitted on 1 Apr 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Reactive Molecular Beam Epitaxy Growth of a 1T-FeS₂ Single-Layer–Atomic Structure, Moiré, and Decoupling via Intercalation

Mahesh Krishna Prabhu,* Philippe David, Valérie Guisset, Lucio Martinelli, Johann Coraux, and Gilles Renaud*

<figure><img src="image_2.png" /></figure>

Cite This: https://doi.org/10.1021/acsnano.4c17873

<figure><img src="image_3.png" /></figure>

Read Online

## ACCESS

<figure><img src="image_4.png" /></figure>

Metrics & More

<figure><img src="image_5.png" /></figure>

Article Recommendations

<figure><img src="image_6.png" /></figure>

Supporting Information

**ABSTRACT:** Two-dimensional (2D) iron disulfide (FeS₂), in its 1T polymorph, is a promising candidate for high-Curie-temperature ferromagnetic applications. Unlike typical van der Waals materials, FeS₂ lacks a naturally lamellar bulk structure and thus cannot be prepared by exfoliation. Consequently, it exists solely as a synthetic 2D magnet, primarily produced via chemical vapor deposition. Here, we propose an alternative synthesis method: reactive molecular beam epitaxy, where an iron layer predeposited on a Au(111) substrate is sulfurized to form FeS₂. Structural and compositional analyses of the resulting 2D layer—employing scanning tunneling microscopy, electron diffraction, Auger electron spectroscopy, and synchrotron surface X-ray diffraction—confirm a nominal Fe ratio of 1:2, essential for achieving a high Curie temperature. Modeling and fitting the three-dimensional X-ray diffraction data further reveals that the layer crystallizes in the desired 1T polymorph. This 1T-FeS₂ grown on Au(111) exhibits exceptional crystalline quality, largely surpassing that of other 2D transition metal dichalcogenides epitaxially grown on substrates. In addition, it shows pronounced atomic distortions from an ideal 1T structure, attributed to the strain induced by the substrate to achieve a perfectly commensurate 5 × 5 moiré pattern. The 1T-FeS₂ and moiré atomic structures are fully determined with high accuracy on atomic coordinates. Finally, through Cs intercalation, we demonstrate complete decoupling of the FeS₂ layer from the substrate and the release of heteroepitaxial strains.

**KEYWORDS:** Two-dimensional, FeS₂, Moiré, GIXD, STM, MBE, intercalation

<figure><img src="image_7.png" /><figcaption>Single layer 2D 1T-FeS₂ synthesis and atomic structure</figcaption></figure>

## INTRODUCTION

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) are rich playgrounds for condensed matter and device physicists exploring spin-valley optoelectronics,¹,² ultimately thin field-effect transistors,³ or electron-correlated phases such as charge-density waves and superconductors.⁴,⁵ This class of materials has recently expanded to include magnetic materials. Like other 2D magnetic materials, they bring new concepts to spintronics, e.g. an extreme sensitivity to mechanical strain, the control of properties via interfaces, (e.g., by using proximity effects or electric fields), and the spatial modulation of magnetic interactions in moiré patterns between 2D layers.⁶ Among magnetic 2D transition metal dichalcogenides, at least two compounds have been identified as potential² high-Curie-temperature 2D ferromagnets with applications in mind: 1T-CrTe₂⁷⁻⁹ and more recently, 1T-FeS₂¹⁰⁻¹²

The latter raises interesting questions and challenges. First, it is predicted to be a high-spin compound with strong magnetic anisotropy, two properties that are favorable for a high Curie

temperature.¹¹ While a recent experimental report on magnetism in this new 2D compound has confirmed perpendicular magnetic anisotropy,¹⁰ the experimental assessment of the Curie temperature does yet meet these expectations.¹⁰,¹² It has been argued that, in 1T-FeS₂ grown by chemical vapor deposition, an uncontrolled amount of defects could limit the Curie temperature to about 10 K, well below the theoretical estimate of over 300 K.¹¹ In addition, strain has been predicted to have a strong effect on the magnetism in this compound by modifying the strength of the ferromagnetic spin-spin interactions.¹¹ The second interesting question relates to the ability to actually form the 1T targeted structure. In the 1:2 Fe:S stoichiometry, the stable bulk form is pyrite, which,

**Received:** December 10, 2024

**Revised:** March 22, 2025

**Accepted:** March 24, 2025

<figure><img src="image_8.png" /></figure>
despite having a nonlamellar structure, has been recently
exfoliated as a single layer with controversial magnetic
properties.<sup>13,14</sup> The routes to 1T-FeS<sub>2</sub> therefore require growth
from the bottom up. Chemical vapor deposition (CVD) is one
such route, and ferromagnetic ordering in CVD-grown few-
layer 1T-FeS<sub>2</sub> has been demonstrated recently.<sup>10,12</sup> However,
CVD also yields other kinds of Fe<sub>x</sub>S<sub>y</sub> 2D crystal structures, and
achieving uniform, high-quality single layers using this
synthesis route is a significant challenge.<sup>10,12</sup> Actually,
transition metals in general tend to adopt different oxidation
states, coordination numbers, and arrangements of chalcogen
atoms around them, making it challenging to form a given
crystal with a unique well-defined structure, as shown for e.g.
1T-TaS<sub>2</sub><sup>15,16</sup> or 1T-CrTe<sub>2</sub><sup>9,17</sup>

Here, we investigate an alternative approach using reactive
molecular beam epitaxy (rMBE), and a very fine *in situ* analysis
of the structure of the grown 2D material. The growth consists
of metal evaporation onto a selected substrate (in this case,
Au(111)) followed by *in situ* sulfurization under a H<sub>2</sub>S
atmosphere. This method has been successfully used to
 synthesize other 2D transition metal dichalcogenides, including
MoS<sub>2</sub><sup>18-24</sup> WS<sub>2</sub><sup>25</sup> TaS<sub>2</sub><sup>15,16,26,27</sup> RuS<sub>2</sub><sup>28</sup> and CoS<sub>2</sub><sup>29</sup> We
perform *in situ* structural analyses using scanning tunneling
microscopy (STM), electron diffraction (both low-energy,
LEED, and reflection high-energy, RHEED), Auger electron
spectroscopy (AES), and high-resolution grazing incidence
synchrotron surface X-ray diffraction (GIXD/SXRD). We
derive four main experimental results. First, the single layer
crystallizes exclusively in the 1T structure, and has an Fe/S
stoichiometry close to the nominal 1:2 ratio. Second, the
structural quality of the epitaxial 2D FeS<sub>2</sub> on Au(111) is
exceptionally high, comparable to that of the single-crystal
substrate. Third, surface X-ray crystallography reveals the
atomic structure within the unit cell of the moiré pattern,
showing pronounced in-plane and out-of-plane distortions of
the 1T structure according to a 5 × 5 commensurate moiré
pattern with the gold substrate. Fourth, while self-intercalation
of S or Fe in the as-grown material is ruled out, intentional
intercalation of Cs atoms is demonstrated. This weakens the
strong coupling of the 1T-FeS<sub>2</sub> layer to the substrate, reducing
moiré-related distortions, and is a reversible process.

RESULTS AND DISCUSSION

Morphological and Low-Resolution Structural Anal-
yses. After sulfurizing 0.4 ML of Fe on Au(111) at 573 K (see
Materials and Methods), STM reveals islands attached to the
atomic step edges of Au(111), altering their morphology as the
islands appear to ‘dig’ laterally into the Au terraces. These
islands, spaced hundreds of nanometers apart, extend from
several tens to a few hundreds of nanometers in size and
exhibit an apparent height generally lower than an atomic step
of Au(111) (Figure 1a, SI S1). The island heights were
measured with samples voltage ranging from 0.8 to 1.6 V, in
both empty and filled state scanning modes within an
uncertainty of ± 0.1Å. A closer view of the island surfaces
reveals a highly regular, nanoscale hexagonal pattern with a
periodicity of 1.44 nm (Figure 1b, SI S1). In the higher-
resolution image of Figure 1c, atomic-scale details become
visible, and the bright protrusions are presumed to correspond
to the electronic orbitals of S atoms. The unit cell is composed
of two triangular halves with slight contrast differences, similar
to observations by Kibsgaard et al.<sup>30</sup> Fourier transformation
(not shown) of these images indicates that the pattern fits four

interatomic distances within the 1.44 nm period, which also
aligns with five unit cells of the Au(111) surface. This
alignment suggests a commensurate 5 × 5 moiré pattern
between the lattice-mismatched, untwisted 2D FeS<sub>2</sub> and
Au(111), as we will confirm below with higher-resolution data.

Consistent with the STM images' Fourier transform, LEED
patterns, such as shown in Figure 1d, make the 5 × 5,
untwisted moiré pattern apparent. All spots are sharp and the
intensities of the moiré spots are similar to those of FeS<sub>2</sub> and
Au(111). This is indicative of a highly ordered moiré pattern,
with a well-defined orientation on the surface reflecting the
well-defined orientation of the 2D FeS<sub>2</sub>, and coming together
with a substantial modulation of FeS<sub>2</sub> and/or Au surface's
structure (see also, SI S1).

<figure><img src="image_9.png" /></figure>

Figure 1. (a) STM image (−1.5 V sample bias, 300 pA tunneling current) of single-layer 1T-FeS₂ islands grown on Au(111) by rMBE. Inset highlights the islands (black) and the substrate step edges (white). The amount of FeS₂ grown is far lower than 1 single layer. (b) Closer-scale STM image (−1.2 V, 300 pA, differentiated) of the islands marked with a `b' in the inset of (a), revealing the moiré of 1T-FeS₂/Au(111). (c) Atomic-scale STM image (−0.2 V, 700 pA) of the moiré. (d) LEED pattern (80 eV electron energy); diffraction spots from Au, 1T-FeS₂ and the moiré are highlighted with red, blue and yellow circles, respectively. The (0,0) spot is marked with a white circle, and is off-axis (electron beam not perpendicular to the surface).
<figure><img src="image_10.png" /><figcaption>Figure 2. a) A 77° sector map of the in-plane reciprocal space parallel to the surface of 2D FeS₂/Au(111) plotted on a logarithmic color scale. The intensity is integrated from L = 0.05 to 0.65. The different peaks are identified as due to Au, FeS₂ and the moiré pattern, along the H0 axis, at the bottom of the figure. The gray hexagons are the Brillouin zones of Au. b) High-resolution radial scan (logarithmic scale) along the [H,K = 0] direction. Rings of scattered intensities are seen in a). They arise from small Au polycrystals at the edges of the sample, an artifact of the crystal polishing from the manufacturer. The yellow dashed parallelogram is the 2D reciprocal unit cell of the 5 × 5 moiré pattern. The blue dashed parallelogram is the 2D reciprocal unit cell of FeS₂ (a 1 × 1 structure).</figcaption></figure>

At this stage, it is evident that the 2D layer displays a high degree of structural order, with a precise crystallographic orientation and minimal variation of its lattice parameter, which measures approximately 3.6 Å. This value is over 10% larger than the density functional theory calculation for a single FeS₂ layer in the 1T polytype,¹¹ and also exceeds the experimentally reported lattice parameter for CVD-grown 1T-FeS₂.¹² The stretching of the layer may indeed be advantageous; allowing it to form what appears to be a commensurate 5 × 5 moiré pattern with the substrate. While this alignment incurs an elastic energy penalty, it likely maximizes interfacial bonding with the substrate within a relatively small period of the moiré pattern.

**High-Resolution, Surface X-Ray Diffraction Characterization.** For the GIXD characterization, a 2D FeS₂ layer with almost 100% coverage of the Au(111) surface was prepared (see *Materials and Methods* section).

Figure 2a presents an in-plane reciprocal space map with the successive Brillouin zones of Au, centered at the (n,p) Γ points (with (n,p) ∈ Z²) where the CTRs of Au(111) are

intercepted, are depicted as gray hexagons. The 2D rods from 2D FeS₂ are apparent at the (4n/5,4p/5) H,K locations (yellow circles). Between two neighboring Au CTRs, four additional 2D rods are visible, including, along high symmetry directions, one from the parent FeS₂ phase. Altogether, the full set of peaks observed in the reciprocal space map can be precisely indexed with *H* = *i*/5 and *K* = *j*/5 coordinates, with (*i*,*j*) ∈ Z². An in-plane radial scan of the scattered intensity along the *K* = 0 direction (Figure 2b) summarizes the reciprocal lattice indexing, highlighting where the Au CTRs (red arrows), the FeS₂ 2D layer's rods (blue arrows), and the rods of the moiré pattern (orange arrows) are intercepted. Note that the Au, and/or FeS₂ and/or moiré rods are superimposed at specific locations. The period of the moiré pattern can be determined with a high precision, to 1.4432 ± 0.0004 nm, and the lattice parameter of FeS₂ as well, to 3.607 ± 0.004 Å. This value is in line with that obtained with samples produced by CVD¹² (smaller values, 7% lower, have also been reported via this technique¹⁰).
A unique aspect of FeS₂/Au(111) is its exceptionally high structural order, clearly indicated by the extreme sharpness of all surface peaks in the X-ray data. From the change in rocking scans peak widths with increasing in-plane momentum transfer Q// values, we estimate an average crystallite size of approximately 0.6 µm—an unusually large size—and a very small macroscopic mosaic spread of 4 × 10⁻⁴ radians, constrained only by that of the Au substrate (see SI, section S2). As the X-ray beam probes several mm of the sample, such a low macroscopic mosaic spread indicates that the large FeS₂ crystallites are highly aligned over the grains of the Au(111) substrate whose sizes, of several millimeters, exceed the FeS₂ domain sizes. The FeS₂ peaks are also notably narrow along the radial directions. Tracking their width along these directions at increasing Q// values reveals a similar crystallite size of about 0.55 µm, with only minor inhomogeneous variations in lattice parameter within or between these crystallites, as low as 0.0023 Å. This clearly demonstrates the very high crystalline quality of the 2D layer. By comparison, MoS₂/Au(111) and SPtSe/Pt(111) exhibit crystallite sizes more than ten times smaller,²³ while even TaS₂/Au(111), known for its high-quality epitaxial properties, has crystallite sizes that are several times smaller.¹⁶ Here, the FeS₂ crystallites are only limited by the steps of the Au substrate.

Such a high level of structural coherence may seem puzzling at first, given that the epitaxial relationship between 1T-FeS₂ and Au(111) is multiply degenerate: a 5 × 5 moiré pattern implies the existence of 25 energy-equivalent translational variants, and each of which may have a 180° twin rotational variant. However, on a (111) surface of a face-centered cubic crystal such as Au, the two 180° twin variants are not strictly equivalent; as it turns out, our SXRD measurements detect only one of the two possible orientations. This leaves 25 possible variants coexisting on the surface. From the STM (Figure 1a), it appears that the nucleation density of FeS₂ islands is low, more or less corresponding to the average distance between the substrate step edges (several 100 nm). It is therefore reasonable to assume that the islands each grow in one of the 25 possible variants and that their coalescence determines the microstructure of the entire 2D film. Where the islands coalesce, we exclude so-called antiphase boundaries (discommensurations) that accommodate the Angstrom-scale lateral shift of the crystal lattice between coalesced islands. Whether and how these boundaries relax (via more or less extended strain fields) is unknown, but the distance between these boundaries (which is related to the distance between island nuclei) corresponds to the crystallite size as assessed by the diffraction peak widths discussed in the previous paragraph. The near perfect angular alignment of FeS₂ with Au, the very large crystallite sizes, and the intense superstructure peaks in the *HK* maps all suggest a strong interaction with the Au substrate. Further supporting this view, some of the superstructure peaks, e.g. those at *H* = 1.8 and 2.6, are even more intense than the neighboring parent FeS₂ peaks at *H* = 1.6 and 2.4 (Figure 2b). Such a strong interaction is expected to affect the atomic positions in both the upper substrate layers and FeS₂, modulating them at the scale of the unit cell of the moiré pattern.

**Composition of the 2D Iron Sulfide.** To gain deeper insights into the chemical nature of the 2D FeS₂ layer, we analyzed our sample with AES. We performed the measurements in situ, keeping the sample in ultrahigh vacuum (UHV) all along the GIXD and AES characterizations (at the BM32

beamline of ESRF, see *Materials and Methods* section). The AES spectra (Figure 3) shows the signatures of Au, S (150 eV),

<figure><img src="image_11.png" /><figcaption>**Figure 3.** Auger electron spectrum of FeS₂ single-layer on Au(111), measured at room temperature.</figcaption></figure>

and Fe (580–710 eV). To determine the stoichiometry of the 2D layer, we first analyzed the intensities of the Fe and S components by accounting for the relative sensitivity factors and subtracting any potential Au contributions in the measured intensities (which is crucial concerning the S signature at 150 eV). An Fe:S ratio of 1:2.1 ± 0.1 is found, with an Fe coverage of 0.96 ± 0.05 ML relative to Au (see SI, section S3 for details). The small ~4% loss in surface coverage of Fe should not be a surprise. Indeed, the Fe surface density is obviously smaller in FeS₂ than in a pure Fe layer. Given the moderate temperature employed to assist the sulfurization process, we do not expect desorption of Fe to vacuum, but rather diffusion of the small excess of Fe atoms into the bulk of the substrate. The possible slight excess (0.1, i.e. within uncertainties) of sulfur derived from the AES data would point to the presence of dissociatively chemisorbed H₂S in the system, which can hardly be avoided. For the detailed calculation, we refer to the SI, section S3. The Fe:S ratio, being very close to 1:2, indicates the presence of two atomic S layers for every atomic Fe layer, strongly suggesting that the sample consists of a single-layer of a S–Fe–S sandwich. If multilayers were present, then the measured Fe coverage would be much lower than the starting value of 1 ML prior to sulfurization, due to the additional attenuation of electrons from buried layers, which is clearly not the case here. Besides, we only detect a single kind of structure in the GIXD data, while multilayers would certainly differ from the single layer, in terms of in-plane lattice parameter for instance.

**Atomic Structure of 1T-FeS₂.** At this stage, we have established that a highly ordered 2D overlayer forms on Au(111), with an Fe:S composition of 1:2 (±0.1), and obtained precise measurements of the in-plane lattice constant, its alignment with the substrate and the formation of a (4 × 4)FeS₂/(5 × 5)Au moiré super lattice. However, the exact atomic arrangement within this 2D layer and super lattice remains unclear. While STM reveals atomic-scale details, the intertwining of structural and electronic density of states complicates the interpretation, and STM would only provide indirect information about subsurface layers—specifically, two of the three layers in the FeS₂ structure. GIXD, for its part, has thus far informed us only about the positions and widths of peaks in the in-plane maps.

To delve deeper, we turn to surface X-ray crystallography, starting by extracting quantitative details about atomic arrangements within the unit cell of the moiré pattern from
<figure><img src="image_12.png" /><figcaption>Figure 4. a) Experimental in-plane Patterson map within a Au-(5 × 5) supercell, calculated from the integrated intensities of all in-plane (actually integrated from L = 0.15 to 0.25, resulting in a slightly out-off plane average value of L = 0.2, or -0.2 for the + -60 or 180° rotations) experimental rods except the Au CTRs. b) Theoretical Patterson map with the same intensity levels. The contour lines in a) and b) stand for iso-intensities in the Patterson map, in units of squared electron densities, normalized to 1. Here, the maps were plotted with 8 equally spaced contours between 0 and 1, with a maximum of 1 at the origin of the unit cell. c) Top view of the candidate atomic model of the single S-Fe-S layer onto one Au layer, yielding the best fit to the data (a). d) Plot comparing the in-plane (actually slightly out-off plane thus the double circles with slightly differing radii) experimental and theoretical intensities from the model. The disk area (respectively radii) are proportional to the diffracted intensities (respectively structure factor moduli).</figcaption></figure>

SXRD in-plane maps. The in-plane scattering intensities offer interference patterns tied to specific relative atomic positions, which we analyze to propose an initial candidate structure. We will further refine this model through analysis of the rod data (intensities scattered perpendicular to the plane).

Our goal for now is to derive a Patterson map from experimental in-plane data of reciprocal space,³¹ such as presented in Figure 2a. We construct this map (Figure 4a) using the 2D layer's and the moiré pattern's main peak coordinates and integrated intensities (corrected for polarization and scattering area), from data measured at L = 0.2 (from 0.15 to 0.25 s.l.r.u.), after having removed the background thermal diffuse scattering stemming from the Au substrate (Figure 4a).

By comparison of the rods within the sector map in Figure 2a, we find that the (slightly out-off plane since L = 0.2 and not 0) diffraction pattern of FeS₂ has a 3-fold rather than a 6-fold symmetry and is best described by the P3m1 plane group with a 94% agreement (see SI, Tables S6c-d). This finding strongly indicates that the FeS₂ layer is a 1T polymorph rather than 1H. Hence, our starting model is an on-substrate 2D single layer, altogether with P3m1 plane group symmetry. The local arrangement around the Fe atoms in this structure assumes an octahedral geometry, corresponding to the 1T polymorph. To compute a model Patterson map,³¹ we consider a gold layer along with the S-Fe-S structure, which results in a supercell, corresponding to a moiré pattern's unit cell (Figure 4b), with parameters a = b = 5×aAu = 14.432 Å, c = 7.064 Å, α = β = 90°,

γ = 120° (see Materials and Methods section). We do not account for an Au(111) herringbone reconstruction here (which would require a much larger supercell), since the corresponding signature is absent from SXRD as well as the STM data (probably due to the strong overlayer-substrate interaction). The first step of our analysis consists in exploring the in-plane positions of all atoms (the out-of-plane positions are not free at this stage), while maintaining the P3m1 symmetry constraints, to find the calculated Patterson map that will match best the experimental one (Figure 4a).

We used an adaptive simulated annealing algorithm to refine the atomic positions, following a tailored pathway to achieve a low χ² value while preserving the model's physical integrity.³² The best-fitting model, yielding χ² = 3.4, is displayed in Figure 4c where the corner Fe atom is on top of a 3-fold hollow site of the Au layer. The corresponding theoretical Patterson map (Figures 4b) closely reproduces the primary atomic vectors observed in the experimental one (Figures 4a). We also explored more complex structural models, incorporating additional Au layers, which further reduced the χ², while indicating that the most significant atomic distortions are concentrated in the top Au layer. For simplicity, we focus here on the one-layer Au model shown in Figure 4c. The in-plane intensities derived from this model are plotted alongside the experimental intensities in Figure 4d, showing an excellent match given the experimental uncertainties.

The second phase of our analysis utilizes the refined model to interpret out-of-plane structural data. These data are
<figure><img src="image_13.png" /><figcaption>Figure 5. a-c) Set of experimental structure factor amplitudes, i.e. square-root of the corresponding intensities (filled black squares together with error bars) along rods of 2D FeS₂/Au(111) and of the moiré, and best fit to the full experimental data set (red empty squares), calculated assuming a three-layer S-Fe-S on a single Au layer. The rods of 2D FeS₂/Au(111) are shown in a) and those of the moiré are shown in b) and c). For the locations of the rods on the sector map, we refer to the SI, section S7. The experimental rods were obtained after integration and correction of the intensity at each point using the Binocular/FitAid suite of programs.³³ The fits were performed using the Rod program.³² The fit primarily focuses on 0.5<|L| < 4.2 for all the rods. For the scattered intensities in 0.05<|L| < 0.5 region, the strong contribution of thermal diffuse scattering from Au alters the signal-to-background ratio of the relevant experimental signal. This L-range is only included in the fit for those rods having a decent signal-to-background ratio. The data has been displaced along the y-axis for the ease of viewing and comparison.</figcaption></figure>

obtained by measuring the scattering intensity along the rods of FeS₂, measured along the *L* direction at several *H*, *K* locations marked in the Figure S7, Supporting Information. Using an adaptive simulated annealing algorithm in an iterative procedure (see also SI, section S4), we fit the rod data by adjusting the atomic heights in the *S*, *Fe*, and *Au* layers while keeping the in-plane coordinates fixed. To ensure realistic interatomic distances, the *S* atoms were constrained to move in unison with the *Fe* atoms.

We initially fit all the rods of the parent FeS₂ peaks (Figure 5a-e) at (*H*,*K*) points (0.8, 0.8), (0.8, 1.6), (1.6, 0.8), (2.4, 0), and (0, 2.4) (as shown in the *HK* map, Figure 2a). Although this set of rods captures some information about the moiré pattern, the latter's contribution across all (*H*,*K*) values remains relatively minor. Thus, the structure refined from these five rods ($\chi^2$ = 1.8) serves as a preliminary model, leading to the final fit that includes ten additional moiré-specific rods (Figure 5f-o). Incorporating moiré rods is essential to accurately evaluate the impact of in-plane atomic coincidences on out-of-plane atomic positions across the moiré pattern. The final fit, achieving $\chi^2$ = 3.2, indicates high accuracy. Beyond this numerical metric, the fit quality is visually apparent in Figure 5, where nearly all qualitative features in the experimental rods are closely matched, some with striking fidelity. Minor deviations occur near integer *L* values (e.g., -3, -1, 1, 3) along the rods (1, 0.4), (0.6, 1), and (0.6, 0.4) in Figure 5b, where the Au thermal diffuse scattering in the raw data is significant compared to the rod intensity. Despite these few deviations, fitting 15 surface rods enforces stringent constraints on the model, enhancing its physical validity.

The fully refined structural model, illustrated in Figure 6a, reveals notable atomic displacements within the FeS₂ layer and the Au(111) substrate. Focusing first on the in-plane distortions, we observe that these displacements make the Au atoms (orange spheres) visible through the FeS₂ layer in the left-circled region of the top-view ball model in Figure 6a. In this region, the Fe atoms (brown spheres), which in an undistorted structure would align with the hcp sites of Au(111) (positioned directly above a second-layer Au atom, see SI, section S5), exhibit considerable Fe-S bond distortions. These distortions reach up to approximately 12%, deviating from the ideal octahedral coordination seen in a pristine 1*T* structure. Meanwhile, in the right-circled region (where Fe atoms sit above fcc sites, aligned with third-layer Au atoms, see SI, section S5), in-plane distortions are relatively minor. Additional details on the fitting parameters and the model coordinates are provided in the SI, S6.

Out-of-plane displacements are shown in Figure 6b and further quantified in Figures 6b and 6c for Fe and Au atoms, respectively. These height variations reach at most 1 Å for Fe atoms and around 0.86 Å for Au atoms across the unit cell. The FeS₂-Au(111) interlayer gap also varies, with a minimum distance of 2.01 Å, which is much smaller than the van der Waals gap typical of weakly interacting systems.³⁴ This reduced gap supports the presence of strong atomic distortions, both in- and out-of-plane, that align with the moiré pattern's commensurate structure and the extended structural order over large areas. Such periodicity confirms that these local distortions are part of a broader, highly ordered arrangement.

The corner Fe atoms in the unit cell occupying 3-fold Au sites exhibit a downward displacement toward the Au layer,
<figure><img src="image_14.png" /><figcaption>Figure 6. Ball models of the atomic structure of the moiré-modulated 1T-FeS₂ on Au(111), deduced from the analysis of the surface X-ray diffraction data. a) Top view and side view (slightly tilted in the z-direction) along the direction marked by the red arrow in the top view. b) Color map plot showing the vertical displacements in the Fe and Au layers in the 5 × 5 unit cell, respectively. The blue and green vectors indicate the axes of the Fe and Au layers, respectively. The combined cell is shown in Figure S8, Supporting Information.</figcaption></figure>

while those positioned on top sites show an upward movement, with the highest Fe atom located directly above an Au atom (see also SI, S8). Although P3m1 symmetry constraints were applied to the out-of-plane displacements, achieving optimal fits to the experimental data—particularly for the rods of the moiré pattern—required deviating from this symmetry for the Fe atoms close to top Au sites. This behavior was consistently observed regardless of the initial configuration of the Fe layer relative to the Au substrate. The observed asymmetry in vertical displacements suggests a slight torsional distortion of the FeS₂ layer about the longer diagonal of the unit cell. This distortion could also account for the asymmetry in the STM contrasts within the unit cell, as seen in Figure 1c (see also SI, section S8). To fully uncover the origins of these deviations, a detailed analysis of the FeS₂-Au interaction energetics is needed. While such theoretical modeling lies beyond the scope of this study, it will form an integral part of our future investigations.

**Decoupling from the Substrate by Intercalation.** As previously discussed, the FeS₂ monolayer binds strongly to its Au(111) substrate, resulting in substantial atomic displacements relative to the ideal 1T structure, shaped by the 5 × 5 moiré pattern. This strong FeS₂-Au(111) interaction raises the question of whether the dichalcogenide can still be stable as an independent 2D entity. A natural approach to assess this is mechanical exfoliation, which would also facilitate the integration of the 2D material into van der Waals heterostructures or devices. Rather than this macroscopic method, however, we opted for an alternative *in situ* technique involving intercalation of alkali metal atoms in the overlayer-

<figure><img src="image_15.png" /><figcaption>Figure 7. (a) STM image (–1.6 V sample bias, 300 pA tunneling current) of Cs-intercalated 1T-FeS₂ islands (covering about 0.4 ML). Inset highlights the intercalated islands and the Cs-covered substrate. The amount of FeS₂ grown is far lower than 1 single layer. (b) Atomic-scale STM image of Cs-intercalated 1T-FeS₂ (–0.4 V, 800 pA). Inset shows a FFT of the STM image. (c) LEED pattern (72 eV electron energy) of Cs-intercalated 1T-FeS₂. (d) STM image (–0.75 V, 500 pA) of deintercalated 1T-FeS₂ and of an ordered surface alloy on a region devoid of 1T-FeS₂ (lower terrace in the bottom-right corner). (e) Closer-scale STM image (–0.2 V, 850 pA) revealing the recovered (5 × 5) moiré pattern after deintercalation. Inset shows the atomic-scale details of the moiré. (f) LEED pattern (80 eV electron energy) of the deintercalated sample, revealing the recovered (5 × 5) moiré pattern. The central (0,0) spot is off-axis in (c,d) (electron beam not perpendicular to the surface).</figcaption></figure>
substrate gap. This technique is frequently applied to decouple epitaxial 2D materials<sup>35-37</sup>—including, more recently, dichalcogenides<sup>16,38</sup> from their growth substrate. The signature of successful intercalation and decoupling is the disappearance of the moiré pattern, whereas the pattern’s reappearance indicates recoupling of the layers.<sup>16,38</sup> We have chosen to intercalate Cs, and have characterized the system by a combined STM/LEED study.

After Cs deposition and annealing to 550 K (see Experimental Methods section) of a submonolayer deposit of FeS₂/Au(111), the surface topography comprises two kinds of regions (Figure 7a). We recognize the Au(111) atomic step edges, and observe a relatively rough surface. Except for flat islands attached to the ascending step edges; these islands have size and density corresponding to the FeS₂ flakes. The structure in the rough regions could not be determined at atomic scale. We tentatively ascribe these regions to an Au–Cs alloy that is presumably essentially disordered (no specific diffraction signals are observed). The flat islands exhibit a smooth meandering pattern superimposed with a well-developed hexagonal lattice of about 7 Å period (Figure 7b). This is actually more or less twice the FeS₂ lattice constant, suggesting that the flat islands are indeed FeS₂ flakes intercalated with Cs atoms forming a (2 × 2) reconstruction underneath them. Such kinds of Cs-intercalated superstructures, which may lock onto either the substrate or the 2D layer as it is the case here, have been observed previously in the case of graphene.<sup>39,40</sup> The LEED patterns confirm this view: peaks from both FeS₂ and the (2 × 2) lattice are observed, but no moiré peak persists. We conclude that the 1T-FeS₂ islands are fully decoupled from their substrate, and are free of moiré-induced distortions. Coming back to the meandering background observed in the STM data, one may invoke strain inhomogeneity (due to the release of tensile stress in the 2D layer when it gets decoupled from its substrate), or a purely electronic effect, e.g. 2D quasiparticle interferences related to the electronic band structure of the material (the Fourier transform of the STM image shown in the inset of Figure 7a reveals a contribution at the center of the Brillouin zone, suggestive of interference patterns observed at low temperature in another transition metal dichalcogenide;<sup>41</sup> note that quasiparticle interference patterns have already been observed at 300 K, like here, for instance with graphene<sup>40,43</sup>).

Annealing at 650 K for 15 min, under a H₂S atmosphere (back-pressure of 1 × 10⁻⁷ mbar) used to maintain FeS₂'s stoichiometry, changes the surface morphology once more. The disordered regions corresponding to the AuCs alloy prior to this last annealing are now highly ordered (bottom left corner in Figure 7d, also see SI, section S9). The FeS₂ islands have recovered a highly ordered 5 × 5 moiré pattern (Figure 7d,e). The LEED patterns confirm this view, showing the FeS₂ and moiré peaks, together with a new set of peaks that we ascribe to a now ordered AuCs alloy. The latter adopts three different domains on the surface (see SI, section S9), due to the mismatch of the lattice symmetry of this alloy and of Au(111), consistent with previous GIXD observations on a AuCs alloy.<sup>16</sup> All this points to Cs deintercalation and concomitant recoupling of FeS₂ on Au(111). Intercalation/decoupling and deintercalation/recoupling are thus reversible processes.

The reversible coupling and decoupling of the FeS₂ layer indicates that the strong interaction with Au is not necessary for the thermodynamic stability of the S–Fe–S layered system,

especially given that this new phase of FeS₂ is unlike any other known bulk phases of Fe sulfides. Note that we cannot exclude that Cs could play a role (invisible with our tools) in stabilizing the decoupled FeS₂ 2D layer. Particularly, the ready formation of this phase with the classic 2D TMDC layered structure on Au indicates the catalytic nature of Au, in terms of likely lowering of the formation barriers. In general, the synthesis of a stable 1T phase of FeS₂ indicates that there may exist similar 2D TMDC phases of other group 7 to 10 transition metals without an equivalent thermodynamically stable layered bulk structure that exists in nature. The choice of the support with strong interfacial interactions plays a crucial role in the successful synthesis of high-quality single layers via rMBE.

## CONCLUSIONS

We used reactive molecular beam epitaxy, more specifically atomic beam Fe evaporation on an Au(111) surface followed by in situ sulfurization using a low H₂S backpressure in ultrahigh vacuum, to grow epitaxial single-layer FeS₂/Au(111). The layer presents the sought-for 1:2 stoichiometry, as attested by Auger electron spectroscopy. Scanning tunneling microscopy, electron and X-ray diffraction all find that the layer has exceptionally high structural quality (perfect epitaxial orientation, well-defined lattice parameter; large crystallite size only limited by the size of Au terraces), compared to other 2D epitaxial dichalcogenides. A careful quantitative analysis of the surface X-ray diffraction data, in plane and perpendicular, along the 2D rods, led to a precise determination of the full, three-dimensional atomic structure, within the unit cell of the moiré pattern. We find that FeS₂ adopts the 1T polymorph with an average lattice in-plane parameter of 3.607 ± 0.004 Å, with significant distortions due to the interaction with the substrate. This interaction is modulated across a 5 × 5, fully commensurate moiré pattern. It is characterized by a small distance between the 2D layer and the substrate. Altogether, these demonstrated a strong interaction between FeS₂ and Au. We further show that the layer can be decoupled from the substrate using (reversible), temperature-induced intercalation with a layer of Cs atoms. In its intercalated form, FeS₂ exhibits no moiré pattern, and shows no signs of significant atomic distortions.

In summary, we have developed a robust r-MBE-based approach for the synthesis of high quality monolayer FeS₂, a critical milestone. Our method successfully produces very large single layer high crystallites, ~ 0.6 µm in size, which are highly aligned with the single crystal grains of the gold substrate, spanning several millimeters. This achievement represents a significant advance in the r-MBE-based synthesis of 2D TMDCs. In addition, we use synchrotron-based surface X-ray crystallography to rigorously determine the phase and atomic structure of the synthesized material, concluding that it is a 1T-FeS₂ polymorph single layer whose structure differs significantly from all other known bulk Fe disulfides. By decoupling the FeS₂ layer from the substrate through Cs intercalation, we also demonstrate that this novel 2D disulfide is intrinsically stable.

Future work should address the electronic and magnetic properties of 1T-FeS₂ and the influence of intercalates or defects, possibly of different types, on these properties. In this sense, 1T-FeS₂/Au(111) seems to be a relevant platform, since it is directly accessible to surface sensitive probes such as X-ray magnetic circular dichroism, and to in situ modifications (via intentionally introduced defects and intercalates). Ab initio
calculations predict strong strain effects on the magnetism, in particular via the superexchange interaction coupling the spins of neighboring Fe ions.¹¹ This interaction is particularly sensitive to the bond length and the angle along the cation-anion-cation paths, and may change in magnitude or sign.⁴⁴,⁴⁵ Understanding the role of heteroepitaxial strain, with Au(111) and possibly other substrates, and the role of local distortions within the moirés patterns, seems to be an exciting direction of research and a possible way to tune the Curie temperature.

## MATERIALS AND METHODS

Our experiments were carried out in two UHV systems. In the first one, the growth chamber is held by a large goniometer with the sample in the center and includes a Be window for the incident X-ray synchrotron beam delivered by the European Synchrotron (ESRF) at the CRG-IF, BM32 beamline, allowing surface diffraction measurements in UHV, in situ during growth. For sample positioning and motion, in addition to two perpendicular 360° rotations of the goniometer, the system includes a hexapod mechanism providing three translations and three rotations. These additional goniometric motions are transferred to the sample placed in the UHV chamber via bellows and rotary feedthroughs, allowing high-precision sample motions decoupled from the UHV chamber. These are three rotations of perpendicular axes with 0.0001° accuracy and three perpendicular translations with submicron (μm) accuracy. These sample motions are precisely aligned with the other goniometer axes (general rotation to define the angle of incidence of the beam with respect to the sample, and two rotations of the 2D detector, with perpendicular axes), either parallel or perpendicular, with alignment accuracy within 0.001° and a 50 μm sphere of confusion.

The chamber operates at a base pressure of $1 \times 10^{-10}$ mbar. It contains a quartz microbalance, a Staib 35 kV RHEED system with camera and an Omicron cylindrical mirror analyzer, together with an Omicron Auger electron spectroscopy instrument with an electron beam (energy up to 3.5 kV) in normal incidence on the sample. The second UHV system, located at Institut Néel (Grenoble), includes an Omicron V1 STM instrument, a low energy electron diffraction (LEED) instrument (BDL800IR-4GR, Scienta-Omicron), a reflection high energy electron diffraction (RHEED) instrument (Dr. Gassler Electron Devices GmbH), and a quartz microbalance. Both systems are equipped with electron beam evaporators, gas lines providing H₂S within UHV, and variable temperature sample holders. After sample preparation in these systems, we perform investigations using LEED, RHEED, AES, STM, and GIXD/SXRD. Temperature measurements are made with pyrometers, although differences in the pyrometers and chamber configurations between the two systems can lead to variability of up to ± 50 K. The Institut Néel UHV instrument has also been equipped with SAES Grabber Cs evaporators. The UHV chambers are designed so that the synthesis can be performed reproducibly on both setups, allowing tandem characterization in real and reciprocal space with chemical insight, and thus full structure determination.

The Au(111) substrate, single crystals purchased from Surface Preparation Laboratory and Mateck, were mounted on 1-molybdenum block holders using tungsten rings, applying only slight stress with nearly cylindrical symmetry. The Au surfaces underwent preparation in a UHV environment through repeated cycles of room-temperature sputtering with 1 keV Ar⁺ ions, followed by annealing at ~ 923 K resulting in atomically flat terraces of up to ~ 300 nm extension on the sample at Institut Néel and ~ 600 nm for the sample on the BM32 beamline. Surface cleanliness was verified through STM imaging and RHEED in the Institut Néel system, and with AES and GIXD at BM32/ESRF. A well-defined herringbone reconstruction was consistently observed in both systems.

The 2D FeS₂ layers were synthesized following an identical reactive molecular beam epitaxy (rMBE) process in both setups. First, Fe was evaporated from a 99.9% purity rod (Goodfellow), at a rate of 0.125 ML/min, onto the clean Au(111) substrate at room temperature, with

coverages up to 0.4 ML (monolayer, with respect to 1 Au substrate layer) for STM (constant current mode) and LEED measurements at Institut Néel, and up to 1 ML (calibrated with quartz microbalance) for GIXD and AES measurements at BM32/ESRF. Whenever possible, the coverage was confirmed with analysis of AES signatures of Fe LMM Auger peaks with respect to the Au substrate peaks acquired post evaporation with good agreement. A high coverage was chosen for the GIXD/SXRD measurements to maximize the X-ray intensity scattered along the so-called 2D rods of the overlayer. The Fe/Au(111) samples were then sulfurized by annealing in an H₂S background of $1 \times 10^{-5}$ mbar for 5 min at 573 K (heating rate 20 K/min), followed by cool down to room temperature in UHV. In the first UHV setup, the H₂S is provided by a specific fully automated and remote control gas distribution system that is described in detail elsewhere.⁴² The gas injector is a CBE system bought from Riber, and equipped with a long quartz tube whose end can be brought by translation very close to the sample surface, allowing for a local increase of pressure at this location. This possibility was not used here. The pressure was measured by a Pirani Cold cathode gauge located about 200 mm away from both the sample and the gas injector. The pressure is uniform in the growth chamber. In the second UHV setup, H₂S is provided via a leak valve, also equipped with a long quartz tube which may be approached to the sample surface. This option was not used here, and the pressure is considered uniform in the chamber. It is measured with a Pirani Cold cathode and Bayard-Alpert gauges located about 200 mm away from the sample. In both chambers residual gas analysis reveals the expected signature for H₂S.

For the intercalation experiments, Cs was evaporated (up to 1 ML on the surface in 20 min) under UHV by resistive heating of a high purity Cs dispenser (SAES Grabber) with the 2D FeS₂/Au(111) sample held at room temperature. Subsequently, intercalation was promoted by heating the sample at 550 K for 10 min. Deintercalation was achieved by annealing to 650 K for 10 min in an H₂S background of $1 \times 10^{-6}$ mbar.

Diffraction measurements were performed using the z-axis diffractometer installed at the BM32 CRG/IF beamline of the ESRF, optimized for grazing incidence surface X-ray diffraction. Setting the energy to 11.8 keV, just below the Au L₁₁₁ absorption edge to avoid Au fluorescence, we position the incident angle at 0.24°, below the critical angle for total external reflection, to enhance the 2D material's signal while reducing bulk background interference. The diffraction signal is recorded by a Maxipix hybrid pixel photon-counting detector (256 × 1288 pixels, each measuring 55 × 55 µm²), placed 700 mm from the sample and oriented with its largest dimension perpendicular to it. The detector spans a 5.8° angle perpendicular to the surface and 1.15° parallel to it, with an angular resolution of 0.0045° per pixel, corresponding to a resolution of $4.7 \times 10^{-6}$ pm⁻¹ in momentum Q space. Under grazing incidence conditions, the detector captures a perpendicular momentum transfer ranging from 0 to $0.6 \times 10^{-2}$ pm⁻¹. GIXD intensity data are typically presented in photon/s, integrated over specific regions of interest in the detector, covering from 0.2 to $0.6 \times 10^{-2}$ pm⁻¹ perpendicular to the surface and from $4 \times 10^{-5}$ to $2 \times 10^{-4}$ pm⁻¹ parallel to it. The active area is defined by the incident beam's 0.3 mm square width parallel to the surface, the detector slits located 238 mm from the sample, set between 0.5 and 5 mm, and the detector angle δ parallel to the surface.

To describe the structure of the samples, we define the primitive direct hexagonal surface unit cell vectors of the Au(111) surface. The three relevant unit vectors, of gold's bulk face-centered cubic (subscript c) lattice, are $a_1=0.5 \times [101]_c$, $a_2=0.5 \times [110]_c$, $a_3=(1/3) \times [111]_c$.¹⁶ Their lengths are $|a_1|=|a_2|=a_{Au} = 2.8864$ Å, and $|a_3| = 7.064$ Å. The unit vectors in reciprocal space, $b_1$ with $i=1,2,3$ satisfying $a_1 \cdot b_1=2\pi\delta_{ij}$ have lengths $|b_1|=|b_2|=2.5160$ Å⁻¹ and $|b_3|=0.8896$ Å⁻¹. We use Miller indices H,K,L to express momentum transfers, $Q=\text{Hb}_1+\text{Kb}_2+\text{Lb}_3$, and label general reflection (HKL) including in-plane ones, with L = 0, (HK). Scans of the X-ray scattered intensity along the H,K,L directions are expressed in surface
reciprocal lattice units (s.r.l.u.) using the above-defined Au(111) surface unit cell as the reference, unless otherwise specified.

The X-ray data processing was carried out within the Binoculars software³³ package and the fitting of the atomic model was performed using the ANA-ROD open source C-program³² with the computational facilities at ESRF. Corrections were applied for the beam polarization, surface active area, and Gaussian beam profile. The correction for beam refraction at interfaces were used to calculate Q⊥ inside the sample.

## ASSOCIATED CONTENT

### Data Availability Statement

All data are available in the paper or in the Supporting Information

**SI Supporting Information**

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.4c17873.

It contains X-ray crystallographic structure determination such as determination of the crystallite size, lattice parameter, stoichiometry, in-plane symmetry, along with more supporting STM images and electron diffraction data, as well as information on the in-plane and out-of-plane fitting algorithm used (PDF)

## AUTHOR INFORMATION

### Corresponding Authors

Mahesh Krishna Prabhu – Université Grenoble Alpes, CEA, IRIG/MEM/NRX, Grenoble 38000, France; ● orcid.org/0000-0002-3708-2463; Email: mahesh-krishna.prabhu@esrf.fr

Gilles Renaud – Université Grenoble Alpes, CEA, IRIG/MEM/NRX, Grenoble 38000, France; ● orcid.org/0000-0001-7607-9446; Email: gilles.renaud@cea.fr

### Authors

Philippe David – Université Grenoble Alpes, CNRS, Institut NEEL, Grenoble 38000, France

Valérie Guisset – Université Grenoble Alpes, CNRS, Institut NEEL, Grenoble 38000, France

Lucio Martinelli – Université Grenoble Alpes, CNRS, Institut NEEL, Grenoble 38000, France

Johann Coraux – Université Grenoble Alpes, CNRS, Institut NEEL, Grenoble 38000, France

Complete contact information is available at: https://pubs.acs.org/10.1021/acsnano.4c17873

### Author Contributions

M.K.P. conceived the methodology; performed the experiments, data analysis, and data curation; participated in the conceptualization; and wrote the original draft. G.R. secured funding and contributed to the conceptualization, the data analysis, and reviewing and editing the draft. J.C. contributed to data analysis, conceptualization, writing and reviewing and editing the draft, and secured part of the funding. P.D. and V.G. provided support for experiments, securing the operation of the UHV system at Institut Néel (growth, electron diffraction, STM). LM. provided support for the experiments, securing the operation of the INS2 setup on the BM32 beamline.

### Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

This work is supported by France 2030 government investment plan managed by the French National Research Agency under grant reference PEPR SPIN – SPIN-MAT ANR-22-EXSP-0007. Funding from French ANR PIA3 Equipex project MAGNIFIX under grant agreement ANR-21-ESRE-0011, and ANR PEPR PIA4 project DIADEM-ESRF under grant agreement 22-PEXD-0011 are also acknowledged. The authors thank the BM32 team for their assistance and knowledge during the X-ray experiment. The European Synchrotron Facility is gratefully acknowledged for beam time allocation at the French beamline BM32-CRG_IF.

## REFERENCES

(1) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically Thin MoS₂: A New Direct-Gap Semiconductor. *Phys. Rev. Lett.* **2010**, *105* (13), No. 136805.

(2) Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C. Y.; Galli, G.; Wang, F. Emerging Photoluminescence in Monolayer MoS₂. *Nano Lett.* **2010**, *10* (4), 1271–1275.

(3) Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, V.; Kis, A. Single-Layer MoS₂ Transistors. *Nat. Nanotechnol.* **2011**, *6* (3), 147–150.

(4) Ugeda, M. M.; Bradley, A. J.; Zhang, Y.; Onishi, S.; Chen, Y.; Ruan, W.; Ojeda-Aristizabal, C.; Ryu, H.; Edmonds, M. T.; Tsai, H. Z.; Riss, A.; Mo, S. K.; Lee, D.; Zettl, A.; Hussain, Z.; Shen, Z. X.; Crommie, M. F. Characterization of Collective Ground States in Single-Layer NbSe₂. *Nat. Phys.* **2016**, *12* (1), 92–97.

(5) Xi, X.; Zhao, L.; Wang, Z.; Berger, H.; Forró, L.; Shan, J.; Mak, K. F. Strongly Enhanced Charge-Density-Wave Order in Monolayer NbSe₂. *Nat. Nanotechnol.* **2015**, *10* (9), 765–769.

(6) Gibertini, M.; Koperski, M.; Morpurgo, A. F.; Novoselov, K. S. Magnetic 2D Materials and Heterostructures. *Nature Nanotechnology.* **2019**, *14*, 408–419.

(7) Purbawati, A.; Coraux, J.; Vogel, J.; Hadj-Azzem, A.; Wu, N. J.; Bendiab, N.; Jegouso, D.; Renard, J.; Marty, L.; Bouchiat, V.; Sulpice, A.; Aballe, L.; Foerster, M.; Genuzio, F.; Locatelli, A.; Menteş, T. O.; Han, Z. V.; Sun, X.; Núñez-Regueiro, M.; Rougemaille, N. In-Plane Magnetic Domains and Neél-like Domain Walls in Thin Flakes of the Room Temperature CrTe₂ Van Der Waals Ferromagnet. *ACS Appl. Mater. Interfaces* **2020**, *12* (27), 30702–30710.

(8) Sun, X.; Li, W.; Wang, X.; Sui, Q.; Zhang, T.; Wang, Z.; Liu, L.; Li, D.; Feng, S.; Zhong, S.; Wang, H.; Bouchiat, V.; Nunez Regueiro, M.; Rougemaille, N.; Coraux, J.; Purbawati, A.; Hadj-Azzem, A.; Wang, Z.; Dong, B.; Wu, X.; Yang, T.; Yu, G.; Wang, B.; Han, Z.; Han, X.; Zhang, Z. Room Temperature Ferromagnetism in Ultra-Thin van Der Waals Crystals of 1T-CrTe₂. *Nano Res.* **2020**, *13* (12), 3358–3363.

(9) Zhang, X.; Lu, Q.; Liu, W.; Niu, W.; Sun, J.; Cook, J.; Vaninger, M.; Miceli, P. F.; Singh, D. J.; Lian, S. W.; Chang, T. R.; He, X.; Du, J.; He, L.; Zhang, R.; Bian, G.; Xu, Y. Room-Temperature Intrinsic Ferromagnetism in Epitaxial CrTe₂ Ultrathin Films. *Nat. Commun.* **2021**, *12* (1), 2492.

(10) Nair, G. K. R.; Ji, X.; Guo, D.; Zhu, C.; Xu, X.; Zheng, X.; Yang, X.; Cui, J.; Li, P.; Wang, X.; Yao, W.; Zhou, J.; Salim, T.; Yi, J.; Ma, F.; Yang, C.; Ke, H.; Qu, F.; Shen, J.; Jing, X.; Liu, Z.; Li, X.; Liu, G.; Lu, L. 1T-Fe₅: A New Type of Two-Dimensional Metallic Ferromagnet. 2022, 252, *arXiv*. (accessed August 05, 2024).

(11) Yang, K.; Ma, Y.; Liu, L.; Ning, Y.; Lu, D.; Zhou, Y.; Li, Z.; Wu, H. Fe₅ Monolayer: A High-Valence and High-TCIsing Ferromagnet. *Phys. Rev. B* **2024**, *109* (1), No. 014431.

(12) Zhou, J.; Zhu, C.; Zhou, Y.; Dong, J.; Li, P.; Zhang, Z.; Wang, Z.; Lin, Y. C.; Shi, J.; Zhang, R.; Zheng, Y.; Yu, H.; Tang, B.; Liu, F.; Wang, L.; Liu, L.; Liu, G. B.; Hu, W.; Gao, Y.; Yang, H.; Gao, W.; Lu, L.; Wang, Y.; Suenaga, K.; Liu, G.; Ding, F.; Yao, Y.; Liu, Z. Composition and Phase Engineering of Metal Chalcogenides and Phosphorous Chalcogenides. *Nat. Mater.* **2023**, *22* (4), 450–458.
(13) Puthirath, A. B.; Balan, A. P.; Oliveira, E. F.; Sreepal, V.; Robles Hernandez, F. C.; Gao, G.; Chakingal, N.; Sassi, L. M.; Thibeorchews, P.; Costin, G.; Vajtai, R.; Galvao, D. S.; Nair, R. R.; Ajayan, P. M. Apparent Ferromagnetism in Exfoliated Ultrathin Pyrite Sheets. *J. Phys. Chem. C* **2021**, *125* (34), 18927–18935.

(14) Wang, D.; Chen, X.; Sanyal, B. Unraveling Complex Magnetism in Two-Dimensional FeS₂. *Phys. Rev. B* **2021**, *104* (24), No. 245410.

(15) Dombrowski, D.; Samad, A.; Mehlich, K.; Chagas, T.; Schwingenschlögl, U.; Busse, C. Phase Engineering in Tantalum Sulfide Monolayers on Au(111). *2D Mater.* **2023**, *10* (2), No. 025005.

(16) Weng, X.; David, P.; Guisset, V.; Martinelli, L.; Geaymond, O.; Coraux, J.; Renaud, G. Superstructures, Commensurations, and Rotation of Single-Layer TaS₂ on Au(111) Induced by Cs Intercalation/Deintercalation. *ACS Nano* **2023**, *17* (6), 5459–5471.

(17) Chua, R.; Zhou, J.; Yu, X.; Yu, W.; Gou, J.; Zhu, R.; Zhang, L.; Liu, M.; Breese, M. B. H.; Chen, W.; Loh, K. P.; Feng, Y. P.; Yang, M.; Huang, Y. L.; Wee, A. T. S. Room Temperature Ferromagnetism of Monolayer Chromium Telluride with Perpendicular Magnetic Anisotropy. *Adv. Mater.* **2021**, *33* (42), No. 2103360.

(18) Helveg, S.; Lauritsen, J. V.; Lægsgaard, E.; Stensgaard, I.; Nørskov, J. K.; Clausen, B. S.; Topsøe, H.; Besenbacher, F. Atomic-Scale Structure of Single-Layer MoS₂ Nanoclusters. *Phys. Rev. Lett.* **2000**, *84* (5), 951–954.

(19) Sørensen, S. G.; Füchtbauer, H. G.; Tuxen, A. K.; Walton, A. S.; Lauritsen, J. V. Structure and Electronic Properties of in Situ Synthesized Single-Layer MoS₂ on a Gold Surface. *ACS Nano* **2014**, *8* (7), 6788–6796.

(20) Bana, H.; Travaglia, E.; Bignardi, L.; Lacovig, P.; Sanders, C. E.; Dendzik, M.; Michiardi, M.; Bianchi, M.; Lizzit, D.; Presel, F.; De Angelis, D.; Apostol, N.; Das, P. K.; Fujii, J.; Vobornik, I.; Larciprete, R.; Baraldi, A.; Hofmann, P.; Lizzit, S. Epitaxial Growth of Single-Orientation High-Quality MoS₂ Monolayers. *2D Mater.* **2018**, *5* (3), No. 035012.

(21) Bruix, A.; Lauritsen, J. V.; Hammer, B. Effects of Particle Size and Edge Structure on the Electronic Structure, Spectroscopic Features, and Chemical Properties of Au(111)-Supported MoS₂ Nanoparticles. *Faraday Discuss.* **2016**, *188*, 323–343.

(22) Krane, N.; Lotze, C.; Franke, K. J. Moiré Structure of MoS₂ on Au(111): Local Structural and Electronic Properties. *Surf. Sci.* **2018**, *678*, 136–142.

(23) Sant, R.; Gay, M.; Marty, A.; Lisi, S.; Harrabi, R.; Vergnaud, C.; Dau, M. T.; Weng, X.; Coraux, J.; Gauthier, N.; Renault, O.; Renaud, G.; Jamet, M. Synthesis of Epitaxial Monolayer Janus SPtSe. *npj 2D Mater. Appl.* **2020**, *4* (1), 41.

(24) Silva, C. C.; Dombrowski, D.; Atodiresei, N.; Jolie, W.; Farwick Zum Hagen, F.; Cai, J.; Ryan, P. T. P.; Thakur, P. K.; Caciuc, V.; Blügel, S.; Duncan, D. A.; Michely, T.; Lee, T. L.; Busse, C. Spatial Variation of Geometry, Binding, and Electronic Properties in the Moiré Superstructure of MoS₂ on Au(111). *2D Mater.* **2022**, *9* (2), No. 025003.

(25) Dendzik, M.; Michiardi, M.; Sanders, C.; Bianchi, M.; Miwa, J. A.; Grønborg, S. S.; Lauritsen, J. V.; Bruix, A.; Hammer, B.; Hofmann, P. Growth and Electronic Structure of Epitaxial Single-Layer WS₂ on Au(111). *Phys. Rev. B: Condens. Matter Mater. Phys.* **2015**, *92* (24), No. 245442.

(26) Sanders, C. E.; Dendzik, M.; Ngankeu, A. S.; Eich, A.; Bruix, A.; Bianchi, M.; Miwa, J. A.; Hammer, B.; Khajetoorians, A. A.; Hofmann, P. Crystalline and Electronic Structure of Single-Layer TaS₂. *Phys. Rev. B* **2016**, *94* (8), No. 081404.

(27) Dombrowski, D.; Samad, A.; Murray, C.; Petrović, M.; Ewen, P.; Michely, T.; Kralj, M.; Schwingenschlögl, U.; Busse, C. Two Phases of Monolayer Tantalum Sulfide on Au(111). *ACS Nano* **2021**, *15* (8), 13516–13525.

(28) Cai, T.; Song, Z.; Rodriguez, J. A.; Hrbek, J. Preparation and Structural Characterization of RuS₂ Nanoislands on Au(111). *J. Am. Chem. Soc.* **2004**, *126* (29), 8886–8887.

(29) Prabhu, M. K.; Boden, D.; Rost, M. J.; Meyer, J.; Groot, I. M. N. Structural Characterization of a Novel Two-Dimensional Material:

Cobalt Sulfide Sheets on Au(111). *J. Phys. Chem. Lett.* **2020**, *11* (21), 9038–9044.

(30) Kibsgaard, J.; Tuxen, A.; Knudsen, K. G.; Brorson, M.; Topsøe, H.; Lægsgaard, E.; Lauritsen, J. V.; Besenbacher, F. Comparative Atomic-Scale Analysis of Promotional Effects by Late 3d-Transition Metals in MoS₂ Hydrotreating Catalysts. *J. Catal.* **2010**, *272* (2), 195–203.

(31) Spagna, R. Crystal Structure Determination. In *Encyclopedia of Condensed Matter Physics*; Bassani, F.; Liedl, G. L.; Wyder, P., Eds.; Elsevier: Oxford, 2005; 294–304.

(32) Vlieg, E. ROD: A Program for Surface X-Ray Crystallography. *J. Appl. Crystallogr.* **2000**, *33*, 401–405.

(33) Roobol, S.; Onderwaater, W.; Drnec, J.; Felici, R.; Frenken, J. BINoculars: Data Reduction and Analysis Software for Two-Dimensional Detectors in Surface X-Ray Diffraction. *J. Appl. Crystallogr.* **2015**, *48*, 1324–1329.

(34) Samad, L.; Bladow, S. M.; Ding, Q.; Zhuo, J.; Jacobberger, R. M.; Arnold, M. S.; Jin, S. Layer-Controlled Chemical Vapor Deposition Growth of MoS₂ Vertical Heterostructures via van Der Waals Epitaxy. *ACS Nano* **2016**, *10* (7), 7039–7046.

(35) Grüneis, A.; Vyalikh, D. V. Tunable Hybridization between Electronic States of Graphene and a Metal Surface. *Phys. Rev. B - Condens. Matter Mater. Phys.* **2008**, *77* (19), No. 193401.

(36) Riedl, C.; Coletti, C.; Iwasaki, T.; Zakharov, A. A.; Starke, U. Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation. *Phys. Rev. Lett.* **2009**, *103* (24), No. 246804.

(37) Brugger, T.; Ma, H.; Iannuzzi, M.; Berner, S.; Winkler, A.; Hutter, J.; Osterwalder, J.; Greber, T. Nanotexture Switching of Single-Layer Hexagonal Boron Nitride on Rhodium by Intercalation of Hydrogen Atoms. *Angew. Chemie - Int. Ed.* **2010**, *49* (35), 6120–6124.

(38) Sant, R.; Lisi, S.; Nguyen, V. D.; Mazaleyrat, E.; Gómez Herrero, A. C.; Geaymond, O.; Guisset, V.; David, P.; Marty, A.; Jamet, M.; Chapelier, C.; Magaud, L.; Dappe, Y. J.; Bianchi, M.; Hofmann, P.; Renaud, G.; Coraux, J. Decoupling Molybdenum Disulfide from Its Substrate by Cesium Intercalation. *J. Phys. Chem. C* **2020**, *124* (23), 12397–12408.

(39) Petrović, M.; Šrut Rakić, I.; Runte, S.; Busse, C.; Sadowski, J. T.; Lazić, P.; Pletikosić, J.; Pan, Z. H.; Milun, M.; Pervan, P.; Atodiresei, N.; Brako, R.; Šokčević, D.; Valla, T.; Michely, T.; Kralj, M. The Mechanism of Caesium Intercalation of Graphene. *Nat. Commun.* **2013**, *4*, 2772.

(40) Lisi, S.; Guisset, V.; David, P.; Mazaleyrat, E.; Herrero, A. C. G.; Coraux, J. Two-Way Twisting of a Confined Monolayer: Orientational Ordering within the van Der Waals Gap between Graphene and Its Crystalline Substrate. *Phys. Rev. Lett.* **2022**, *129* (9), No. 096101.

(41) Yankowitz, M.; McKenzie, D.; Leroy, B. J. Local Spectroscopic Characterization of Spin and Layer Polarization in WSe₂. *Phys. Rev. Lett.* **2015**, *115* (3), No. 136803.

(42) Cantelli, V.; Geaymond, O.; Ulrich, O.; Zhou, T.; Blanc, N.; Renaud, G. The in Situ Growth of Nanostructures on Surfaces (INS) Endstation of the ESRF BM32 Beamline: A Combined UHV-CVD and MBE Reactor for in Situ X-Ray Scattering Investigations of Growing Nanoparticles and Semiconductor Nanowires. *J. Synchrotron Radiat.* **2015**, *22*, 688–700.

(43) Yang, H.; Mayne, A. J.; Boucherit, M.; Comtet, G.; Dujardin, G.; Kuk, Y. Quantum Interference Channeling at Graphene Edges. *Nano Lett.* **2010**, *10* (3), 943–947.

(44) Blei, M.; Lado, J. L.; Song, Q.; Dey, D.; Erten, O.; Pardo, V.; Comin, R.; Tongay, S.; Botana, A. S. Synthesis, Engineering, and Theory of 2D van Der Waals Magnets. *Applied Physics Reviews.* **2021**, *8*, No. 021301.

(45) Jiang, X.; Liu, Q.; Xing, J.; Liu, N.; Guo, Y.; Liu, Z.; Zhao, J. Recent Progress on 2D Magnets: Fundamental Mechanism, Structural Design and Modification. *Applied Physics Reviews.* **2021**, *8*, No. 031305.