Field of Invention

Disclosed herein is a compound comprising a plurality of layers of a transition metal dichalcogenide or a semi-conductor material, wherein there are vacancies between adjacent layers and the vacancies are occupied by a transition metal.

Background

The listing or discussion of a prior-published document in this specification should not necessarily be taken as an acknowledgement that the document is part of the state of the art or is common general knowledge.

The surge in two-dimensional (2D) materials research has heralded a new branch of condensed-matter physics concerned with the description of electrons in atomically thin structures. Thus far, research efforts have primarily focused on 2D monolayers and their hetero-stacked structures, in which new properties can be engineered by generating superlattices of different Moire wavelengths. However, these hetero-stacked structures are currently produced by bottom-up methods that have low yield and poor reproducibility.

An alternative way of compositional tuning is based on the intercalation of foreign atoms in the van der Waals (wdW) gap sandwiched by the chalcogen atoms. This has been shown to induce pseudo-2D characteristics in bulk crystals and modify their electronic properties. Depending on the interlayer stacking registries, the vdW gaps in transition metal dichalcogenides (TMDs) contain octahedral, tetrahedral vacancies or trigonal-prismatic vacancies, which provide docking sites for a diverse range of intercalants. Examples of successful intercalants include alkali metals such as Li, Na, K; transition metals such as Cu, Co, Ni, Fe, Nb, Sn; noble metals such as Ag, Au, Pt; and various organic molecules. Charge transfer from the intercalants, or increased spin-orbit coupling owing to the presence of heavy atoms, can enhance superconductivity, thermoelectricity, or spin polarization.

The intercalation process typically involves post-growth, diffusion-limited processes such as electrochemical or solid-state intercalation. A well-defined intercalated phase with long-range crystalline order is difficult to obtain by such methods and usually requires drastic treatment conditions. Moreover, an intercalation phase diagram that correlates the density and spatial distribution of intercalation atoms with mesoscopic properties of the intercalated compound is currently lacking. Compared with foreign atom intercalation, intercalation of a TMD by its native metal atoms (also termed as self-intercalated TMD compounds) has so far received scant attention. Therefore, there is a need for improved processes for preparing self-intercalated compounds.

Summary of Invention

Aspects and embodiments of the invention will now be described by reference to the following numbered clauses.

1. A compound comprising: a plurality of layers of a transition metal dichalcogenide or a similar semiconductor material, where between any two adjacent layers there is a first set of vacancies; and a transition metal occupying from 25% to 100% of the first set of vacancies in the compound.

2. The compound according to Clause 1 , wherein the first set of vacancies are octahedral vacancies or trigonal prismatic vacancies.

3. The compound according to Clause 1 or Clause 2, wherein between any two adjacent layers there is also a second set of vacancies, where the transition metal occupies from 0 to 100% of the second set of vacancies.

4. The compound according to Clause 1 , wherein the second set of vacancies are octahedral vacancies or trigonal prismatic vacancies, provided that if the first set of vacancies are octahedral vacancies then the second set of vacancies are trigonal prismatic vacancies or vice versa, optionally wherein the first set are octahedral vacancies.

5. The compound according to any one of the preceding clauses, wherein the transition metal dichalcogenide or the similar semiconductor material have the formula I:

M _a X _b I where:

M is a transition metal;

X is a chalcogenide; a is from 1 to 3; and b is from 1 to 3. 6. The compound according to any one of the preceding clauses, wherein the transition metal is selected from one or more of the group consisting of Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, Ge, Zr, Nb, Mo, Pd, In, Sn, Hf, Ta, W, and Pt, optionally wherein the transition metal is selected from one or more of the group consisting of Fe, V, Cr, Mn, Nb, In, and Ta.

7. The compound according to any one of the preceding clauses, wherein the chalcogenide is selected from one or more of the group consisting of S, Se and Te.

8. The compound according to any one of the preceding clauses, wherein the similar semiconductor material is selected from one or more of ln ₂ S ₃ , ln2Se3, SnS, SnSe, GeS, and GeSe.

9. The compound according to any one of the preceding clauses, wherein the compound is an ultrathin 3-dimensional compound that has 7+(4n) atomic layers, where n is 0 or a positive integer (e.g. n is from 0 to 1000, such as from 0 to 100, such as from 0 to 10).

10. The compound according to any one of the preceding clauses, wherein the transition metal occupying the first set of vacancies occupies 25%, 33.3%, 50%, 66.7% or 100% of the first set of vacancies.

11. The compound according to Clause 10, wherein when the transition metal occupies 100% of the first set of vacancies, then the transition metal also occupies from 0 to 100% of the second set of vacancies, such as from 0 to 50%, such as from 5% to 25%.

12. The compound according to any one of the preceding clauses, wherein the compound is ferromagnetic, optionally wherein the transition metal within the compound is non-magnetic and/or the Curie temperature is greater than 180K.

13. The compound according to Clause 12, wherein the transition metal occupying the plurality of octahedral vacancies occupies greater than 30% and less than 50% of the octahedral vacancies.

14. The compound according to Clause 12 or Clause 13, wherein the compound has the formula M _x X ₁₂ , where M is selected from In, Ta, Mo, W, Nb, Co, and Ti, X is selected from S, Se or Te, and x is from 6 to 7. 15. The compound according to any one of Clauses 12 to 14, wherein the transition metal is selected from In, Ta, Mo, W, Nb, Co, and Ti, optionally wherein the compound is selected from one or more of the group consisting of: Ta ₇ S ₁₂ ; Ta ₇ Se ₁₂ ; Ta ₇ Te ₁₂ ; Mo ₇ S ₁₂ ; Mo ₇ Se ₁₂ ; Mo ₇ Te ₁₂ ; W ₇ S ₁₂ ; W ₇ Se ₁₂ ; W ₇ Te ₁₂ ; Nb ₇ S ₁₂ ; Nb ₇ Se- ₁₂ ; Nb ₇ Te- ₁₂ ; Co ₇ S ₁₂ ; Co ₇ Se- ₁₂ ; Co ₇ Te ₁₂ ; Ti ₇ S ₁₂ ; Ti ₇ Se ₁₂ ; Ti ₇ Te ₁₂ ; ln ₇ S ₁₂ ; ln ₇ Se ₁₂ ; and ln ₇ Te ₁₂ .

16. The compound according to any one of Clauses 1 to 11, wherein the compound is in the form of a Kagome lattice, optionally wherein the transition metal occupying the first set of vacancies occupies greater than 60% of the first set of vacancies.

17. The compound according to Clause 16, wherein the compound has the formula M _x X ₁₂ , where M is selected from In, Ta, Mo, W, Nb, Co, and Ti, X is selected from S, Se or Te, and x is from 8 to 9, such as 8.

18. The compound according to Clause 16 or Clause 17, wherein the transition metal is selected from Ta, Nb, and Ti, optionally wherein the compound is selected from one or more of the group consisting of: Ta ₈ S ₁₂ ; Ta ₈ Se ₁₂ ; Ta ₉ S ₁₂ ; Ta ₉ Se ₁₂ ; Nb ₈ S ₁₂ ; Nb ₈ Se ₁₂ ; Nb ₉ S ₁₂ ; Nb ₉ Se ₁₂ ; Ti ₈ S ₁₂ ; Ti ₈ Se ₁₂ ; Ti ₉ S ₁₂ ; Ti ₉ Se ₁₂ .

19. The compound according to any one of Clauses 1 to 11 , wherein the compound is a multiferrotic compound formed from an M _x X _y layers, with M occupying the first set of vacancies between the M _x X _y layers, where M is In, Ga, Sn, or Ge, X is S or Se, x is 1 or 2 and y is 1 or 3 (e.g. the compound is ln _{1 1} Se ₁₆ ).

20. The compound according to any one of the preceding clauses, wherein the compound has the formula II:

McXd II where:

M is a transition metal;

X is a chalcogenide; c is from 7 to 16 (e.g. from 7 to 12); and d is 12 or 16.

21. The compound according to Clause 20, wherein the transition metal is selected from one or more of the group consisting of Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, Ge, Zr, Nb, Mo, Pd, In, Sn, Hf, Ta, W, and Pt, optionally wherein the transition metal is selected from one or more of the group consisting of Fe, V, Cr, Mn, Nb, In, and Ta.

22. The compound according to Clause 20 or Clause 21 , wherein the chalcogenide is selected from one or more of the group consisting of S, Se and Te.

23. The compound according to any one of Clauses 20 to 22, wherein the compound is selected from one or more of the group consisting of:

Ta ₉ S ₁₆ ; Ta ₉ Se ₁₆ ; Ta ₉ Te ₁₆ ; Ta ₇ S ₁₂ ; Ta ₇ Se ₁₂ ; Ta ₇ Te ₁₂ ; Ta ₁₀ S ₁₆ ; Ta ₁₀ Se ₁₆ ; Ta ₁₀ Te ₁₆ ; Ta ₈ S ₁₂ ; Ta ₈ Se ₁₂ ; Ta ₈ Te ₁₂ ; Ta ₉ S ₁₂ ; Ta ₉ Se ₁₂ ; Ta ₉ Te ₁₂ ;

V _{1 1} S ₁₆ ; V ₇ S ₁₂ ; V10S16; V ₈ S ₁₆ ; V ₉ S ₁₂ lniiSe ₁₆ ;

Fe ₉ S ₁₆ ; Fe ₉ Se ₁₆ ; Fe ₉ Te ₁₆ ; Fe ₇ S ₁₂ ; Fe ₂ Se ₁₂ ; Fe ₇ Te ₁₂ ; Fe ₁₀ S ₁₆ ; Fe ₁₀ Se ₁₆ ; Fe ₁₀ Te ₁₆ ; Fe ₉ S ₁₂ ; Fe ₉ Se ₁₂ ; and Fe ₉ Te ₁₂ , optionally wherein the compound is selected from one or more of the group consisting of:

Ta ₉ S ₁₆ ; Ta ₉ Se ₁₆ ; Ta ₇ S ₁₂ ; Ta ₇ Se ₁₂ ; Ta ₁₀ S ₁₆ ; Ta ₁₀ Se ₁₆ ; Ta ₈ S ₁₂ ; Ta ₈ Se ₁₂ ; Ta ₉ S ₁₂ ; Ta ₉ Se ₁₂ ;

V11S16; and lniiSe ₁₆ ; ln ₇ Se ₁₂ ; ln ₁₀ Se ₁₆ ; ln ₈ Se ₁₂ ; ln ₉ Se ₁₂ .

24. A method of manufacturing a compound as described in any one of Clauses 1 to 23 by molecular beam epitaxy and/or chemical vapour deposition (e.g. metal organic chemical vapour deposition).

Drawings

Certain embodiments of the present disclosure are described more fully hereinafter with reference to the accompanying drawings.

Figure 1. Self-intercalation in TaS ₂ crystals. Schematic illustration showing the MBE growth of (a) pristine TaS ₂ and (b) self-intercalated Ta ₇ S ₁₂ under a low and high Ta-flux environment, respectively. The lower Ta flux produces stoichiometric TaS ₂ , whereas higher Ta flux leads to a self-intercalated phase, (c) Photographs of MBE-grown 1 L -TaS ₂ and 2L- Ta ₇ S ₁₂ on 2-inch SiO ₂ /Si wafer. (d) Atomic-resolution STEM-ADF image of monolayer TaS ₂ under Ta rich conditions with abundant Ta interstitials locating at the (e) center of honeycomb or (f) on top of the Ta site. Corresponding atomic models were depicted in the right panels, (g) Schematic illustration depicting the layer-by-layer growth of ic-2d crystals. (h) Calculated formation energies of various self-intercalated Ta _x S _y phases where the intercalation concentrations are 25%, 33.3%, 50%, 66.7%, and 100%, respectively, as a function of sulfur chemical potential. Scale bars: 2 nm in (d); 0.5 nm in (e-f).

Figure 2. Compositional engineering of self-intercalated Ta _x S _y (Ta _x Se _y ) with different intercalated Ta concentrations, (a) Atomic-resolution STEM-ADF image of the MBE grown self-intercalated Ta ₇ S ₁₂ showing well defined √3a x √3a superstructure and (b) the enlarged image overlaid with the atomic model, (c) corresponding FFT pattern of (a) with √3 a superspots highlighted by the circles, (d) Atomic model of self-intercalated Ta ₇ S ₁₂ . (e) STEM cross-section view of 100% Ta-intercalated Ta ₉ Se _12, and (f) its corresponding simulated image derived from the DFT optimized atomic model. Atomic-resolution STEM images of (g) 25% self-intercalated Ta ₉ S ₁₆ , (h) 50% self-intercalated Ta ₁₀ S ₁₆ , (i) 66.7% self-intercalated TasSe ₁₂ , and (j) 100% self-intercalated Ta ₉ Se ₁₂ ic-2d crystals, (k-n) Enlarged white box regions from (g-j), respectively, and their corresponding FFT patterns and atomic models are depicted in the right, and lower panels, respectively. Scale bars: 2 nm in (a, g-j); 0.5 nm in (b, e, k-n).

Figure 3. Ferromagnetism in self-intercalated Ta ₇ S ₁₂ ic- 2d crystals, (a) Atomic-resolution STEM-ADF image of a typical self-intercalated Ta ₇ S ₁₂ film, (b) Optical microscopy image of Ta ₇ S ₁₂ Hall bar device encapsulated with h-BN. (c) Resistivity as a function of temperature. Temperature dependent (d) longitudinal resistance (R _xx ) and (e) Hall resistance (R _xy ) under the out-of-plane magnetic field, (f) Contour plot of charge density difference in Ta-intercalated Ta ₇ S ₁₂ . Orbital-resolved (g) spin up and (h) spin down band structures of Ta ₇ S ₁₂ . (i) Top view and the side view spin density isosurface of Ta-intercalated Ta ₇ S ₁₂ . (j) Calculated magnetic moments as a function of Ta intercalation concentration in nonstoichiometric Ta _x S _y . The STEM-ADF image shown in Fig. 3a was collected using a half-angle range from ~30 to 110 mrad to enhance the contrast of S. Scale bar: 0.5 nm in (a); 20 μm in (b).

Figure 4. A library of ic- 2d crystals, (a) Periodic table showing metal and chalcogen combinations that form ic-2d crystals according to our DFT calculation; the list is non- exhaustive. Triangles indicate that the self-intercalation can be experimentally realized, whereas ** indicate that intercalation was not successful under our experimental conditions. Intrinsic ferromagnetic MX2 are marked by ^{^ ^} . (b) DFT calculated ic-2d atomic models showing ferromagnetism. STEM-ADF images of self-intercalated (c) V11S16, (d) ln _{1 1} Se ₁₆ , and (e) Fe _x Te _y . Their enlarged images and corresponding FFT patterns are depicted in (f-h), respectively. 2 nm in (c-e); 0.5 nm in (f-h); 5 nm ^-1 for all FFT patterns in (f-h). Figure 5. (a) Magnetization vs. magnetic field (M-H) curves at 10 K (purple curve) and at 400 K (blue curve) of the Ta ₇ S ₁₂ film, (b) Temperature dependence (M-T curves) of FC and ZFC magnetization.

Figure 6. STEM characterizations of bilayer 2H _c -TaS ₂ . (a) Atomic-resolution STEM-ADF image of bilayer 2H _c -TaS ₂ and (b) the enlarged image from a. (c) Fast Fourier transform (FFT) pattern of a. Scale bars: 2 nm in (a); 0.5 nm in (b). Pristine 2H _c -phase TaS ₂ can be grown when the Ta:S flux ratio is -1:10 at 600 °C.

Figure 7. Surface Ta adatoms in monolayer TaS ₂ . Atomic resolution STEM-ADF images of MBE grown monolayer TaS ₂ when Ta:S flux ratio is set at (a) 1:10, (b) 1 :8, (c) 1:6, and (d) 1:4. The growth time is set around 1.5 to 2 hours. Scale bars: 2 nm.

Figure 8. EDS and EELS analysis of Ta ₇ S ₁₂ - (a) Energy dispersive x-ray spectroscopy (EDS) and (b) electron energy loss (EEL) spectrum of the Ta ₇ S ₁₂ ic-2d films.

Figure 9. XPS of Ta ₇ S ₁₂ . X-ray photoelectron spectroscopy (XPS) spectra of the Ta ₇ S ₁₂ ic-2d film showing (a) a wide scan, (b) Ta 4f, and (c) S 2p core levels, respectively. The Ta ₇ S ₁₂ ic- 2d film is slightly oxidized due to air exposure during sample transfer from the MBE growth chamber to the XPS chamber.

Figure 10. Raman spectrum of Ta ₇ S ₁₂ ic- 2d film. A series of peaks from 100 to 170 cm ^-1 can be seen in Ta ₇ S ₁₂ as highlighted.

Figure 11. DFT calculated zone center phonon modes of Ta ₇ S ₁₂ , and TaS ₂ . New phonon vibrations exist in Ta ₇ S ₁₂ ranging from 110 to 160 cm ^-1 as highlighted, and these modes are absent in pristine TaS ₂ .

Figure 12. STEM analysis of Ta ₉ S ₁₆ . (a) STEM-ADF image showing the lateral size of the MBE grown Ta ₉ S ₁₆ . (b) Atomic-resolution STEM-ADF images showing the coexistence of ic- 2dTa ₉ S ₁₆ and TaS ₂ . The monolayer TaS ₂ and Ta ₉ S ₁₆ regions are highlighted by dashed lines, (c-d) FFT patterns extracted from the box regions in b show typical square and hexagonal lattices, respectively. (e) STEM-ADF image showing the interface between monolayer TaS ₂ and bilayer Ta ₉ S ₁₆ . (f) The intensity line profile extracted from the horizontal line in e. Scale bars: 10 nm in (a); 2 nm in (b); 1 nm in (e). The amorphous step edges shown in the STEM image e are due to oxidization during the sample transfer in air. Figure 13. Glassy state of Ta ₁₀ S ₁₆ . (a) Atomic-resolution STEM-ADF image of 50% Ta- intercalated Ta ₁₀ S ₁₆ ic- 2d film in which the intercalated Ta atoms reveal a glassy phase where (b) the intercalated Ta atoms were highlighted. The calculated Ta-intercalation concentration is -50% after mass processing tens of images by Python scripts. Scale bar: 2 nm.

Figure 14. STEM analysis of Ta ₁₀ S ₁₆ . (a) STEM-ADF image showing the large field of view of glassy phase Ta ₁₀ S ₁₆ ic-2d films, (b) Atomic-resolution STEM-ADF image confirms the 7 atomic layers of Ta ₁₀ S ₁₆ and (c) its corresponding FFT pattern, (d) Atomic resolution STEM- ADF image showing the interface between monolayer TaS ₂ and bilayer Ta ₁₀ S ₁₆ . (e) The intensity line profile extracted from the horizontal line in d. Scale bars: 10 nm in (a); 5 nm in (b); 1 nm in (d).

Figure 15. STEM analysis of Ta ₉ S ₁₂ . (a) STEM-ADF image showing the interface from monolayer TaS ₂ to 100% Ta-intercalated Ta ₉ S ₁₂ ic-2d film, (b) The intensity line profile extracted from the line in a. Scale bars: 2 nm.

Figure 16. Crystal size of Ta ₈ Se ₁₂ grown by CVD. (a) Optical image of the CVD grown 66.7% Ta-intercalated Ta ₈ Se ₁₂ ic-2d flakes, (b) STEM image showing a typical Ta ₈ Se ₁₂ ic-2d flake. Scale bar: 50 μm in (a); 1 μm in (b). The lateral size of the Ta ₈ Se ₁₂ flakes ranges from a few micron up to several tens of micron.

Figure 17. STEM analysis of Ta ₈ Se ₁₂ . (a) STEM-ADF image showing a highly crystalline Ta ₈ Se ₁₂ ic-2d flake, (b) Enlarged image of Ta ₈ Se ₁₂ revealing a Kagome lattice, and (c) corresponding STEM-ABF (annular bright field) image captured simultaneously, (d) Simulated STEM-ADF image based on the (e) DFT optimized Ta ₈ Se ₁₂ atomic model where the intercalated Ta atoms were highlighted. Scale bars: 5 nm in (a); 0.5 nm in (b-d).

Figure 18. STEM cross-section view of Ta ₉ Se ₁₂ . STEM-ADF image showing the cross- section view of 100% Ta-intercalated Ta ₉ Se ₁₂ ic-2d crystals. Scale bar: 5 nm

Figure 19. EDS analysis of Ta _x S _y and Ta _x Se _y . EDS of various intercalated phases of (a) Ta _x S _y and (b) Ta _x Se _y .

Figure 20. Determination of stacking order in 2H _a -stacked Ta ₇ S ₁₂ . (a) Atomic-resolution STEM-HAADF, and (b) its corresponding simulated image derived from the DFT optimized 2H _a -stacked Ta ₇ S ₁₂ . Intensity line profiles extracted from (c) line 1 , and (d) line 2 in a-b, respectively, (e) Atomic-resolution STEM-MAADF, and (f) its corresponding simulated image derived from the DFT optimized 2H _a -stacked Ta ₇ S ₁₂ . Intensity line profiles extracted from (g) line 1, and (h) line 2 in e-f, respectively, (i) DFT optimized atomic model of 2H _a -stacked Ta ₇ S ₁₂ and corresponding (j) simulated diffraction pattern where √3 a x √3 a super spots were highlighted by the circles. The side view was depicted in the lower panel, (k) FFT pattern from a with a large field of view. √3a x √3a super spots were highlighted by the circles. The STEM- MAADF images were collected using a half-angle range from ~30 to 110 mrad to enhance the contrast of S. Scale bars: 0.5 nm.

Figure 21. STEM analysis of 2H _a -stacked Ta ₇ S ₁₂ . (a) Atomic-resolution STEM-MAADF image showing a 2H _a -stacked Ta ₇ S ₁₂ , and (b) enlarged STEM-ABF image captured simultaneously. Notably, periodic √3a x √3a contrast enhancement induced by Ta self- intercalation can be visualized in STEM-ABF image as highlighted by the circles. The STEM- MAADF image was collected using a half-angle range from ~30 to 110 mrad. (c) STEM-ADF image showing the interface between monolayer TaS ₂ and bilayer Ta ₇ S ₁₂ . (d) The intensity line profile extracted from the horizontal line in c. Scale bars: 2 nm in (a), 0.5 nm in (b), and 1 nm in (c).

Figure 22. Calculated magnetization as a function of the temperature using the Monte Carlo simulation based on the Ising Model.

Figure 23. Ferromagnetic order in Ta ₈ Se ₁₂ . (a) Optical microscopy image of Ta ₈ Se ₁₂ Hall bar device encapsulated with h-BU. (b) Resistivity as a function of temperature, with CDW induced resistivity peak at ~ 150 K. (c) Temperature dependent Hall resistance (R _xy ) under out-of-plane magnetic field. Scale bar: 5 μm.

Figure 24. Formation energy (eV/atom) for the 14 self-intercalated compounds relative to the formation energy of the non-self-intercalated counterpart, including Ta ₇ S ₁₂ , Ta ₇ Se ₁₂ , Ta ₇ Te ₁₂ , Nb ₇ S ₁₂ , Nb ₇ Se ₁₂ , Nb ₇ Te ₁₂ , M0 ₇ S ₁₂ , Mo ₇ Se ₁₂ , Ti ₈ S ₁₂ , Ti ₈ Se- ₁₂ , Ti ₈ Te ₁₂ , Co ₈ S ₁₂ , Co ₈ Se ₁₂ , and Co ₈ Te ₁₂ .

Figure 25. DFT calculated formation energies in various Ta _x S _y and Mo _x S _y . DFT calculated formation energies of various phases of self-intercalated (a) Ta _x S _y , and (b) Mo _x S _y where the intercalation concentrations are 16.7%, 25%, 33.3%, 50%, 66.7%, and 100%, respectively, as a function of sulfur chemical potential. The horizontal black line indicates the formation energy of TaS ₂ , and M0S ₂ , respectively. It can be seen that for Mo _x S _y , the formation energies of all compounds are above the stoichiometric M0S ₂ phase, whereas in the case of Ta _x S _y , the formation energy can be negative compared to stoichiometric TaS ₂ , especially at high Ta chemical potential window. Hence, the self-intercalation of M0S ₂ or other group VI TMDC is discouraged by the much more stable electron configuration of MX2 compared to sub- stochiometric M _x X _y phases.

Figure 26. V-intercalated V _{1 1} S ₁₆ . (a-b) DFT optimized atomic models of V self-intercalated ic-2d V _{1 1} S ₁₆ . (b) Side views of the V _{1 1} S ₁₆ . (c) Simulated STEM image of V _{1 1} S ₁₆ , which greatly resembles the experimental image and (d) corresponding simulated diffraction pattern of V _{1 1} S ₁₆ revealing a clear 2 x 2 superstructure. (e) STEM image showing the morphology of the CVD grown V11S16, and (f) corresponding EEL spectrum. Scale bar: 2 μm.

Figure 27. In-intercalated In _{1 1} Se ₁₆ . (a) DFT optimized atomic model of In self-intercalated ic- 2d lniiSe ₁₆ . (b) The top view of intercalated In atoms, (c-d) Side views of ln _{1 1} Se ₁₆ . (e) Simulated STEM image of ln _{1 1} Se ₁₆ agrees with the experimental image and (f) corresponding simulated diffraction pattern of ln _{1 1} Se ₁₆ revealing a clear 2 x 2 superstructure, (g) STEM image showing the morphology of the MBE-grown ln _{1 1} Se ₁₆ , and (h) corresponding EDS. Scale bar: 20 nm. The Mo signals in EDS are from the Mo Quantifoil TEM grid.

Figure 28. Fe-intercalated Fe _x Te _y . (a) STEM image showing the morphology of the CVD- grown Fe _x Te _y , and (b) corresponding EDS. (c) Atomic-resolution STEM-ADF image showing the coexistence of Fe-intercalated ic-2d Fe _x Te _y and pristine FeTe domains. Enlarged box regions in a showing the (d) pristine FeTe and (e) Fe-intercalated ic-2d Fe _x Te _y domains. Atomic structure of (f) pristine FeTe and (g) proposed Fe _x Te _y . Corresponding side views were depicted in the lower panels. Scale bars: 500 nm in (a); 1 nm in (c); 0.2 nm in (d-e).

Figure 29. V-intercalated V _x Te _y . (a) STEM-BF image showing the morphology of the CVD- grown V _x Te _y . and (b) STEM-ADF image showing the spatial distribution of pristine VTe2 and V _x Te _y phase, and (c) corresponding FFT pattern from V _x Te _y phase. New superspots were highlighted by dashed circles, (d) Atomic-resolution STEM-ABF image showing the coexistence of V-intercalated ic-2d V _x Te _y and pristine VTe2 domains. Enlarged black box regions in d showing the (e) pristine VTe2 and (f) V-intercalated ic-2d V _x Te _y domains, (g) EDS of V _x Te _y . Scale bars: 500 nm in (a); 5 nm in (b); 1 nm in (d); 0.2 nm in (e-f).

Figure 30. A library of 14 types of ferromagnetic ic- 2d films as calculated by high- throughput DFT calculation.

Description In a first aspect of the invention, there is provided a compound comprising: a plurality of layers of a transition metal dichalcogenide or a similar semiconductor material, where between any two adjacent layers there is a first set of vacancies; and a transition metal occupying from 25% to 100% of the first set of vacancies in the compound.

In embodiments herein, the word “comprising” may be interpreted as requiring the features mentioned, but not limiting the presence of other features. Alternatively, the word “comprising” may also relate to the situation where only the components/features listed are intended to be present (e.g. the word “comprising” may be replaced by the phrases “consists of” or “consists essentially of”). It is explicitly contemplated that both the broader and narrower interpretations can be applied to all aspects and embodiments of the present invention. In other words, the word “comprising” and synonyms thereof may be replaced by the phrase “consisting of” or the phrase “consists essentially of’ or synonyms thereof and vice versa.

The phrase, “consists essentially of” and its pseudonyms may be interpreted herein to refer to a material where minor impurities may be present. For example, the material may be greater than or equal to 90% pure, such as greater than 95% pure, such as greater than 97% pure, such as greater than 99% pure, such as greater than 99.9% pure, such as greater than 99.99% pure, such as greater than 99.999% pure, such as 100% pure.

Broadly put, the terms “transition metal dichalcogenides” and “similar semiconductor materials” relate to 2-dimensional materials with weak bonding between the 2-dimensional materials. Said 2-dimensional materials have covalent bonding in one plane (in-plane), while having much weaker van der Waals bonding in the out of plane direction. Examples of such 2- dimensional materials include compounds with the formula MX, MX2, M2X ₃ and the like. Examples of transition metal dichalcogenides include, but are not limited to MOS ₂ , TaS ₂ , NbSe2). Examples of similar 2-dimensional semiconductors include, but are not limited to lmS3, lmSe3, SnS, SnSe, GeS, and GeSe.

Unless otherwise specified, the term “layer” is intended to refer to a single 2-dimensional material, that is, the material as an integral unit. Each of said layers are in turn formed from three atomic layers, where one atomic layer of transition metal atoms are sandwiched between two atomic layers of chalcogenide atoms. As such, the term “atomic layer” will be used herein to describe a sub-unit of an overall “layer” (i.e. a 2-dimensional layer formed from a transition metal dichalcogenide) or the single atomic layer of transition metal atoms sandwiched between two transition metal dichalcogenide “layers”. In the current invention, the layers of 2-dimensional materials mentioned above (that is, layers of transition metal dichalcogenides and similar semiconductor materials) are covalently bonded together to form 3-dimensonal structures. This is achieved by the insertion of transition metal atoms into vacancies between two adjacent layers of 2-dimensional materials (i.e. a transition metal dichalcogenide or a similar semiconductor material). The thinnest form of the resulting material will have seven atomic layers (each 2-dimensional “layer” has three atomic layers, so six in total, with one further atomic layer being formed in the van der Waals gap between the 2-dimensional layers). As such, the 3-dimensional materials disclosed herein may have 7+(4n) atomic layers. As will be appreciated, each additional 2-dimensional material layer will be attached to the rest of the 3-dimensional material through a further atomic layer of transition metal atoms, thereby increasing the total number of atomic layers by four. Any suitable number of layers may be included, so n may be from 0 to 1000, such as from 0 to 100, such as from 0 to 10.

The inserted transition metal atoms occupy a first set of vacancies within the van der Waals gap between two layers of 2-dimensional material. In embodiments of the invention, the first set of vacancies occupied may be octahedral vacancies or trigonal prismatic vacancies. In particular embodiments of the invention that may be mentioned herein, the first set of vacancies may be octahedral vacancies. In certain embodiments of the invention, there may also be a second set of vacancies within the van der Waals gap between two layers of 2- dimensional material. This second set of vacancies may exist but not be occupied by any transition metal atoms, as the first set of vacancies may be preferentially filled first. For example, the second set of vacancies may not start to be filled until the first set of vacancies has been completely filled. In any event, the transition metal may occupy from 0 to 100% of the second set of vacancies.

As will be appreciated, the second set of vacancies may be octahedral vacancies or trigonal prismatic vacancies. As will be appreciated, if the first set of vacancies are octahedral vacancies then the second set of vacancies are trigonal prismatic vacancies, or if the first set of vacancies are trigonal prismatic vacancies then the second set of vacancies may be vacancies octahedral vacancies. In embodiments that may be mentioned herein, the first set of vacancies may be octahedral vacancies. In embodiments of the invention where the first set of vacancies are octahedral vacancies, the second set of vacancies may not begin to be occupied until 100% of the octahedral vacancies are occupied by a transition metal. In particular embodiments of the invention that may be mentioned herein, the transition metal dichalcogenide or the similar semiconductor material may have the formula I:

M _a X _b I where:

M is a transition metal;

X is a chalcogenide; a is from 1 to 3; and b is from 1 to 3.

While compounds of formula I that may be mentioned herein may be ones wherein a and b are integers, it is possible for b and, more particularly, a to be non-integer numbers as well (e.g. a may be 1.4). In particular embodiments that may be mentioned herein b may be an integer and a may be a non-integer or, more particularly, an integer number.

The transition metals mentioned herein may be selected from any transition metal. Particular transition metals that may be mentioned herein include, but are not limited to, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, Ge, Zr, Nb, Mo, Pd, In, Sn, Hf, Ta, W, Pt, and combinations thereof. More particularly, the transition metal may be selected from one or more of the group consisting of Fe, V, Cr, Mn, Nb, In, and Ta.

Any suitable chalcogenide may be used in embodiments of the invention. Examples of suitable chalcogenides include, but are not limited to S, Se, Te, and combinations thereof.

Specific examples of similar semiconductor materials include, but is not limited to ln ₂ S ₃ , ln ₂ Se ₃ , SnS, SnSe, GeS, GeSe, and combinations thereof.

In embodiments of the invention, the transition metal occupying the first set of vacancies may occupy 25%, 33.3%, 50%, 66.7% or 100% of the first set of vacancies. For example, these vacancies may be octahedral vacancies. The second set of vacancies (e.g. trigonal prismatic vacancies) may be completely unoccupied when the first set vacancies are less than 100% occupied. For example, when the transition metal occupies 100% of the first set of vacancies, then the transition metal may also occupy from 0 to 100% of the second set of vacancies, such as from 0 to 50%, such as from 5% to 25%.

Specific compounds disclosed herein may display ferromagnetic properties. This may occur even when the transition metal(s) used to form the compound is non-magnetic, which is particularly surprising. In particular embodiments, these ferromagnetic compounds of the invention may have ferromagnetic properties when the Curie temperature is greater than 180K. In embodiments of the invention where the compound is ferromagnetic, the transition metal occupying the first set of vacancies (e.g. octahedral vacancies) may occupy greater than 30% and less than 50% of the octahedral vacancies. In embodiments where the compound of the current invention is ferromagnetic, the compound may have the formula M _x X ₁₂ , where M is selected from In, Ta, Mo, W, Nb, Co, and Ti (e.g. M is selected from In, Ta, Mo, W, Nb, Co, and Ti), X is selected from S, Se or Te, and x is from 6 to 7 (non-integer numbers between 6 and 7 are also possible forx). In more particular embodiments that may be mentioned herein, when the compound is ferromagnetic, it may be selected from one or more of the group consisting of: Ta ₇ S ₁₂ ; Ta ₇ Se ₁₂ ; Ta ₇ Te ₁₂ ; Mo ₇ S ₁₂ ; Mo ₇ Se ₁₂ ; Mq ₇ Te ₁₂ ; W ₇ S ₁₂ ; W ₇ Se ₁₂ ; W ₇ Te ₁₂ ; Nb ₇ S ₁₂ ; Nb ₇ Se ₁₂ ; Nb ₇ Te ₁₂ ; Co ₇ S ₁₂ ; Co ₇ Se ₁₂ ; Co ₇ Te ₁₂ ; Ti ₇ S ₁₂ ; Ti ₇ Se ₁₂ ; Ti ₇ Te ₁₂ ; In ₇ S· ₁₂ ; n ₇ Se· ₁₂ ; and ln ₇ Te ₁₂ .

The compounds of the current invention may also be provided in the form of a Kagome lattice. In such cases, the transition metal occupying the first set of vacancies (e.g. octahedral vacancies) may occupy greater than 60% of the octahedral vacancies. In embodiments displaying a Kagome lattice, the compound may have the formula M _X X ₁₂ , where M is selected from In, Ta, Mo, W, Nb, Co, and Ti (e.g. M is Ta, Nb, and Ti), X is selected from S, Se or Te, and x is from 8 to 9, such as 8 (again, non-integer numbers between 8 and 9 are possible for x). For example, the compounds displaying a Kagomi lattice may be selected from one or more of Ta ₈ S ₁₂ ; Ta ₈ Se ₁₂ ; Ta ₉ S ₁₂ ; Ta ₉ Se ₁₂ ; Nb ₈ S ₁₂ ; Nb ₈ Se ₁₂ ; Nb ₉ S ₁₂ ; Nb ₉ Se ₁₂ ; Ti ₈ S ₁₂ ; Ti ₈ Se ₁₂ ; Ti ₉ S ₁₂ ; Ti ₉ Se ₁₂ .

The compounds of the current invention may also display multiferrotic properties. Thus, the is also disclosed a multiferrotic compound formed from M _x X _y layers, with M occupying the first set of vacancies (e.g. octahedral vacancies) between the M _x X _y layers, where M is In, Ga, Sn, or Ge, X is S or Se, x is 1 or 2 and y is 1 or 3 (e.g. the compound is ln _{1 1} Se ₁₆ ). Again, non- integer numbers are possible for y and, more particularly, x.

The compounds described herein may have the generic formula II:

McXd II where:

M is a transition metal; X is a chalcogenide; c is from 7 to 16 (e.g. from 7 to 12); and d is 12 or 16.

While compounds of formula II that may be mentioned herein may be ones wherein c and d are integers, it is possible for b and, more particularly, a to be non-integer numbers as well (e.g. c may be 1.4). In particular embodiments that may be mentioned herein d may be an integer and c may be a non-integer or, more particularly, an integer number.

As mentioned above, the transition metal may be selected from one or more of the group consisting of Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, Ge, Zr, Nb, Mo, Pd, In, Sn, Hf, Ta, W, and Pt. For example, the transition metal may be selected from one or more of the group consisting of Fe, V, Cr, Mn, Nb, In, and Ta.

The chalcogenide may be selected from one or more of the group consisting of S, Se and Te. Particular compounds of formula II that may be mentioned herein include, but are not limited to:

Ta ₉ S ₁₆ ; Ta ₉ Se ₁₆ ; Ta ₉ Te ₁₆ ; Ta ₇ S ₁₂ ; Ta ₇ Se ₁₂ ; Ta ₇ Te ₁₂ ; Ta ₁₀ S ₁₆ ; Ta ₁₀ Se ₁₆ ; Ta ₁₀ Te ₁₆ ; Ta ₈ S ₁₂ ; Ta ₈ Se ₁₂ ; Ta ₈ Te- ₁₂ ; Ta ₉ S ₁₂ ; Ta ₉ Se ₁₂ ; Ta ₉ Te- ₁₂ ;

V11S16; V ₇ S ₁₂ ; V10S16; V ₈ S ₁₆ ; V ₉ S ₁₂ lniiSe ₁₆ ;

Fe ₉ S ₁₆ ; Fe ₉ Se ₁₆ ; Fe ₉ Te ₁₆ ; Fe ₇ S ₁₂ ; Fe ₇ Se ₁₂ ; Fe ₇ Te- ₁₂ ; Fe ₁₀ S ₁₆ ; Fe ₁₀ Se ₁₆ ; Fe ₁₀ Te ₁₆ ; Fe ₉ S ₁₂ ; Fe ₉ Se ₁₂ ; and Fe ₉ Te ₁₂ , optionally wherein the compound is selected from one or more of the group consisting of:

Ta ₉ Si ₈ ; Ta ₉ Se ₁₆ ; Ta ₇ S ₁₂ ; Ta ₇ Se- ₁₂ ; Ta ₁₀ S ₁₆ ; Ta ₁₀ Se ₁₆ ; Ta ₈ S ₁₂ ; Ta ₈ Se ₁₂ ; Ta ₉ S ₁₂ ; Ta ₉ Se ₁₂ ;

V11S16; and lniiSe ₁₆ ; ln ₇ Se ₁₂ ; lni ₀ Se ₁₆ ; ln ₈ Se ₁₂ ; ln ₉ Se ₁₂ .

The compounds described herein may be made by any suitable method. For example, the compounds disclosed herein may be formed by a method of manufacturing that involves molecular beam epitaxy and/or chemical vapour deposition (e.g. metal organic chemical vapour deposition). Further details of said methods will be provided in the examples below.

As shown in Example 1 below, the compound may comprise ultrathin large-scale 2D magnets, i.e., Ta-intercalated Ta ₇ S ₁₂ , from non-ferromagnetic elements. The thickness of the grown layer in this case can be as thin as 7 layers of atoms, and up to multiples of this thickness, extending periodically in space in the z direction. At intercalated M concentration of less than 50% (with respect to the octahedral vacancy site between two layers of chalcogen (X)), the material becomes ferromagnetic. At 33% octahedral vacancy filling (33% of the total number of octahedral vacancy sites are filled by Ta), strong ferromagnetism develops. The intercalated Ta atoms form a √3 x √3 superlattice that is sandwiched by two layers of TaS ₂ .

As shown in Examples 1 and 2 below, in addition to 33.3% Ta-intercalated Ta ₇ S ₁₂ , a full spectrum of Ta _x S _y , including 25% intercalated Ta ₉ S ₁₆ , 50% Ta ₁₀ S ₁₆ , 66.7% TasS ₁₂ , and 100%

Ta ₉ S ₁₂ , have been successfully grown. Self-intercalated V _x S _y , ln _x Se _y , and Fe _x Te _y , etc, was also grown under metal rich environments by chemical vapor deposition (CVD), as shown in Example 6. Therefore, it is shown that self-intercalation is a unique approach to grow ultrathin 3D materials from 2D bilayers with stoichiometry or composition-dependent properties, e.g., ferromagnetism or kagome lattice.

Further aspects and embodiments of the invention are provided in the following non-limiting examples.

Examples

In this work, we studied the growth of 2D TMDs under conditions of high metal chemical potential using both molecular beam epitaxy (MBE) and chemical vapor deposition (CVD). We discovered that independent of the employed growth method, a metal-rich chemical potential promotes the self-intercalation of M into MX, MX ₂ , or M ₂ X ₃ layered 2D compounds to produce a covalently bonded ic-2d M _x X _y compound (M = metal, X = chalcogen).

Using TaS ₂ as an example, intercalated Ta atoms occupy the octahedral vacancies in the vdW gap to form distinct topographical patterns, as verified by the atomic resolution scanning transmission electron microscopy - annular dark field (STEM-ADF) imaging. By varying the ratio of intercalated atoms to the octahedral vacancies in the vdW gap, we were able to grow Ta _x S _y or Ta _x Se _y films with σ% of Ta-intercalation, where σ% refers to the ratio of occupied vacancy sites to the initial total vacancy sites.

Our results indicate that self-intercalation is generic to a broad class of vdW crystals and it offers a powerful approach to transform layered 2D materials into ultrathin, covalently bonded ic-2d crystals with ferromagnetic properties. General methods

Sample characterization. XPS was performed using SPECS XR 50 X-ray Al Ka (1486.6eV) source with a pass energy of 30 eV. The chamber base pressure is lower than 8 ^x 10-1 ⁰ mbar. Raman spectra were collected at room temperature using the confocal WiTec Alpha 300R Raman Microscope (laser excitation: 532 nm).

STEM sample preparation, image characterization, and image simulation. The as-grown TMD films were transferred via a PMMA method under the protection of graphene. Continuous graphene film was coated on fresh Ta ₇ S ₁₂ film to protect the surface oxidation via conventional PMMA method. Subsequently, graphene/Ta ₇ S ₁₂ composites were immersed in 1 M KOH solution to detach the PMMA/ Ta ₇ S ₁₂ composite from the S1O2 substrate, followed by rinsing in Dl water. The PMMA/graphene/Ta ₇ S ₁₂ film was then placed onto Cu quantifoil TEM grid which was precoated with continuous graphene film (Nat. Commun. 8, 394 (2017)). The TEM grid was then immersed in acetone to remove the PMMA films. Atomic-resolution STEM-ADF imaging was performed on an aberration-corrected ARM200F, equipped with a cold field- emission gun and an ASCOR corrector operating at 60 kV. The STEM-ADF images were collected using a half-angle range from ~81 to 280 mrad unless indicated elsewhere. The convergence semiangle of the probe was ~30 mrad. Image simulations were done with the QSTEM package assuming an aberration-free probe with a probe size of ^≈ 1 Å. The convergence semiangle of the probe was set as ~30 mrad, and the accelerating voltage is 60 kV in line with the experiments. The collection angle for HAADF and MAADF images were from 81 to 280 mrad and 30 to 110 mrad, respectively. The thermal diffuse scattering (TDS) was set as 30 with defocus value 0. The STEM-EDS were collected and processed in an Oxford Aztec EDS system.

The extent of intercalation can be quantitively identified by energy dispersive spectroscopy (EDS). Using TaS ₂ bilayer as an example, if the intercalation concentration is 33%, then the chemical stoichiometry is the sum of 2 ^* (TaS ₂ ) + 0.33 ^* (intercalated Ta) to give Ta ₇ S ₁₂ . The calculation can be reversed to determine the extent of intercalation from the EDS obtained chemical stoichiometry.

Example 1 : MBE growth of self-intercalated Ta _x S _y films

We first describe the self-intercalation of a TaS ₂ bilayer by native atoms (i.e., Ta) during MBE deposition on a silicon wafer. This demonstrates the transformation of a 2D bilayer film into an ic-2d film via octahedral vacancy filling. Wafer-scale Ta-intercalated TaS ₂ bilayer films were grown on 2-inch 285 nm SiO 2/ Si wafers in a dedicated MBE system (J. Am. Chem. Soc. 139, 9392-9400 (2017)). Ultra-pure Ta and S molecular beams were evaporated from an e-beam evaporator and sulfur cracker cell equipped with a valve, respectively (Fig. 1a-b). The experimental details are described below.

Experimental

Ta-intercalated Ta _x S _y films were grown in a dedicated MBE chamber (base pressure < 6x10- ¹⁰ torr). Prior to the growth, the 2-inch S1O2 substrates were degassed in the same chamber at 500 °C for 2 h. Ultrapure Ta (99.995%, Goodfellow) and S powders (99.5% Alfa Aesar) were evaporated from a mini electron-beam evaporator and a standard sulphur valved cracker, respectively. The flux density of Ta was precisely controlled by adjusting the flux current. The S cracker cell temperature was maintained at 110 °C, and the flux density was controlled by the shutter of the cracker valve. The substrate temperature was maintained at 600 to 650 °C and the growth time is about 3 hours for all thin films.

25% Ta-intercalated Ta ₉ S ₁₆ , 33.3% Ta ₇ S ₁₂ , and 50% Ta ₁₀ S ₁₆ films were controlled grown when the Ta/S ratio is set as ~1 :8, ~1:6, and ~1 :5, respectively. A slightly higher growth temperature will facilitate the self-intercalation process. After growth, both sources were turned off and the sample was further annealed for another 30 mins before cooling down to the room temperature.

Characterization of Ta ₇ Si2 films

We can routinely grow 2H-phase TaS ₂ bilayer films using a high S chemical potential, i.e., Ta to S flux ratio -1:10 (Fig. 1 a and Fig. 6) for 3 hours, and a substrate temperature of 600 °C. It can be seen that 2H _c -TaS ₂ has a signature honeycomb structure and each atom blob in the honeycomb (Fig. S1b) appears with nearly identical contrast in line with the contrast pattern in typical 2H _c -stacked TMDs.

When the Ta:S flux ratio was increased to 1 :6 (Fig. 1c), the film became non-stoichiometric with respect to TaS ₂ owing to the excess Ta atoms. A fingerprint of the Ta-rich environment is the presence of Ta adatoms (Fig. 1d) occupying the center of the honeycombs (Fig 1e) or atop of the Ta sites (Fig. 1f) in monolayer TaS ₂ film, as observed by STEM when the growth was interrupted mid-way (Fig. 7). Surface Ta atoms can be clearly spotted by the contrast enhancement. By continually supplying Ta and S in the requisite ratio, the Ta adatoms become embedded and occupy the octahedral vacancies between two S layers (Fig. 1g). Therefore, the growth mechanism of ic-2d crystals follows a sequential TaS ₂ -Ta-TaS ₂ -Ta layer-by-layer growth, such that multilayer or bulk phase ic-2d crystals can be readily accessed by simply increasing the growth time.

The thermodynamic stability of such intercalated phases is analyzed by the energy- composition phase diagram generated through our DFT calculations (Fig. 1h). It can be seen that stoichiometric H-phase TaS ₂ is only formed under S rich conditions (μs > -5.3 eV), whereas under low μs, various Ta-intercalated Ta _x S _y configurations, ranging from Ta ₉ S ₁₆ (33.3% Ta intercalation) to Ta ₉ S ₁₂ (100% Ta intercalation), entered a thermodynamically stable state.

A —1 :6 Ta:S ratio in the beam flux produced a √3a x√3a superlattice of Ta atoms (Fig. 2a) sandwiched between two TaS ₂ monolayers. The coverage s was 33.3%, and the overall stoichiometry of the crystal thus became Ta ₇ S ₁₂ , as corroborated by both the real space STEM image (Fig. 2b) and the corresponding fast Fourier transform (FFT) pattern (Fig. 2c). Image simulation and sequential STEM images capturing the diffusion of intercalated atoms proved that the periodically arranged bright spots in the STEM image were induced by the Ta intercalation (see Fig. 2d). We have also collected STEM cross-section image (Fig. 2e-f) to prove the existence of an intercalated Ta atomic layer in the vdW gap of ic-2d films grown by CVD. From Fig. 21d), the intensity ratio between the monolayer, bilayer without intercalation, and bilayer with intercalation region is roughly 1: 2: 3. Therefore, we can conclude the Ta ₇ S ₁₂ is bilayer thick or consists of 7 atomic layers (comprising of 6 atomic layers+1 intercalated layer).

The homogeneous Ta ₇ S ₁₂ phase was grown directly on a 2-inch silicon wafer. The Ta ₇ S ₁₂ film was formed by coalescence of nano-domain crystals (~50 nm) separated by mirror twin boundaries or tilted grain boundaries. Amorphous islands and gaps seen in the STEM images were due to the poor stability of Ta _x S _y and sample damage during the sample transfer.

Energy dispersive x-ray spectroscopy (EDS) and electron energy loss (EEL) spectroscopy (Fig. 8) verified that the chemical composition comprised solely of Ta and S with no foreign elements. X-ray photoelectron spectroscopy (XPS) (Fig. 9) confirmed that the chemical stoichiometry agrees very well with Ta ₇ S ₁₂ . The chemical stoichiometry was calculated to be ~Ta _7.2 S ₁₂ . The Raman spectra of the film exhibited two prominent E ³ _g and A ³ _1g peaks at 300 cm ^-1 and 400 cm ^-1 , respectively, matching those of H-phase TaS ₂ films. The fingerprint of the intercalation came from a series of minor peaks in the 100 cm ^-1 to 170 cm ^-1 range (Fig. 10), which were absent in pure H-phase TaS ₂ attributed to the covalent bonds between the intercalated Ta atoms and their octahedrally coordinated S atoms (Fig. 11).

Characterization of Ta ₉ S ₁₆ , Ta ₁₀ S ₁₆ and Ta ₉ S ₁₂ films

25% Ta-intercalated TaS ₂ has a stoichiometry of Ta ₉ S ₁₆ and was produced at a slightly lowered Ta chemical potential, corresponding to a ~1 :8 Ta:S ratio. The intercalated Ta atoms occupy the octahedral vacancies in every 2a x √3 a unit length, and this phase was distinguished by the square symmetry of the intercalated atomic lattice (Fig. 2g, 2k, and Fig. 12). From Fig. 12f), the intensity ratio between the monolayer, and bilayer with intercalation region, is 1: 3. Therefore, we can conclude that Ta ₉ S ₁₆ is bilayer thick

When the Ta:S flux ratio was further increased to 1 :5, a Ta ₁₀ S ₁₆ phase (σ = 50%) was successfully grown (Fig. 2h). The intercalation concentration was determined to be exactly 50% via atom counting (Fig. 13). Interestingly, this phase is characterized by short-range interconnected atomic chains forming an overall glassy phase (or maze-like topology). Clear diffusive rings were observed in the proximity of the first order FFT spots (Fig. 2I and Fig. 14), confirming the presence of this short-range ordered structure. From Fig. 14e, the intensity ratio between the monolayer, bilayer without intercalation, and bilayer with intercalation region, is 1: 2: 3. Therefore, we can conclude that the Ta ₁₀ S ₁₆ is bilayer thick.

When we further enhanced the Ta:S flux ratio, 100% intercalated Ta ₉ S ₁₂ film was formed. The glassy phase was retained, but the short Ta atomic chains became denser until it fully evolved into a complete atomic plane when s reached -100% (Fig. 15. It can be seen from Fig. 15b the intensity of intercalated sites is two times higher than the monolayer region. Hence, each atom blob in the right-hand side domain contains three Ta atoms, thus confirming the phase is a 100% Ta-intercalated Ta ₉ S ₁₂ . When the growth condition straddles between two high- symmetry phases, phase separations occur and atomically sharp domain boundaries separating two high-symmetry phases can be clearly seen.

Example 2: CVD growth of self-intercalated Ta _x Se _y films

To verify that ic-2d films could be produced by methods other than MBE, we employed CVD to grow self-intercalated Ta _x Se _y crystals by using excess Ta precursors. Experimental

CVD growth of self-intercalated TMD films. Ta- intercalated Ta _x Se _y crystals were grown by CVD. Prior to the growth, the S1O2 substrate was sequentially cleaned by water and acetone, followed by 5 min of O2 plasma. The furnace was purged by 300 seem Ar gas for 5 mins. Se powders and mixed Ta/TaCIs powders were applied as precursors that were located upstream in a one-inch quartz tube. 40 seem Arand 10 seem H2 were used as a carrier gas. The samples were grown at 800 °C for 30 mins. After growth, the sample was cooled down quickly in a continuous stream of Ar. 66.7% Ta-intercalated TasSe ₁₂ , and 100% Ta-intercalated Ta ₉ Se ₁₂ were controlled grown when the Se powders and mixed Ta/TaCI ₅ powders are 1 g/15 mg/1.5 mg, and 1 g/30 mg/3 mg, respectively.

The method can also be extended to NbSe ₂ , VS ₂ , and FeTe ₂ materials under metal rich environments.

Results and discussion

The crystal domains of Ta-intercalated Ta _x Se _y films grown by CVD are in the micron-sized range, which are significantly larger than the nanosized domain grown by MBE (Fig. 16). A typical TasSe ₁₂ crystal (σ =66.7%) is depicted in Fig. 2i. Interestingly, it reveals a signature Kagome lattice belonging to the P ₆ wallpaper symmetry group. A well-defined √3a x √3a periodic lattice can be unambiguously identified in the atomic-resolution STEM image (Fig. 2m and the simulated image in Fig. 17).

At even higher Ta chemical potential, Ta ₉ Se ₁₂ crystals (σ = 100%) were successfully synthesized, arising from the full occupation of the prismatic vacant sites in AA-stacked

Ta ₉ Se ₁₂ (Fig. 2j), as seen in the STEM top view (Fig. 2n) and side view images (Fig. 2e & Fig. 18).

By precisely controlling the metal:chalcogen ratio during the growth, a full spectrum of Ta- intercalated Ta _x Se _y or Ta _x S _y compounds with intercalation ratio ranging from σ = 25% to over 100% can be grown, as further verified by EDS (Fig. 19 & Table 1).

Table 1 Calculated and EDS obtained chemical stoichiometry of various forms of Ta _x S _y and Ta _x Se _y . A relatively large Ta content obtained in experiments, especially in Ta _x Se _y , is due to multiple Ta intercalated layers in CVD grown multilayer Ta _x Se _y whereas the chemical stoichiometry is calculated based on a single intercalated layer in a bilayer film. In addition, the presence of surface Ta adatoms and chalcogen defects could further impact the EDS results. Example 3: Magneto-transport measurements of Ta ₇ S ₁₂ and TaeSe ₁₂

In the above examples, the intercalated Ta atoms were octahedrally coordinated to the S ₆ cage as opposed to the trigonal prismatic coordination adopted by pristine TaS ₂ . Charge transfer from the intercalated Ta atoms to the TaS ₂ host layers creates new electron ordering and modified its d band splitting. The tunability in this system stems from the fact that the amount of charge transfer is dependent on the intercalation concentration. To investigate if ferromagnetic order was present in the intercalated samples, magneto-transport measurements were carried out on MBE-grown Ta ₇ S ₁₂ (σ = 33.3%) with a predominantly 2H _a stacking registry (Fig. 3a and Fig. 20) with bilayer thickness (Fig. 21). The effects of self- intercalation on the electrical properties of TMDCs are further tested on the Kagome lattice TasSe ₁₂ (σ = 66.7%). Device fabrication and measurements

MBE-grown Ta ₇ S ₁₂ and CVD-grown TasSe ₁₂ (prepared according to Example 1 and 2, respectively) were selected to fabricate Hall-bar devices using e-beam lithography and e- beam evaporation of Ti/Au (2/60 nm). The MBE-grown Ta ₇ S ₁₂ film was then etched into Hall- bar geometry using deep reactive ion etching. The final devices were encapsulated with h-BN flakes using a dry-transfer method in the glovebox (both O ₂ and H ₂ O less than 1 ppm), to avoid degradation of Ta ₇ S ₁₂ and TasSe ₁₂ under ambient conditions. Low-temperature Transport measurements were carried out in Oxford Teslatron system. All resistances were derived from four-terminal measurements using SR830 lock-in amplifier, with constant excitation current of 1 mA.

Ferromagnetism in Ta ₇ S ₁₂

Fig. 3c shows the temperature-dependent resistivity, where a non-saturating upturn is observed below 30 K, due to the disorder-induced metal-insulator transition in the polycrystalline sample. Linear magneto-resistance (MR) up to 9 T at low temperature is observed in Ta ₇ S ₁₂ (Fig. 3d) due to the density and mobility fluctuations.

The anomalous Hall effect (AHE) arises from the interplay of spin-orbit interactions and ferromagnetic order, and is a potentially useful probe of spin polarization. We observed AHE in Ta ₇ S ₁₂ on top of the linear ordinary Hall effect (OHE). Fig. 3e shows the nonlinear Hall effect at the proximity of zero magnetic field and linear OHE at high field. While both multiband conduction and AHE contribute to nonlinear Hall effect, the observed linear OHE suggests single carrier conduction (hole) in Ta ₇ S ₁₂ and thus excludes multiband transport as the origin of the nonlinear Hall effect. The nonlinear Hall effect is thus ascribed to AHE, which stems from ferromagnetism in conductors. After subtracting the linear OHE, anomalous hall resistance up to 0.75 W is observed at 1.5 K; it decreases with increasing temperature and vanishes at 10 K in line with Monte Carlo simulation based on Ising model (Fig. 22).

The emergence of ferromagnetism in Ta ₇ S ₁₂ is ascribed to the charge transfer from the intercalated Ta atoms to TaS ₂ layer. The discovery of a ferromagnetic phase in ic-2d suggests them to be an interesting platform to explore ferromagnetism in low-dimension quantum matter. Ferromagnetism in Ta ₈ Se ₁₂

It was observed that the intercalation of Ta atoms and formation of Kagome lattices stabilize the charge density wave (CDW) states. Temperature dependent Hall signal reveals AHE below 15 K and confirms the ferromagnetic order in Ta ₈ Se12 (Fig. 23).

Fig. 23b shows the temperature dependent resistivity of the Ta ₈ Se ₁₂ , where a resistivity maximum is observed at ~ 150 K as a result of charge density wave (CDW) states. We note that the CDW onset temperature extends above room temperature and the CDW-induced resistivity kink becomes more pronounced compared to intrinsic TaSe with CDW onset temperature of ~ 120 K. While CDW ordering and its effect on resistivity are generally suppressed by dopants because of the enhanced scattering, here we observed that intercalation of Ta and formation of Kagome lattices stabilize the CDW states. This may be caused by the pining effect of the Ta intercalation sites on CDW. The charge order caused by strong electron-electron or electron-phonon correlations can be stabilized by the interaction between the CDW and the potential associated with highly ordered Ta intercalation. The resistivity upturn below 5 K is also a manifestation of strong electron-electron and electron- phonon interaction in the ultrathin Ta ₈ Se ₁₂ crystals.

We further probed the magnetic properties of Ta ₈ Se ₁₂ using the Hall effect. Fig. 23c shows the temperature dependent Hall signal in the presence of out-of-plane magnetic field, where the anomalous Hall effect (AHE) is observed below 15 K and confirms the ferromagnetic order in Ta ₈ Se ₁₂ . DFT calculations corroborated the spontaneous ferromagnetism and the net magnetic moment is 0.339 μ _B /unit cell. The AHE decreases with temperature increase and vanishes at 15 K, indicating an extrinsic origin (scattering) of the AHE.

Magnetic properties of Ta ₇ S ₁₂ films

The as-grown 2-inch Ta ₇ S ₁₂ film show clear magnetic field (M-H) curves as collected by a SQUID magnetometer. As seen in Fig. 5a, well-defined magnetization hysteresis loops are obtained at 10 K and 300 K confirming the ferromagnetic nature of Ta S ₁₂ film. The remanence (MR) and saturation magnetization (Ms) at 10 K are calculated to be 0.60 x 10 ^-6 emu, and 2.7 x 10 ^-6 emu, respectively. A clear divergence is found with changing temperature (M-T curves, Fig. 5b) as confirmed in zero-field-cooling (ZFC) and field-cooling (FC) curves. The Curie temperature (Tc) is identified to be 180 K. Example 4: DFT studies on the origin of magnetization in self-intercalated Ta ₇ S ₁₂

We performed DFT calculations to gain an understanding of the origin of the magnetization in self-intercalated Ta ₇ S ₁₂ .

DFT calculations

First-principles calculations based on Density Functional Theory (DFT) were implemented in the plane wave code VASP using the projector-augmented wave (PAW) potential approach. For the exchange and correlation functional, both the local density approximation (LDA) and the PBE flavor of the generalized gradient approximation are used and found no significant differences in the results. A kinetic energy cutoff of 500 eV is used for the TaS ₂ . A Monkhorst Pack k-grid samplings with a k-point density of 6.0 Å ^-1 were used for geometry optimization. For thin-film calculations, a vacuum thickness of 20 Å is added in the slab to minimize the interaction between adjacent image cells. Geometry optimization was performed with the maximum force convergence criterion of 0.005 eV/ Å. To treat the strong on-site Coulomb interaction of localized Ta-d orbitals, we use Dudarev’s approach with an effective U parameter of U _eff =3.0 eV. The zone center phonon modes were calculated by using the density functional perturbation theory (DFPT) with the local density approximation functionals.

Results and discussion

Perfect bilayer 2H _a -stacked TaS ₂ possesses a non-magnetic ground state. Ferromagnetism can be induced by the double exchange mechanism triggered by the charge transfer from intercalated Ta to pristine TaS ₂ (Fig. 3f). When the intercalated Ta adopts a √3a x √3a superstructure, six S atoms bond with one intercalated Ta atom to form an octahedral unit in the vdW gap. In contrast, each S atom is shared by three Ta atoms in the pristine TaS ₂ layer. This difference in local bonding arrangement induces charge transfer from the octahedral- coordinated intercalated Ta atom to the prismatic-coordinated Ta atom in the TaS ₂ layer (Fig. 3f). In the pristine H-phase TaS ₂ , the Ta d and S p orbitals are well separated in terms of energy, with the states at the Fermi level having mainly Ta d _z2 and Ta d _x2 characteristics. In Ta ₇ S ₁₂ (σ = 33.3%), the intercalated Ta atoms introduce additional spin-split bands across the Fermi level, and a magnetic ground state develops (Fig. 3g-h). The magnetic moments are localized on the d orbitals of the intercalated Ta atom, as evidenced by the calculated orbital- resolved spin up and spin down band structures in Fig. 3g and Fig. 3h, respectively. The states at the Fermi level comprise the prismatic-centred Ta d _zi orbitals hybridized with the spin-up band of the d _x2-y2 orbital of the intercalated Ta. However, only the intercalated Ta atoms exhibit a net spin density, as illustrated in Fig. 3i, where the top view spin density isosurface matches the shape of the d _x2-y2 orbital. In addition, the non-magnetic 3a x 3a CDW state of Ta ₇ S ₁₂ can be ruled out owing to its relative instability compared to the ferromagnetic state.

The existence of a magnetic moment correlates with a strong charge transfer between the intercalated Ta and the TaS ₂ layers. Strong charge transfer occurs in the dilute Ta-intercalated compound, whereas the charge transfer becomes relatively weak in a heavily intercalated (Fig. 3j) compound in accordance with the calculated charge difference and the variation of Bader charge in the Ta atoms (Table 2 (Supplementary Table 2)).

Table 2 DFT calculated charge differences between the Bader charge and the corresponding nominal valence charge for different atoms in various intercalated Ta _x S _y when the intercalation concentration is 16.6%, 25%, 33.3%, 50%, 66.7%, and 100%.

Example 5: High-throughput DFT calculations for other TMDs

To investigate whether the self-intercalation phenomenon occurred for other TMDs, we performed a high-throughput DFT study of 48 different intercalated TMD bilayers using a semi- automated workflow for maximal consistency and veracity. Specifically, we considered TMDs of the transition metals Mo, W, Nb, Ta, Ti, Zr, Hf, V, Cr, Mn, Fe, Co, Ni, Pd, Pt, and Sn, and the chalcogens S, Se, and Te when s equals 33.3% or 66.7%. Method

High-throughput DFT calculations were carried out with the electronic structure code GPAW (Journal of Physics Condensed Matter 22, 253202 (2010)) following a semi-automated workflow for maximal consistency and accuracy (2D Materials 5, 042002 (2018)). The relaxations of the self-intercalated bilayers are done on a Monkhorst-Pack (Phys. Rev. B 13, 5188-5192 (1976)) grid with a k-point density of 6.0 A ^-1 using the PBE (Phys. Rev. Lett. 77, 3865-3868 (1996)) and BEEF-vdW functionals (Phys. Rev. B 85, 235149 (2012)) for describing exchange-correlation effects. 15 A vacuum is used in the out-of-plane direction to avoid non-physical periodic interactions. The plane-wave expansion is cut-off at 800 eV. All systems are relaxed until the maximum force on any atom is 0.01 eV/A and the maximum stress on the unit cell is 0.002 eV/ Å ^-3 . All systems are calculated in the intercalated structure with both a spin-paired calculation and a spin-polarized calculation. If the total energy of the spin-polarized structure is found to be over 0.01 eV/atom lower than the spin-paired structure, the structure is concluded to be magnetically more stable than its non-magnetic counterpart. The atomic structures of calculated self-intercalated TMDs (33.3% and 66.7% intercalation concentration) were presented in Fig. 30, in which the polymorphism of single layer MoX ₂ , WX ₂ , NbX ₂ , and TaX ₂ (X = S, Se, and Te) reveals an H-phase, whereas the rest TMDs are T- phase taking an AA stacking polytype. MoX ₂ , and WX ₂ comply the AA’ stacking order whereas NbX ₂ , and TaX ₂ take the AB’ stacking registry. All intercalants occupy the octahedral vacancies in the vdW gap.

Results and discussion

Out of the set of TMDs considered, we observed that 14 bilayer configurations, Ti ₈ S ₁₂ , Ti ₈ Se ₁₂ , Ti ₈ Te ₁₂ , Co ₇ S ₁₂ , Co Se ₁₂ , Co ₇ Tb ₁₂ , Nb ₇ S ₁₂ , Nb ₇ Se ₁₂ , Nb ₇ Te ₁₂ , Mo ₇ S ₁₂ , Mo Se ₁₂ , Ta ₇ S ₁₂ , Ta Se ₁₂ , and Ta Te ₁₂ , (highlighted in Fig. 4a and Table 3 for magnetic moment) develop ferromagnetic order upon self-intercalation, whereas their parental MX ₂ are nonferromagnetic. Notably, group V and VI TMDs, exhibit strong ferromagnetism after self-intercalation (Fig. 4b). Intrinsic ferromagnetic MX ₂ (VX ₂ , CrX ₂ , MnX ₂ , and FeX ₂ ) retain ferromagnetism upon self- intercalation (marked by ^{^^} in Fig. 4a). Among the 14 types of self-intercalated 2D ferromagnets, the formation energies of 12 of them (the 2 exceptions being MoS ₂ and MoSe ₂ ) were lower than or similar to those of the non-intercalated materials (Fig. 24-25), indicating that self-intercalation is energetically feasible. Example 6: Validation of self-intercalation through growth of V _{1 1} S ₁₆ , In _{1 1} Se ₁₆ , and Fe _x Te _y

To validate the theoretical predictions, we attempted to grow a wide variety of ic-2d, as highlighted by the markings in the top left corner in Fig. 4a. Triangles indicate that the self- intercalation can be experimentally realized (Nat. Mater. (2019); Adv. Mater. 32, 1905896 (2020)), whereas ** indicate that intercalation was not be successful under our experimental conditions. We had succeeded to grow several ic-2d crystals, namely V _{1 1} S ₁₆ (Fig. 4c and Fig. 26), lniiSe ₁₆ (Fig. 4d and Fig. 27), and Fe _x Te _y (Fig. 4e and Fig. 28) by CVD or MBE. Their clear topological features and corresponding FFT patterns are depicted in Fig. 4f-h.

Experimental

V- intercalated V _x S _y crystals were grown by CVD. Prior to the growth, the S1O2 substrates were treated by the same method as indicated in growing Ta _x Se _y (Example 2). Two quartz boats containing 0.5 g S, and 0.3 g VCI ₃ were loaded in the upstream of the one-inch quartz tube serving as precursors. Carrier gases were 40 seem Ar together with 10 seem H2. The sample was grown at 680 °C for 30 mins. After growth, the sample was cooled down quickly under the protection of 100 seem Ar. V _x Te _y were grown by CVD by analogy to procedure for growing V _x S _y crystals.

Fe- intercalated Fe _x Te _y crystals were grown by CVD. Prior to the growth, the S1O2 substrates were treated by the same method as indicated in growing Ta _x Se _y (Example 2). Two quartz boats containing Te (>99.997%) and FeCl ₂ (>99.9%) were placed in the upstream in sequence of the one-inch quartz tube serving as precursors. The sample was grown at 600 °C for 30 mins. After growth, the sample was cooled down quickly under the protection of 100 seem Ar.

In-intercalated ln _x Se _y were grown in a customized MBE chamber (base pressure < 6x10 ^-10 torr). Prior to growth, the 1 cm x 1 cm SiO ₂ substrate was degassed in the chamber at 600 °C for 1 h. Ultrapure ln ₂ Se ₃ powder (99.99%) and Se pellets (99.999%) were evaporated from a mini electron-beam evaporator and an effusion cell, respectively. The Se effusion-cell temperature was set at 150 °C with a hot-lip at 220 °C. The substrate temperature was maintained at 400 °C and the growth time is about 2 hours. ln _{1 1} Se ₁₆ films were controlled grown when the ln2Se3/Se ratio is set as ~1:3. Discussion

The intercalated V _{1 1} S ₁₆ revealed a 2a x 2a superstructure, and the intercalation ratio was estimated at 75% (Fig. 4f). ln _{1 1} Se ₁₆ also showed a 2a x 2a superstructure, but in this case, the intercalated In atoms reveal a signature honeycomb structure (Fig. 4g).

The crystal structure of self-intercalated Fe _x Te _y was rather complicated with additional Fe intercalated into the atomic network of the pristine FeTe matrix as interstitials because telluride based TMDs offer the largest spacing between the host atoms. Upon intercalation, the novel Fe _x Te _y phase reveals new symmetries as confirmed by the emergence of superspots in the FFT pattern (Fig. 4h). Similar complex intercalation network has also been observed in V _x Te _y (Fig. 29).

Conclusion

We have discovered a robust way to perform composition engineering of a broad class of TMD by self-intercalation with native metal atoms during growth. The main principle is to apply a high chemical potential of metal atoms to provide the driving force for intercalation during growth, thus it should work for most growth methods. The metal intercalants occupy octahedral vacant sites in the vdW gap, and depending on the coverage patterns, distinct stoichiometric phases are produced. High throughput DFT simulations, supported by growth experiments, show that the self-intercalation method is applicable to a large class of 2D layered materials, thus allowing a whole new library of materials with potentially new properties to be created from existing layered materials. Owing to the versatility in composition control, it is possible to tune in one class of materials, properties that can vary from ferromagnetic to non- ferromagnetic, and spin-frustrated Kagome lattices. In particular, ferromagnetic order can be introduced into non-magnetic layered materials via the self-intercalation approach, giving rise to a unique topological phase such as ferromagnetic Kagome lattices. The implication of this work is that bilayer TMD (or thicker) can be transformed into ultrathin covalent bonded 3D material, with a stoichiometry that is tuneable by the concentration of the intercalants over a broad range. Example 7: Growth of lr ₁₂ Se ₂ and its ferromagnetic properties ln Se were grown following the procedure set out in Example 6 for growing ln _x Se _y except that the ln Se /Se ratio was set as 1 :6 or lower.

Using this method, we have transformed ln Se to Indium-intercalated ln Se , which shows ferromagnetic properties with a Curie’s temperature (Tc) above room temperature. Combined with the intrinsic ferroelectric property, we have transformed the material into a multiferroic material. The measured J(V) characteristics with bias applied to the graphene electrode show a rectifying behavior and a strong hysteresis in the negative bias range, in which a sharp increase of current density is observed at -2.8 V. Remarkably, the ratio between the high- resistance state (HRS) and low-resistance state (LRS) is as high as 1.1 x 10 ⁴ , exhibiting a giant electroresistance ratio. This device performance demonstrates that self-intercalated ln ₂ Se ₃ ferroelectric semiconductor junction can be used as random access memory, requiring a low voltage of -4 V to write and approximately -2 V to read. At the reading voltage of -2 V, the current density is at least 8 A/cm ² . Such high current density provides unambiguous differentiation of the “on” and “off” states for memory sense amplifiers.