Room-temperature intrinsic ferromagnetism in epitaxial CrTe2 ultrathin films

While the discovery of two-dimensional (2D) magnets opens the door for fundamental physics and next-generation spintronics, it is technically challenging to achieve the room-temperature ferromagnetic (FM) order in a way compatible with potential device applications. Here, we report the growth and properties of single- and few-layer CrTe2, a van der Waals (vdW) material, on bilayer graphene by molecular beam epitaxy (MBE). Intrinsic ferromagnetism with a Curie temperature (TC) up to 300 K, an atomic magnetic moment of ~0.21 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{{\rm{B}}}$$\end{document}μB/Cr and perpendicular magnetic anisotropy (PMA) constant (Ku) of 4.89 × 105 erg/cm3 at room temperature in these few-monolayer films have been unambiguously evidenced by superconducting quantum interference device and X-ray magnetic circular dichroism. This intrinsic ferromagnetism has also been identified by the splitting of majority and minority band dispersions with ~0.2 eV at Г point using angle-resolved photoemission spectroscopy. The FM order is preserved with the film thickness down to a monolayer (TC ~ 200 K), benefiting from the strong PMA and weak interlayer coupling. The successful MBE growth of 2D FM CrTe2 films with room-temperature ferromagnetism opens a new avenue for developing large-scale 2D magnet-based spintronics devices.

8. It is unclear whether the samples investigated with XRD were capped with Te. It is also unclear whether the Te capping layer was later (e.g. for ARPES, XAS and XMCD measurements) desorbed under vacuum. 9. In the sentence "which is also confirmed by the calculated density of states ( Fig. S6)", I guess the authors mean " Fig. S7". I have the feeling (but might be wrong...) that in several instances, the supplementary figures are not properly called in the main text. Please check. 10. Regarding the ARPES measurements and the possible match with DFT simulations performed for thin 1T CrTe2 flakes, I have several questions. The authors write "The observed metallic band further confirms the trigonal phase of the CrTe2 thin films". However, Fig. S9 for instance shows that both the 1T and the 2H phases are predicted metallic (at least in the bulk form). Actually, I find it very difficult to conclude that the observed electronic band structure ressembles the one predicted based on DFT calculations. The bands are actually not nicely resolved, and there are many features that do not really look alike what is calculated (Fig. 4a/b). What about a calculation for the 2H phase of a thin CrTe2 film (not for bulk, like in Fig. S9)? The number of layers seems an important parameter, and systematic calculations for different layer number might be relevant here. By the way, I might have missed the information, but I did not figure out what the layer number is for Fig. 4a. All this needs to be clarified and maybe discussed with more care.
111. Too few details are given about how the DFT calculations and electronic band structure was simulated.
Reviewer #2: Remarks to the Author: Two-dimensional van der Waals magnet is a new class of materials, being recognized as a unique platform for studying the two dimensional magnetism and also an important building block of van der Waals interfaces for novel spintronic functionalities. In this work, authors report the epitaxial growth of a new 2D van der Waals magnet CrTe2 and its magnetic/electronic properties. The results (High transition temperature, perpendicular magnetic anisotropy, and layer dependent magnetic/electronic properties) are clearly indicates the potential of this material. I feel that results are worth publishing in Nature Communications. However, there are several unclear points and I think the authors should further clarify them. 1.Although authors mentioned about the stoichiometry of grown films and excluded the possibilities of CrTe, Cr2Te3, and Cr5Te8, it requires more careful discussion to conclude the stoichiometry. It is known that MBE-grown sample can have its unique stoichiometry (partially intercalated one, for example), which is different from bulk and can even show the thickness dependence. In order to unambiguously clarify it, authors should show the cross-sectional TEM image of their samples with several different thicknesses. 2.I am confused about the valence number of Cr. Considering the stoichiometry of CrTe2, it seems that Cr4+ (and Te2-) is reasonable. Why authors can conclude Cr3+? 3.Related with the above comment, can Cr-Te bond be regarded as covalent bond or ionic bond? 4.I think it is impossible to determine the space group from out-of-plane XRD (line 133-136 in page 6). 5.For monolayer samples, authors only show the ARPES data. They should show the magnetization and XMCD data for monolayer sample. Because it seems that transition temperature of 3 ML samples is around 250 K (Fig. 2 a) and that of monolayer might be lower than it, the word "monolayer" in the title is misleading. 6.They only show the ARPES data at 107 K. More detailed discussion about the temperature dependence of ARPES data (temperature dependent spin splitting value) is required. 7.What is the mechanism of perpendicular magnetic anisotropy? Is it consistent with the bulk 4, Temperature dependence of magnetization in Fig. 3d is apparently different trend with that in Fig. 2a. Fig. 3d shows monotonic increase with decreasing temperature. However, 7 ML data in Fig. 2a steep increase around 250 K, then keep constant at low temperature. This difference should be discussed. If this difference comes from the measurement configuration, in-plane or outof-plane, the authors should provide temperature dependence of out-of-plane magnetization. If this comes from thickness difference or measurement method, it should be explained. 5, PMA is compared with Ku and saturation magnetization. Ku should be explained by equation. The magnetization in CrTe2 is rather small compared to other metal ferromagnets with PMA. Degree of PMA should be discussed on the same measure. For my sense, "strong PMA" is not appropriate for the observed data of CrTe2 in this manuscript because the value is not so large. If the authors try to claim the "strong PMA", please provide the values for famous strong PMA metal ferromagnets to compare. 6, please check carefully following minor points. 6-1, "doping a FM host with specific elements" in page 3, a word of FM means ferromagnetic. What did the word "a FM host" mean? 6-2, "modulating the magnetic order via electrolyte gating" in page 3, gating can modulate the charge density and/or electric field at the interface, resulting in the variation of magnetism. The word of "magnetic order" has some meanings, which may confuse. Please revise carefully. 6-3, Refs.10-12 are really appropriate references for the enhancement of FM order by proximity effect ? 6-4, "FM order of the CrTe2 is insensitive to the thickness" in page 6 is difficult to agree, because the judgement whether sensitive or insensitive depends on the system. The plot for Tc of film/Tc of bulk as a function of thickness for CrTe2 and Cr2Ge2Te6 seem meaningful to compare. 6-5, What does "quantum thickness regime" in page 7 mean? How did the authors define and evaluate the quantum feature?

/ 45
Response to referee reports First of all, we thank all three reviewers for their efforts, and the review comments/ suggestions which we find very helpful and constructive. We have taken them fully into account in our revised paper. We truly hope that you will find it now worthy of publication in Nature Communications.
Below we provide our point-to-point responses to all of the review comments.

Comments:
Xiaoqian Zhang et al. report on a multi-characterization of ultra thin van der Waals CrTe2 films. The films have been grown by MBE on graphene/SiC. This system is a very promising one in terms of (close to) room temperature ferromagnetic, with possible implications for fundamental understanding of low-dimensional magnetism and for spintronics applications.
The authors have used a large set of methods to study their system, including MBE, STM, XRD, SQUID, XMCD-XAS, ARPES measurements, and DFT calculations. This is certainly one of the strong points of the manuscript. The authors provide strong pieces of evidence that the material is indeed magnetic close to room temperature, with a large magnetic anisotropy and significant coercivity, even in the very few-layer thickness regime. Compared to recent works cited in the manuscript, which addressed thicker (still thin) films, this is certainly an important step.
I believe that the work presented here is of potential strong interest for the large communities working on 2D materials or spintronics.

Reply:
We thank the reviewer for his/her positive comments on the manuscript and the fact that he/she thinks that our work is of potential strong interest for the large communities working on 2D materials or spintronics.
Comments: However, I think that the manuscript needs to be improved in several respects. I provide a list of comments/suggestions/questions below.
1. The introduction is generally hard to follow, as it invokes rather advanced condensed matter physics concepts, and overall lacks clarity. Some recent reviews, for instance the one published by Gibertini and coworkers, have managed to introduce key concepts in a rather clear way. The authors might find inspiration in such reviews.

Reply:
We thank the reviewer for this kind suggestion.

/ 45
Revision: Based on the reviewer's suggestion, we have rephrased the introduction in the revised manuscript on page 3. "In a three-dimensional (3D) system, the magnon density of states are consecutive and chiefly determined by exchange interactions. Therefore, a magnetic phase transition could occur at a finite temperature. On the contrary, the long-range magnetic order in 2D systems can be destroyed by thermal fluctuations, according to the Mermin-Wagner theorem 1,2 . Considering the magneto-anisotropy in 2D ferromagnets, it opens up a large spin-wave excitation gap and quenches thermal fluctuations [3][4][5][6][7][8][9] , thereby stabilizing the long-range magnetic order in 2D regime. Opposed to defect or dopant induced magnetism, the ferromagnetism occurring in a stoichiometric compound is defined as intrinsic ferromagnetism." 2. Still in the introduction, the authors make a strong point about the role of dimensionality on the "robustness of 2D ferromagnetic order". Given the thickness of the materials this is certainly an important point, but this cannot be the only one: almost all parent 3D compounds that have been exfoliated as 2D materials already have a low Curie temperature (in the bulk form), for instance, and this is not, at least at first sight, related to a dimensionality issue. I think it is important to convey this idea to the reader, and I advise the authors to include a discussion in the introduction.

Reply:
We thank the reviewer for this valuable comments. This is indeed an important point. We agree with the reviewer that most of parent 3D compounds which could be exfoliated as 2D materials already have a relatively low Curie temperature (TC) in the bulk form, such as CrI3 (61 K) 1 , Cr2Ge2Te6 (68 K) 2 , CrCl3 (17 K) 3 and CrSiTe3 (33 K) 4 . For 3D compounds, the TC is predominately determined by exchange interactions 2 , and is insensitive to small single-ion anisotropies or small fields. Moreover, the interlayer exchange interactions in van der Waals (vdW) crystals is 2-3 orders of magnitude weaker than that of traditional metals 2 . Thereby, the TC of 2D ferromagnets in the bulk form is usually lower than that of traditional 3D materials 5 .
Revision: According to the reviewer's suggestions, we have included the discussion of low TC of 2D ferromagnets in the bulk form in the introduction part of the revised manuscript on page 3. "It mainly results from the enhanced spin fluctuation in reduced dimensions or the relatively weak exchange interactions. Note that the interlayer bonding strength in vdW compounds is 2-3 orders of magnitude weaker than that of traditional 3D materials, which leads to a low TC in the bulk form already." 3. The writing style should be improved in many instances: I find that some sentences are very lengthy, many others are not grammatically correct, the style is sometimes overly emphatic (e.g. outstanding, incredibly significant, particularly significant), and several formulations are obscure. I recommend the authors to thoroughly revise the text of their manuscript in this respect.

Revision:
We have added a discussion of the STM and XRD results about 1T and 2H phase in the revised manuscript on page 6. "A typical X-ray diffraction (XRD) 2- scan was employed to further identify the crystal structure (Fig. 1d) 8 and exfoliated CrTe2 flakes (thicker than 10 nm) reported by Purbawati et al. 9 , which possess in-plane easy axis. Despite these distinct results, we attribute them to the thickness-dependent magnetic anisotropy. The origin of magnetic anisotropy generally originates from three mechanisms, shape anisotropy 10,11 , magneto-crystalline anisotropy 12 and anisotropy of exchange interactions 11 . The shape anisotropy is due to the magnetostatic or dipole interactions, which lead to a preferential in-plane anisotropy for thin films 11 . The PMA in CrTe2 thin films is contrary to it. Thereby, the possibility of shape anisotropy can be ruled out.
The anisotropy of exchange interactions can be verified by performing DFT calculations of exchange interactions using the frozen magnon approach 12 . Fujisawa et al. found that the ferromagnetic (FM) Cr-Cr intra-sublattice exchange interaction dominates in CrTe2 thin films, and the total energy minima for CrTe2 occurs at perpendicular direction 12 . In this vein, the magnetic moments of CrTe2 thin films are driven to perpendicular direction due to the anisotropy of exchange interactions.
The thickness dependent magnetic anisotropy suggests that the lowered symmetry at the interface plays an important role in determining the PMA in CrTe2 thin films. As the magnetic film thickness approaches a few nm, interfacial magnetism and inversion symmetry breaking give rise to intriguing phenomena such as PMA 13 . This is a consequence of spin-orbit interactions, i.e., magneto-crystalline anisotropy, that apparently have a stronger effect in the more anisotropic film limit 10,14,15 . Both experimental results and DFT calculations indicate that, the magnetic moments of CrTe2 thin films are driven to the perpendicular direction, due to the magnetocrystalline anisotropy and the anisotropy of exchange interactions.
Regarding DFT calculations, according to the orbital and surface projection analysis of the band structure of 7 ML CrTe2 in this work, the metallicity is a consequence of the hybridization of Te-5p and Cr-3d orbitals crossing the Fermi level at the center of the Brillouin zone (Fig. S11), which is confirmed by the calculated density of states (Fig.  S12). The hybridization of Te and Cr bands is also verified with DFT calculations (including band structure and density of states) made by Freitas et al 8 . Moreover, the magnetic splitting of ~2-3 eV in bulk CrTe2 is also predicted, suggesting a FM ground state. Similarly, the splitting of majority and minority bands in CrTe2 films corroborates the FM ground state, which highlights the unique interplay of ferromagnetism and electronic structure in CrTe2. "The strong PMA in CrTe2 few-layer films is different from bulk CrTe2 8 and exfoliated flakes (thicker than 10 nm) 16 which have an in-plane easy axis. Here, the thickness dependent magnetic anisotropy suggests that the reduced symmetry at the interface plays an important role in determining the PMA in CrTe2 thin films 15 . As the magnetic 6 / 45 film thickness approaches a few nm, the interfacial magnetism and inversion symmetry breaking give rise to the PMA 13 . This is a consequence of spin-orbit interactions, i.e., magneto-crystalline anisotropy, that apparently have a stronger effect in the more anisotropic film limit 10,14,15 . In addition, based on density functional theory (DFT) calculations, it has been found that the FM Cr-Cr intrasublattice exchange interactions dominate in CrTe2 thin films, and the total energy minima is at perpendicular direction 12 . In general, the magnetic moments of CrTe2 thin films are aligned in the perpendicular direction, due to the magneto-crystalline anisotropy and the anisotropy of exchange interactions." "The hybridization of Te and Cr bands is also verified with DFT calculations (including band structure and density of states) made by Freitas et al 8 ." "The magnetic splitting in bulk 1T-CrTe2 is also predicted by Freitas et al 8 , suggesting a FM ground state." 7. The authors should show SQUID data acquired with the bare SiC/graphene substrate. This is an important piece of information needed to rule out any possible magnetic contribution from possible magnetic impurities in the substrate. I agree that XMCD should not be sensitive to such effects, but given the numerous debates on whether some 2D materials are magnetic or not, I suggest extra care in the presentation and interpretation of the SQUID data.

Reply:
We thank the reviewer for the nice suggestion. Based on this comment, we did the extra control experiments of bare SiC/graphene substrate. As exhibited in Fig. R3, the field dependent magnetization of SiC/graphene substrate at 20 K shows a typical diamagnetic behavior clearly. Instead, the magnetic response of 7 ML CrTe2 film on SiC/graphene substrate displays an obvious FM hysteresis loop superposed on a diamagnetic background. Therefore, the possibility of magnetic contribution from magnetic impurities in the substrate can be ruled out.

Revision:
We have added the data of the control experiment in the supplementary materials (Fig. S4), as well as the discussion of magnetic contribution from substrate in the manuscript on page 7. "Control experiments on the field dependent magnetization of SiC/graphene substrate show a typical diamagnetic behavior ( Supplementary Fig. 4). Therefore, the possibility of magnetic contribution from magnetic impurities in the substrate can be ruled out." 8. It is unclear whether the samples investigated with XRD were capped with Te. It is also unclear whether the Te capping layer was later (e.g. for ARPES, XAS and XMCD measurements) desorbed under vacuum.
Reply: Thank you for the comment. The samples investigated with XRD were capped with 5 nm Te to prevent the contamination and oxidation. Few-layer 2D FM materials are going to degrade under ambient atmosphere 7 , and the capping layers are indispensable. For the ARPES measurements, CrTe2 samples were in-situ transferred under ultra-high vacuum to the ARPES chamber after finishing the film growth. Therefore, there is no need to evaporate a capping layer. For the XAS and XMCD measurements performed on beamline, CrTe2 samples were capped with 5 nm Te to prevent the oxidation and environmental doping during transport to the synchrotron facility. Since the escaping length of photoelectrons by XAS and XMCD characterization in TEY mode is ~10 nm 17 , Te capping layer doesn't need to be desorbed under vacuum.

Revision:
We have added the experimental details about capping layers in the revised manuscript on page 15 and 16. "In order to protect the thin film from contamination and oxidation during XRD, SQUID, XAS and XMCD measurements, a Te capping layer (~5 nm) was deposited on sample surface after growth." "After the growth, the CrTe2 films were in-situ transferred under ultra-high vacuum to the ARPES stage." 9. In the sentence "which is also confirmed by the calculated density of states ( Fig. S6)", I guess the authors mean " Fig. S7". I have the feeling (but might be wrong...) that in several instances, the supplementary figures are not properly called in the main text. Please check.

Reply:
We thank the reviewer for pointing out this. We have corrected the figure number in the revised manuscript on page 12.
10. Regarding the ARPES measurements and the possible match with DFT simulations performed for thin 1T CrTe2 flakes, I have several questions. The authors write "The observed metallic band further confirms the trigonal phase of the CrTe2 thin films". However, Fig. S9 for instance shows that both the 1T and the 2H phases are predicted 8 / 45 metallic (at least in the bulk form). Actually, I find it very difficult to conclude that the observed electronic band structure resembles the one predicted based on DFT calculations. The bands are actually not nicely resolved, and there are many features that do not really look alike what is calculated ( Fig. 4a/b). What about a calculation for the 2H phase of a thin CrTe2 film (not for bulk, like in Fig. S9)? The number of layers seems an important parameter, and systematic calculations for different layer number might be relevant here. By the way, I might have missed the information, but I did not figure out what the layer number is for Fig. 4a. All this needs to be clarified and maybe discussed with more care.
Reply: Thanks for the helpful suggestions. Both 1T and 2H phases are indeed predicted to be metallic. We agree that the observed metallic band can't provide the evidence for the crystal structure. We have corrected this statement in the revised manuscript.
For the quality of measured electronic band structure of CrTe2, actually it is comparable with that of TMDCs (e.g. VSe2 18 and WTe2 19 ) and other 2D ferromagnets (e.g. Fe3GeTe2 20 and CrGeTe3 21 ). In order to distinguish the crystal structure more clearly, we put the calculated 1T (left) and 2H (right) bands on the top of the experimental one, as shown in Fig. R4. The ARPES-intensity plots and calculated band structure for 1T-CrTe2 share most common features. For example, the hole-like bands cross EF around the Г point (marked by the green arrow), and a relatively flat Cr 3d orbital band locates at EB~1 eV. The other hole pockets (marked by the purple arrow) are not observed due to the distinct photon-energy responses of majority and minority bands. In Fig. R4b, many obvious differences are displayed in the bands of 2H phase, such as the flat holelike bands near Γ (marked by the green arrow) and a "M" shape flat band with top at EB~0.6 eV. These characteristic bands establish the intrinsic differences between the electronic states of the 1T and 2H phases, and further confirm the trigonal phase of CrTe2 thin films.
The comparison of theoretical calculation for the bilayer thin film and bulk CrTe2 with 2H phase is shown below. The main features, including flat hole-like bands near Γ point and a "M" shape flat band, remain unchanged when the thickness changes from bulk into bilayer. Accordingly, the variation of thickness cannot account for the disagreement between the experimental band dispersion and the calculated 2H phase. The sample in Fig. 5a is 7 ML CrTe2. We have added this important information in the revised manuscript. To understand the thickness-dependent electronic structure, we carried out first-principles calculations of 1T-CrTe2 with different thicknesses. As shown in Fig. R6, there is an excellent agreement between our experiment and theory.
In particular, the hole-like band near EF and a relatively flat Cr 3d orbital band are similar to that of calculated 1T-CrTe2 with the inclusion of spin polarization. For the 1 ML film, the two parabolic hole pockets are well reproduced by the majority spin projections of the bands, which highlights the FM nature. These results demonstrate that the epitaxial 1T structure and ferromagnetism have been established since 1 ML deposition. Upper panels: band structures of 1T phase from first-principles calculations; Middle panels: calculated minority (red) and majority (blue) spin projections of the bands, respectively; Lower panels: ARPES intensity maps.

Revision:
In the revised manuscript, we have discussed the comparison among ARPES band and DFT calculations of 1T and 2H phases. The relationship between electronic structure against thickness variation has also been included in the new version of the paper on page 13 and 14.
"The electronic structure of 2H-CrTe2 was also calculated, as presented in Supplementary Fig. 15

Reviewer #2 (Remarks to the Author):
Comments: Two-dimensional van der Waals magnet is a new class of materials, being recognized as a unique platform for studying the two dimensional magnetism and also an important building block of van der Waals interfaces for novel spintronic functionalities. In this work, authors report the epitaxial growth of a new 2D van der Waals magnet CrTe2 and its magnetic/electronic properties. The results (High transition temperature, perpendicular magnetic anisotropy, and layer dependent magnetic/electronic properties) are clearly indicates the potential of this material. I feel that results are worth publishing in Nature Communications. However, there are several unclear points and I think the authors should further clarify them.
Reply: First of all, we are grateful to the reviewer for his/her positive comments and the fact that he/she thinks our manuscript are worth publishing in Nature Communications. We also thank the reviewer for the detailed comments and constructive suggestions, which help us to improve our manuscript. The questions raised by the reviewer are answered point by point as follows.
1. Although authors mentioned about the stoichiometry of grown films and excluded the possibilities of CrTe, Cr2Te3, and Cr5Te8, it requires more careful discussion to conclude the stoichiometry. It is known that MBE-grown sample can have its unique stoichiometry (partially intercalated one, for example), which is different from bulk and can even show the thickness dependence. In order to unambiguously clarify it, authors should show the cross-sectional TEM image of their samples with several different thicknesses.

Reply:
We thank the reviewer for the valuable suggestion. TEM characterizations were performed for CrTe2 thin films with different thicknesses, as exhibited in Fig. R7. The high-resolution TEM shows the √3a×a arrangement, indicating that the as-grown thin films correspond to the 1T phase with an octahedral (Oh) symmetry. The corresponding FFT pattern further demonstrates that CrTe2 thin films match its supposed 1T structure very well. Note that Cr atoms are fairly light compared with Te, leading to a quite low intensity contribution in TEM images 22, 23 . In order to further give an accurate stoichiometry of MBE-grown chromium chalcogenides, extra STM characterizations were carried out. As shown in Fig. R8, the atomically resolved STM images demonstrate the layer-bylayer growth mode and homogeneously well-structured CrTe2 thin films. The layered surface morphology with a uniform step height (~0.61 nm) suggests that the films are in a single phase without intercalated ones. Revision: According to reviewer's suggestions, we have included the HAADF-STEM images and atomically resolved STM of CrTe2 thin films with different thicknesses in the supplementary materials (Fig. S1, S2) and the relative discussion in the main text on page 6. "STM measurements carried out on several CrTe2 thin films with different thicknesses (mono-to few-layer) show similar terraces, indicating the layer-by-layer growth mode and homogeneously well-structured thin films ( Supplementary Fig. 1 CrTe2 thin films correspond to the 1T phase with an octahedral (Oh) symmetry ( Supplementary Fig. 2). Both TEM and STM characterizations manifest our as-grown films are stoichiometric CrTe2." 2. I am confused about the valence number of Cr. Considering the stoichiometry of CrTe2, it seems that Cr 4+ (and Te 2-) is reasonable. Why authors can conclude Cr 3+ ?
Reply: As the reviewer notes, within an ionic model, Cr 4+ is the nominal valence. This is based on Te 2-. However, Te 2is a large ion (Shannon crystal radius, 2.07 Å) and Te has relatively low electronegativity (Pauling electronegativity, 2.1), both of which make the ionic model questionable. In fact, the band structure shows evidence for Te-Te bonding in the form of a dispersive Te derived band that crosses the Fermi level in bulk CrTe2. This leads to a partial rather than full occupation of the Te p states, and therefore a Cr valence close to Cr 3+ . This is confirmed by the calculated moments 24 , which are consistent with experiment and correspond closely to Cr 3+ . Moreover, the observed XAS spectral line shape of Cr in CrTe2 is in line with that of spinel Cu(Cr,Ti)2Se4 polycrystals with Cr 3+ cations on Oh sites 25 , providing a direct spectroscopic fingerprint of 1T-type CrTe2 with predominately Cr 3+ cations.
It also should be noted that there is a connection between valence and crystal structure. It is common that TMDs (e.g. MoSe2, MoTe2, etc.) have several phases (e.g. 1T, 2H, 1T', etc.) that determine the physical properties [26][27][28] . As exhibited in Fig. R9, in 1T phase with Oh coordination, the 3d degenerate orbitals of Cr ions are split into two sets of eg and t2g states, with an energy separation of nominal 10 Dq. The t2g states are at lower energy orbitals than the eg states. In this case, the Cr 3+ (d 3 ) configuration with half-filled t2g states causes the reduction of free energy 28 , which increases the stability of the 1T phase. The result is in good agreement with the theoretical calculations of 3 μB/Cr atom made by Fumega et al. 24 . Therefore, 1T-type CrTe2 is conducting and magnetic. For 2H structure, 2 orbital has a lower energy compared with 2 − 2 , , , . Under this circumstances, Cr 4+ (d 2 ) is lower in energy since 2 orbital is fullfilled 28 . Therefore, 2H-type CrTe2 is insulating and non-magnetic.
In this work, according to STM, XRD, XAS and ARPES characterizations, CrTe2 thin films belong to 1T phase, which energetically favors Cr 3+ . The measured FM response of CrTe2 thin films also indicates the Oh coordination. Revision: According to reviewer's comment, we have added the discussion of the valence number of Cr in the main text on page 9. "Due to the Oh coordination, the 3d orbitals of Cr split into eg and t2g states with energy separation of nominal 10 Dq. The t2g states are at lower energy orbitals than the eg states. In this case, the Cr 3+ (d 3 ) configuration with half-filled t2g states causes the reduction of free energy, in good agreement with the theoretical calculations of 3 μB/Cr atom made by Fumega et al. 24 . The observed XAS spectral line shape is in line with that of spinel Cu(Cr,Ti)2Se4 polycrystals with trivalent Cr cations on Oh sites 25 , further providing a spectroscopic fingerprint of 1T-type CrTe2 with predominately Cr 3+ cations." 3. Related with the above comment, can Cr-Te bond be regarded as covalent bond or ionic bond?
Reply: As mentioned above, CrTe2 thin films have the 1T phase, so Cr 3+ (d 3 ) is energetically more favorable. In this case, Cr-Te bond could be regarded as primarily ionic. The Te pz wave functions from two adjacent interfacial Te sublayers overlap at the interlayer region, which is similar to the case of CrSe2 with magnetic moment of ~3 B/Cr 29 . According to the DFT calculations based on a modified Hubbard model made by Wang et al. 29 , both CrTe2 and CrSe2 contain an interlayer wave-function overlapped region, which could be effectively considered as an area accumulating appreciable shared charge from the two interfacial Se/Te sublayers. Essentially, approximately three electrons are removed from the Cr atoms to form Cr 3+ . These electrons are distributed over the Te. The bonding also includes some Te-Te bonding as mentioned above.
Revision: In the revised manuscript, we have given an explanation of Cr-Te ionic bond in the main text on page 9. "Approximately three electrons are removed from the Cr atoms, and distributed over the Te. In this case, Cr-Te bond could be regarded as primarily ionic. The Te pz wave functions from two adjacent interfacial Te sublayers overlap at the interlayer region and form Te-Te bonding, which is similar to the case of CrSe2 29 ." 4. I think it is impossible to determine the space group from out-of-plane XRD (line 133-136 in page 6).

Reply:
We thank the reviewer for pointing it out. We could only tell the lattice constant (c = 6.13 Å) from out-of-plane XRD results, but not the space group.

Revision:
We revised the relative description in the main text on page 6. "The diffraction pattern with perpendicular constant c = 6.13 Å is matched to the (001) crystal planes of the standard 1T-type hexagonal structure (a = 3.79 Å, c = 5.94 Å), rather than 2H phase (a = 3.49 Å, c = 13.64 Å). With STM, TEM and XRD 16 / 45 characterizations, the formation of CrTe2 films with 1T phase and their singlecrystalline nature has been confirmed." 5. For monolayer samples, authors only show the ARPES data. They should show the magnetization and XMCD data for monolayer sample. Because it seems that transition temperature of 3 ML samples is around 250 K (Fig. 2a) and that of monolayer might be lower than it, the word "monolayer" in the title is misleading.

Reply:
We thank the reviewer for this constructive suggestion. Indeed, magnetic characterization for the monolayer sample is meaningful. However, it is quite challenging to accurately detect magnetization in such ultrathin films by SQUID, since the magnetic signal of 1 ML CrTe2 is too weak compared with the overwhelmingly larger background signal from the substrate and beyond the resolution of SQUID. Therefore, we did element-specific XMCD characterization with a much higher sensitivity of 1 ML CrTe2 film. Figure R10 shows the XAS and XMCD spectra of 1 ML CrTe2 film at Cr L2,3 edges taken at different temperatures under out-of-plane magnetic field of 1 T. There is a clear difference in the XAS spectra between left-handed circularly polarized and righthanded circularly polarized setups, indicating the existence of the XMCD signals. Although the dichroism is small compared with 7 ML sample, the clear XMCD signals ( + − − is nonzero) appear near the absorption peaks. It suggests that the intrinsic ferromagnetism of 1 ML CrTe2 film originates from the spin polarization of Cr 3d electrons. Accurate calculation of the magnetic moment remains a challenge since the contribution of Te capping layer to the XAS spectra is so large for 1 ML sample. The XMCD percentage increases with decreasing temperature, in line with the typical FM behavior. The nonzero XMCD percentage persists when temperature approaches 200 K and disappears at 250 K, indicating that 1 ML CrTe2 has a TC of ~200 K.
We agree with the reviewer that the word "monolayer" in the title may cause misunderstanding. In the revised manuscript the title has been modified to: "Roomtemperature intrinsic ferromagnetism in epitaxially grown CrTe2 atomic-layer films." Revision: Following reviewer's requests, we have included the XMCD study of 1 ML CrTe2 film in Fig. 4, and also modified the title of the manuscript accordingly. "The magnetic response of 1 ML CrTe2 film is worth exploring. It is difficult to detect magnetization in such ultrathin films by SQUID, since the magnetic signal of 1 ML CrTe2 is too weak compared with an overwhelmingly larger background signal from the substrate and beyond the resolution of SQUID. Therefore, we did element-specific XMCD characterization of 1 ML CrTe2 film (Fig. 4a). There is a clear difference in the XAS spectra between left-and right-handed circularly polarized setups (Fig. 4b).
Although the dichroism is small compared with 7 ML sample, the clear XMCD signals appear near the absorption peaks. It suggests that the intrinsic ferromagnetism of 1 ML CrTe2 film originates from the spin polarization of Cr 3d electrons. Accurate calculation of the magnetic moment remains a challenge since the contribution of Te capping layer to the XAS spectra is so large for 1 ML sample. The XMCD percentage increases with decreasing temperature (Fig. 4c)   Reply: As suggested by reviewer, to understand the interplay between the band structure and magnetic properties, we carried out the ARPES measurements of 7 ML CrTe2 at 107 K and 300 K, respectively. As shown in Fig. R11, the typical band dispersion hardly changes except for the thermal broadening with increasing temperature.
The energy splitting size could be obtained from the temperature dependent energy distribution curves (EDCs) of the second derivative data. For clarity, the temperature evolution of the EDCs at k = -0.36 Å -1 is summarized in Fig. R11e. The fitted peak-topeak splitting of majority and minority bands at 300 K shows an obvious decreasing trend compared with 107 K, corresponding to the weaker ferromagnetism at higher temperature.

Revision:
We have included the discussion of temperature dependent splitting of hole pockets in the main text on page 13. "The energy splitting value could be obtained from the temperature dependent energy distribution curves (EDCs) of the second derivative data (Supplementary Fig. 14). The fitted peak-to-peak splitting of majority and minority bands at 300 K shows an obvious decreasing trend compared with 107 K, corresponding to the weaker ferromagnetism at higher temperature." 7. What is the mechanism of perpendicular magnetic anisotropy? Is it consistent with the bulk CrTe2?
Reply: The origin of magnetic anisotropy generally originates from three mechanisms, shape anisotropy 10,11 , magneto-crystalline anisotropy 12 and anisotropy of exchange interactions 11 . The shape anisotropy is due to the magnetostatic or dipole interactions, which lead to a preferential in-plane anisotropy for thin films 11 . The PMA in CrTe2 thin films is contrary to it. Thereby, the possibility of shape anisotropy can be ruled out.
The anisotropy of exchange interactions can be verified by performing DFT calculations of exchange interactions using the frozen magnon approach 12 . Fujisawa et al. found that the ferromagnetic (FM) Cr-Cr intra-sublattice exchange interaction dominates in CrTe2 thin films, and the total energy minima for CrTe2 occurs at perpendicular direction 12 . In this vein, the magnetic moments of CrTe2 thin films are driven to perpendicular direction due to the anisotropy of exchange interactions.
CrTe2 few-layer films show a strong PMA. It is contradictory to the bulk CrTe2 reported by Freitas et al. 8 , which possesses in-plane easy axis. The thickness dependent magnetic anisotropy suggests that the lowered symmetry at the interface plays an important role in determining the PMA in CrTe2 thin films. As the magnetic film thickness approaches a few nm, interfacial magnetism and inversion symmetry breaking give rise to intriguing phenomena such as PMA 13 . This is a consequence of spin-orbit interactions, i.e., magneto-crystalline anisotropy, that apparently have a stronger effect in the more anisotropic film limit 10,14,15 . Both experimental results and DFT calculations indicate that, the magnetic moments of CrTe2 thin films are driven to the perpendicular direction, due to the magneto-crystalline anisotropy and the anisotropy of exchange interactions.
Revision: According to reviewer's suggestions, we have included the discussion of PMA in CrTe2 films on page 8. "The strong PMA in CrTe2 few-layer films is different from bulk CrTe2 8 and exfoliated flakes (thicker than 10 nm) 16 which have an in-plane easy axis. Here, the thickness dependent magnetic anisotropy suggests that the reduced symmetry at the interface plays an important role in determining the PMA in CrTe2 thin films 15 . As the magnetic film thickness approaches a few nm, the interfacial magnetism and inversion symmetry breaking give rise to the PMA 13 . This is a consequence of spin-orbit interactions, i.e., magneto-crystalline anisotropy, that apparently have a stronger effect in the more anisotropic film limit 10,14,15 . In addition, based on density functional theory (DFT) calculations, it has been found that the FM Cr-Cr intrasublattice exchange interactions dominate in CrTe2 thin films, and the total energy minima is at perpendicular direction 12 . In general, the magnetic moments of CrTe2 thin films are aligned in the perpendicular direction, due to the magneto-crystalline anisotropy and the anisotropy of exchange interactions." 8. In Fig. 2a, it is written that magnetic field is applied in-plane. It is correct? If so, it is 20 / 45 better to replace it with that under the out-of-plane magnetic field.
Reply: Yes, the magnetic field is applied in-plane in Fig. 2a. Thanks for the nice suggestion. We have replaced the in-plane temperature dependent magnetization (M-T) curves with the out-of-plane ones, as shown in Fig. R12. The high TC (~258 K) is preserved with thickness decreasing to 3 ML. 9. 15ML data in Fig. 2a shows slight decrease at low temperature? What is the origin of this strange behavior?

Reply:
The slight decrease at low temperature for the in-plane measurement could be ascribed to the accelerated process of spin reorientation from the ab plane to the c axis with decreasing temperature at low magnetic field 30 . Based on the fact that CrTe2 film has a strong PMA ( = 5.63×10 6 erg/cm 3 for 7 ML CrTe2), spin intends to align along the perpendicular direction at low temperature.
We did control experiment about the temperature dependence of out-of-plane magnetization with magnetic field of 0.1 T, as shown in Fig. R13. Note that out-ofplane direction is an easy axis. Contradictory to the in-plane one, the out-of-plane magnetization increases with decreasing temperature, indicating the enhanced ferromagnetism at low temperature. Therefore, the slight decrease of in-plane magnetization at low temperature is resulted from the spin reorientation from the ab plane to the c axis, due to the weak in-plane magnetic field (0.1 T). Moreover, we also did control experiment about the temperature dependence of inplane magnetization with a higher magnetic field of 0.5 T. As shown in Fig. R14, the in-plane magnetization at low temperature does not decrease at a high magnetic field, further indicating that the slight decrease of in-plane magnetization at low temperature is due to the spin reorientation from in-plane to the out-of-plane direction. Revision: According to reviewer's advices, we have replaced the in-plane M-T curves with out-of-plane ones in the revised manuscript on page 7, and discussed the origin of slight decrease of in-plane M-T curves at low temperature in Fig. S3. "The out-of-plane magnetization increases with decreasing temperature, indicating the enhanced ferromagnetism at low temperature. On the contrary, the slight decrease of in-plane magnetization at low temperature is resulted from the accelerated process of spin reorientation from the ab plane to the c axis, due to the weak in-plane magnetic field." 10. Authors claim that orbital magnetization is almost negligible. If so, why magnetic anisotropy appears?
Reply: Although the orbital moments are small due to the crystal field scheme, they are apparently sufficient to yield a magneto-crystalline anisotropy and the perpendicular orientation of the moments that underlies the FM order in this 2D system. This has also been found in other systems such as Cr-doped Bi2Se3 31 and CrI3 (~3 B/Cr) 11 . At the same time, the anisotropy of magnetic exchange interactions also contribute to the PMA 12 .
Revision: According to reviewer's comments, we have discussed the relationship between the orbital magnetization and magnetic anisotropy in the revised manuscript on page 10. "Although the orbital moments are small due to the crystal field scheme, they are apparently sufficient to yield a magneto-crystalline anisotropy and the perpendicular orientation of the moments that underlies the ferromagnetic order in this 2D system, similar to that of Cr-doped Bi2Se3 31 and CrI3 11 ."

Comments:
Dear Authors, In this manuscript, the authors report the observation of room temperature ferromagnetism in CrTe2 thin films. The manuscript is organized with interesting experimental results about structural characterization ( Fig. 1 and S1), magnetization (Fig. 2), anomalous Hall effect (Fig. S2), circular dichroism ( Fig. 3 and S3), and ARPES with calculation ( Fig. 4 and S4-S9). I totally agree that the successful fabrication of high quality CrTe2 ultrathin films is quite important advancement. By applying the interface formation, the spintronic function can be expected to work at room temperature. However, in previous studies, the room temperature ferromagnetism has been observed in bulk and exfoliated thin flakes of CrTe2. Of course, XMCD and ARPES are also important experimental results to understand the electronic structures of the CrTe2 films. Considering these points, for my sense, it is difficult to find new significant achievements in the preset manuscript. I provide some comments to improve the manuscript.

Reply:
We appreciate the reviewer for pointing out the importance of the successful fabrication of high quality CrTe2 ultrathin films for spintronics. We also understand the inquires of the reviewer about the comparison with the previous work on bulk and exfoliated thin flakes of CrTe2 (Note: The magnetic properties of the exfoliated thin flakes as reported in refs 9,16 are essentially similar to that of the bulk with in-plane anisotropy, but with enhanced HC). Here, we would like to highlight the significance and novelty of our work, especially after substantial new results added in the revised manuscript following the suggestions from all three reviewers..
1) The successful synthesis of CrTe2 epitaxial films by MBE with controllable size and thicknesses. What is currently stunting the progress in the research of 2D magnetic materials is the lack of stoichiometric 2D materials with intrinsic ferromagnetism and compatibility with large scale solid state device applications, where the MBE growth is critical..
2) The scaling of the CrTe2 thickness down to monolayer. Remarkably, a high TC of ~200 K is still retained with the film thickness down to monolayer, suggesting the robust ferromagnetism in the epitaxially grown CrTe2 thin films. Actually it is much higher than those recently reported ML 2D ferromagnets, such as Fe3GeTe2 (20 K), CrI3 (45 K).
3) The experimental demonstration of strong PMA and large coercivity in CrTe2 thin films. It is contradictory to the previous studies of CrTe2 bulk and exfoliated flakes with in-plane easy axis. The PMA is not only an intriguing fundamental issue, but also important for applications such as magnetic tunneling junctions (MTJs). MTJs with PMA require a smaller switching current and have a faster reversal speed for magnetization switching than one with in-plane anisotropy.

/ 45
Furthermore, materials with large coercivity and PMA represent the mainstay of data storage media, e.g. MRAM, owing to their ability to retain a permanent and stable magnetization state.
4) The first ARPES observation of magnetic splitting band structure of 2D magnets, revealing the unique interplay between macroscopic ferromagnetism and atomic electronic structure in CrTe2. It opens a new pathway to determine the intrinsic ferromagnetism in 2D magnets.
Revision: Following the reviewer's comments, we have improved the discussion about the significance and novelty of this work along with the new results added to the revised manuscript page 5 and 11. "Very recently, a paper reported the observation of above room-temperature ferromagnetism in the exfoliated thin flakes of CrTe2 (10 nm, or ~17 ML) 16 . Their properties were found to be rather similar to that of the bulk with in-plane anisotropy, but with enhanced Hc compared with its bulk counterpart. However, the magnetic response (e.g., TC and PMA) of CrTe2 epitaxial thin films with the thickness down to monolayer limit has not been explored so far." "In order to investigate the dimensionality effect of the ferromagnetism in CrTe2 stemming from thermal fluctuation, we plot the thickness dependent TC (Fig. 4d). The TC of CrTe2 decreases slightly with reducing the film thickness compared with other commonly investigated 2D magnets, such as Cr2Ge2Te6 2 and Fe3GeTe2 7 ( Supplementary  Fig. 8), demonstrating the robustness of ferromagnetism in the epitaxially gown CrTe2 thin films." In the following, we address the specific points raised by the reviewer: 1, appropriate definition should be used.
The definition in this manuscript should be carefully improved, for example "intrinsic ferromagnetism" in the title and "intrinsic 2D ferromagnetism" in the abstract, are described but no discussion is provided in main text. What does "intrinsic" mean ? How did the authors conclude "2D" ferromagnetism ? The meaning of "2D magnet" is a 2D material possessing magnetism. It is generally accepted. However, the meaning of "Intrinsic 2D ferromagnetism" is completely different from that of 2D magnet. The dimensionality of the ferromagnetism has to be examined.

Reply:
The discovery of intrinsic ferromagnetism in 2D materials is vital for understanding the spin behavior in low dimensions. Using "intrinsic ferromagnetism," we intend to limit the discussion to ferromagnetism occurring in a stoichiometric compound or heterostructure of stoichiometric compounds, as opposed to defect or dopant induced ("dilute") ferromagnetism 32 . The term, "2D ferromagnetism," refers to ferromagnetism in 2D materials, which can be stably isolated in atomically thin layers. We agree with the reviewer's opinion that the statement of "intrinsic 2D

/ 45
ferromagnetism" might be not rigorous. According to reviewer's suggestions, we have changed the statement of "intrinsic 2D ferromagnetism" into "intrinsic ferromagnetism in 2D CrTe2 films".
In order to investigate the dimensionality effect of the ferromagnetism in CrTe2, we plot the thickness dependent TC in Fig. R15. The normalized TC of CrTe2 decreases slightly with reducing film thickness, displaying a weak dimensionality effect, compared with that of Fe3GeTe2 for example. Revision: According to reviewer's suggestions, we have changed the statement of "intrinsic 2D ferromagnetism" into "intrinsic ferromagnetism in 2D CrTe2 films". We have also included a brief discussion of "intrinsic ferromagnetism" and the dimensionality of the ferromagnetism in the revised manuscript on page 3 and 11. "Opposed to defect or dopant induced magnetism, the ferromagnetism occurring in a stoichiometric compound is defined as intrinsic ferromagnetism." "In order to investigate the dimensionality effect of the ferromagnetism in CrTe2 stemming from thermal fluctuation, we plot the thickness dependent TC (Fig. 4d). The TC of CrTe2 decreases slightly with reducing the film thickness compared with other commonly investigated 2D magnets, such as Cr2Ge2Te6 2 and Fe3GeTe2 7 ( Supplementary  Fig. 8), demonstrating the robustness of ferromagnetism in the epitaxially gown CrTe2 thin films." If the films have less defect concentration like bulk single crystals, the observed ferromagnetism is supported by similar origin in the bulk crystals. It is great that the authors explain the basis for what is intrinsic and extrinsic magnetism.

Reply:
In magnetism, there is a fundamental distinction between intrinsic and extrinsic properties. Several approaches have been proposed to extrinsically induce long-range magnetic order into 2D materials such as defect engineering, absorption of magnetic ions, or proximity effect. In defect engineering, the simplest strategy for realizing magnetism in non-magnetic materials is to create unpaired electrons by modifying its electronic structure via vacancies, atoms, grain boundaries, or edges. In absorption technique, magnetic ions are absorbed inside 2D vdW materials where magnetic order emerges when the magnetic ions experience exchange coupling. On the other hand, in magnetic proximity effect, 2D vdW materials experience exchange coupling when placed in contact with FM insulating substrates.
However, little attention has been drawn to investigate the intrinsic ferromagnetism in 2D materials because the long-range magnetic order in 2D systems could be destroyed by thermal fluctuations. For example, the Mermin-Wagner theorem indicates that longrange magnetic order is impossible at any finite temperature in an isotropic 2D spin system. To suppress the thermal fluctuations and achieve long range intrinsic ferromagnetism in 2D materials, magnetic anisotropy is necessary. Based on various forms of magnetic anisotropies, recent groundbreaking experiments of intrinsic ferromagnetism in 2D materials have been realized in Cr2Ge2Te6 2 and CrI3 1 .
In this work, by the term of "intrinsic ferromagnetism," we intend to limit the discussion to ferromagnetism occurring in a stoichiometric compound or heterostructure of stoichiometric compounds, as opposed to defect or dopant induced ("dilute") ferromagnetism.
Revision: According to the reviewer's advice, we have included a definition of "intrinsic ferromagnetism" in the revised manuscript on page 3.

"Opposed to defect or dopant induced magnetism, the ferromagnetism occurring in a stoichiometric compound is defined as intrinsic ferromagnetism."
Room temperature ferromagnetism is obtained in only 7 and 15 ML films. These thicknesses are comparable to that in the previous studies of exfoliated flakes. Please describe the results with fair comparison. The plot of Curie temperature as a function of thickness is quite meaningful, because the analysis for Curie temperature of each films is not clearly explained.

Reply:
We fully understand the reviewer's comment. As we discussed before, the properties of the exfoliated thin flakes are essentially equivalent to the bulk with inplane anisotropy according to the result reported by Sun et al 16 . The magnetization of any exfoliated CrTe2 flakes thinner than 10 nm hasn't been explored for the limitation of noise level of Faraday experimental setup and the technical difficulties of exfoliating thinner CrTe2. Here, we have achieved the epitaxial growth of CrTe2 compatible with large-scale solid state device applications, room-temperature ferromagnetism down to 7 ML with PMA and ferromagnetism with TC of 200K in the monolayer films. A fair comparison has been added to the revised manuscript as we discussed in the very first 27 / 45 part.
We agree with the reviewer that the plot of TC as a function of thickness is quite meaningful. Indeed, a method to determine TC is to find the temperature at which the remanent magnetization signal goes to zero. In fact, it is this criterion that distinguishes a ferromagnet from a paramagnet. This is the approach that Gong et al. 2 took in searching for ferromagnetism in atomically-thin Cr2Ge2Te6. The out-of-plane M-T curves and plot of TC as a function of thickness is shown in Fig. R16. By XMCD characterization, the high TC (~200 K) is demonstrated to preserve with thickness decreasing to monolayer. The TC of CrTe2 decreases slightly with reducing the film thickness compared with other commonly investigated 2D magnets, such as Cr2Ge2Te6 2 and Fe3GeTe2 7 , demonstrating the robustness of ferromagnetism in the epitaxially gown CrTe2 thin films. Revision: According to reviewer's suggestions, we have included a fair comparison of this work and previous studies and a plot of thickness dependent TC in the main text on page 5 and 11. "Very recently, a paper reported the observation of above room-temperature ferromagnetism in the exfoliated thin flakes of CrTe2 (10 nm, or ~17 ML) 16 . Their properties were found to be rather similar to that of the bulk with in-plane anisotropy, but with enhanced Hc compared with its bulk counterpart. However, the magnetic response (e.g., TC and PMA) of CrTe2 epitaxial thin films with the thickness down to monolayer limit has not been explored so far." "In order to investigate the dimensionality effect of the ferromagnetism in CrTe2 stemming from thermal fluctuation, we plot the thickness dependent TC (Fig. 4d). The TC of CrTe2 decreases slightly with reducing the film thickness compared with other commonly investigated 2D magnets, such as Cr2Ge2Te6 2 and Fe3GeTe2 7 ( Supplementary  Fig. 8), demonstrating the robustness of ferromagnetism in the epitaxially gown CrTe2 2, magnetic anisotropy should be discussed. In this manuscript, the perpendicular magnetic anisotropy (PMA) is claimed. This feature is different from that in bulk and exfoliated flakes. However, the reason is not discussed well. I recommend to discuss the reason why PMA is obtained in the films. Although Fig. 2a shows temperature dependence of in-plane magnetization, temperature dependence of perpendicular magnetization should be also plotted if the authors try to claim the perpendicular magnetic anisotropy.

Reply:
We appreciate the reviewer's comment and suggestion. We did control experiment about the temperature dependence of out-of-plane and in-plane magnetization with magnetic field of 0.1 T, as shown in Fig. R17. For CrTe2 thin films, the out-of-plane direction is an easy axis, consistent with experimental result reported by Y. Fujisawa 12 .

Fig. R17
Zero-field and field cooled temperature dependence of the magnetization of 7 ML CrTe2 with an applied in-plane and out-of-plane magnetic field of 0.1 T.
The origin of magnetic anisotropy generally originates from three mechanisms, shape anisotropy 10,11 , magneto-crystalline anisotropy 12 and anisotropy of exchange interactions 11 . The shape anisotropy is due to the magnetostatic or dipole interactions, which lead to a preferential in-plane anisotropy for thin films 11 . The PMA in CrTe2 thin films is contrary to it. Thereby, the possibility of shape anisotropy can be ruled out.
The anisotropy of exchange interactions can be verified by performing DFT calculations of exchange interactions using the frozen magnon approach 12 . Fujisawa et al. found that the ferromagnetic (FM) Cr-Cr intra-sublattice exchange interaction dominates in CrTe2 thin films, and the total energy minima for CrTe2 occurs at perpendicular direction 12  exfoliated flakes 9,16 show in-plane easy axis. Note that the thickness of 1T-CrTe2 exfoliated flakes showing in-plane easy axis is larger than 10 nm. Here, the thickness dependent magnetic anisotropy suggests that the lowered symmetry at the interface plays an important role in determining the PMA in CrTe2 thin films. As the magnetic film thickness approaches a few nm, interfacial magnetism and inversion symmetry breaking give rise to intriguing phenomena such as PMA 13 . This is a consequence of spin-orbit interactions, i.e., magneto-crystalline anisotropy, that apparently have a stronger effect in the more anisotropic film limit 10,14,15 . Both experimental results and DFT calculations indicate that, the magnetic moments of CrTe2 thin films are driven to the perpendicular direction, due to the magneto-crystalline anisotropy and the anisotropy of exchange interactions.
Revision: According to reviewer's suggestions, we have included the discussion of PMA in CrTe2 thin films on page 8 and the temperature dependence of perpendicular magnetization in Fig. 2a on page 7. "The strong PMA in CrTe2 few-layer films is different from bulk CrTe2 8 and exfoliated flakes (thicker than 10 nm) 16 which have an in-plane easy axis. Here, the thickness dependent magnetic anisotropy suggests that the reduced symmetry at the interface plays an important role in determining the PMA in CrTe2 thin films 15 . As the magnetic film thickness approaches a few nm, the interfacial magnetism and inversion symmetry breaking give rise to the PMA 13 . This is a consequence of spin-orbit interactions, i.e., magneto-crystalline anisotropy, that apparently have a stronger effect in the more anisotropic film limit 10,14,15 . In addition, based on density functional theory (DFT) calculations, it has been found that the FM Cr-Cr intrasublattice exchange interactions dominate in CrTe2 thin films, and the total energy minima is at perpendicular direction 12  explained by a positive-feedback mean-field modification of the classical Brillouin magnetization theory 35 (Fig. R18). The modified theory incorporates the temperaturedependent quantum-scale hysteretic and mesoscopic domain-scale anhysteretic magnetization processes. Moreover, it includes the effects of demagnetization and exchange fields. It is found that the thermal behavior of the reversible and irreversible segments of the hysteresis loops, as predicted by the theory, is a key to the presence or absence of the "tails."

Fig. R18
Theoretical temperature-dependence of reduced spontaneous magnetization in Ni compared with measurement 35 .

Revision:
Following the reviewer's suggestions, we have included the discussion of weak temperature dependence of magnetization near TC in the revised manuscript on page 7. "The magnetization exhibits weak temperature dependence near TC, which is commonly observed in ferromagnets 2,21,34 . It can be explained by a positive-feedback mean-field modification of the classical Brillouin magnetization theory 35 ." The authors claim that the saturation magnetization value of the films is consistent to the value in the bulk. However, it is apparent that the magnetization value does not linearly follow the thickness in Fig. 2a. The magnetization value should be calculated and presented by number of moment for Cr atoms (B/Cr) as discussed in Fig. 3d. Then, the values can be compared to that in bulks and that evaluated by XMCD. If the magnetization values in the films depends on the thickness, the origin should be discussed.

Reply:
We thank the reviewer for this advice. The M-T curves in Fig. 2a   Revision: Following reviewer's advices, we have discussed the magnetic moment of 3 ML and 5 ML CrTe2 thin films in the main text on page 7 and 8. Fig. 5

3, relationship between magnetization and anomalous Hall effect.
Probably the authors already notice, anomalous Hall (AH) effect reflects the perpendicular magnetization. In Fig. S2, the AH resistance for 3 ML film apparently disappears at 250 K, indicating no or rather weak perpendicular magnetization at 250 K. The AHE is measured with 3-layers film so that the M-T curve for 3ML shown in Fig. 2a seems consistent. However, M-H curve in Fig. 2b is measured with 7ML film. To remove such ambiguity, the authors should show all data set to compare Curie temperature and coercive field between AHE and magnetization for 3ML, 5 ML, and 7 ML, if the authors try to claim that the ferromagnetic order can be obtained in ultrathin 3 ML with perpendicular magnetic anisotropy. Perpendicular magnetic anisotropy should be concluded by the discussion and experimental results on the comparison of M-H curves in-plane and out-of-plane. In the present manuscript, the data set of M-H curves for 3 ML and 5 ML is not provided. The authors have to show these experimental evidences.

Reply:
We thank the reviewer for this suggestion. The AH resistance of CrTe2 thin films with thickness of 3 ML, 5 ML and 7 ML is shown in Fig. R20. The AHE behaviors of 3 ML, 5 ML and 7 ML CrTe2 persist up to 250 K, 250 K and 300 K, respectively. Moreover, the calculated coercive fields by AHE and M-H loops show a good  In order to clarify the PMA in ultrathin CrTe2 thin films, we did field dependent magnetization curves of 3 ML and 5 ML CrTe2 thin films under out-of-plane and inplane configuration (Fig. R21). The nearly square-shaped FM hysteresis loops under out-of-plane magnetic field suggest the robust FM order with the easy axis perpendicular to the thin films. The PMA constants ( = 2 ) of 3 ML and 5 ML CrTe2 films at 10 K are determined to be 6.6×10 6 erg/cm 3 and 6.5×10 6 erg/cm 3 , respectively.

Revision:
Following the reviewer's comments, we have included the electrical transport measurements and magnetic hysteresis loops of CrTe2 thin films as supplementary materials (Fig. S5, S6), and discussed them in the revised manuscript on page 7 and 8. "In order to clarify the thickness dependence of the magnetic properties, we have measured the field dependent magnetization curves of 3 ML and 5 ML CrTe2 thin films under out-of-plane and in-plane configuration ( Supplementary Fig. 5 Fig. 6).

Moreover, the calculated coercive fields by anomalous Hall effect (AHE) and M-H loops show a good agreement."
In addition, what happen in 2 ML and 1 ML film? The authors describe "indicating a negligible dimensionality effect" in page 5, but the Curie temperature and magnetization decreases with decreasing thickness. Please reconsider this point. I agree that it is difficult to detect magnetization in such ultrathin films by SQUID but they may detect it by XMCD. If the authors have measured those films, it is great to provide the discussion for 2 ML and 1 ML. By ARPES measurement, electronic bands are well discussed with increasing thickness. Because ferromagnetism is observed above 3 ML, did the authors detect the critical difference between 1, 2 ML and 3 ML in terms of electronic structures? The relationship between electronic structure and magnetism against thickness variation is an interesting topic in such 2D layered magnetic compounds.
Reply: According to reviewer's constructive suggestions, we have done the elementspecific XMCD characterization of 1 ML CrTe2 film. Figure R22 shows the XAS and XMCD spectra of 1 ML CrTe2 film at Cr L2,3 edges taken at different temperatures under out-of-plane magnetic field of 1 T. There is a clear difference in the XAS spectra between left-handed circularly polarized and righthanded circularly polarized setups, indicating the existence of the XMCD signals.
Although the dichroism is small compared with 7 ML sample, the clear XMCD signals ( + − − is nonzero) appear near the absorption peaks. It suggests that the intrinsic ferromagnetism of 1 ML CrTe2 film originates from the spin polarization of Cr 3d electrons. Accurate calculation of the magnetic moment remains a challenge since the contribution of Te capping layer to the XAS spectra is so large for 1 ML sample. The XMCD percentage increases with decreasing temperature, in line with the typical FM behavior. The nonzero XMCD percentage persists when temperature approaches 200 K and disappears at 250 K, indicating that 1 ML CrTe2 has a TC of ~200 K. After demonstrating the ferromagnetism in 1 ML CrTe2 film, we now discuss the electronic structures of CrTe2 thin films with different thicknesses. To understand the thickness-dependent electronic structure, we carried out first-principles calculations of 1T-CrTe2 with different thicknesses. As shown in Fig. R23, there is an excellent agreement between our experiment and theory. In particular, the hole-like band near EF and a relatively flat Cr 3d orbital band are similar to that of calculated 1T-CrTe2 with the inclusion of spin polarization. For the 1 ML film, the two parabolic hole pockets are well reproduced by the majority spin projections of the bands, which highlights the FM nature. These results demonstrate that the epitaxial 1T structure and ferromagnetism have been established since 1 ML deposition. Revision: Following reviewer's comments, we have included XMCD study of 1 ML CrTe2 film in Fig. 4. We have further discussed the relationship between electronic structure and magnetism against thickness variation in the revised manuscript on page 14.
"The magnetic response of 1 ML CrTe2 film is worth exploring. It is difficult to detect magnetization in such ultrathin films by SQUID, since the magnetic signal of 1 ML CrTe2 is too weak compared with an overwhelmingly larger background signal from the substrate and beyond the resolution of SQUID. Therefore, we did element-specific XMCD characterization of 1 ML CrTe2 film (Fig. 4a). There is a clear difference in the XAS spectra between left-and right-handed circularly polarized setups (Fig. 4b).
Although the dichroism is small compared with 7 ML sample, the clear XMCD signals appear near the absorption peaks. It suggests that the intrinsic ferromagnetism of 1 ML CrTe2 film originates from the spin polarization of Cr 3d electrons. Accurate calculation of the magnetic moment remains a challenge since the contribution of Te capping layer to the XAS spectra is so large for 1 ML sample. The XMCD percentage increases with decreasing temperature (Fig. 4c), in line with the typical FM behavior. The nonzero XMCD percentage persists when temperature approaches 200 K and disappears at 250 K, indicating that 1 ML CrTe2 has a TC of ~200 K." "To understand the thickness-dependent electronic structure, we carried out firstprinciples calculations of 1T-CrTe2 with different thicknesses. As shown in Supplementary Fig. 16 4, Temperature dependence of magnetization in Fig. 3d is apparently different trend with that in Fig. 2a. Fig. 3d shows monotonic increase with decreasing temperature. However, 7 ML data in Fig. 2a steep increase around 250 K, then keep constant at low temperature. This difference should be discussed. If this difference comes from the measurement configuration, in-plane or out-of-plane, the authors should provide temperature dependence of out-of-plane magnetization. If this comes from thickness difference or measurement method, it should be explained.

Reply:
We appreciate the reviewer's comments. The different trends of temperature dependent magnetization come from the measurement configuration. As shown in Fig.  R24, for 7 ML CrTe2 thin films, the out-of-plane direction is an easy axis. The out-ofplane magnetization shows monotonic increase with decreasing temperature. Moreover, as we put the temperature dependent magnetization curves characterized by SQUID and XMCD together (Fig. R25), both of them show monotonic increase with decreasing temperature.

Fig. R25
The temperature dependent out-of-plane magnetization and ms of 7 ML CrTe2 obtained by SQUID and XMCD, respectively.
Revision: According to reviewer's advices, we have discussed the origin of different temperature dependent behavior of out-of-plane and in-plane magnetization in Fig. S3. "The out-of-plane magnetization increases with decreasing temperature, indicating the enhanced ferromagnetism at low temperature. On the contrary, the slight decrease of in-plane magnetization at low temperature is resulted from the accelerated process of spin reorientation from the ab plane to the c axis, due to the weak in-plane magnetic field." 5, PMA is compared with Ku and saturation magnetization. Ku should be explained by equation. The magnetization in CrTe2 is rather small compared to other metal ferromagnets with PMA. Degree of PMA should be discussed on the same measure.

/ 45
For my sense, "strong PMA" is not appropriate for the observed data of CrTe2 in this manuscript because the value is not so large. If the authors try to claim the "strong PMA", please provide the values for famous strong PMA metal ferromagnets to compare.

Reply:
The PMA constant (Ku) can be estimated from the relation = 2 . Apart from the saturated magnetization (Ms), the perpendicular anisotropy field (Hk) is crucial, which can be deduced from the in-plane and out-of-plane magnetization hysteresis loops.  (Table S1). "The sharp distinction between out-of-plane (Fig. 2b) and in-plane (Fig. 2c)  They demonstrated the use of antiferromagnetic exchange coupling in manipulating the magnetic properties of magnetic topological insulators. The AFM-based Proximity effects are shown to induce an interfacial spin texture modulation and establish an effective long-range exchange coupling, which significantly enhances the magnetic ordering temperature in the superlattice.

Revision:
We have revised the references in the main text on page 3.

/ 45
"The second one is constructing heterostructures with FM (or ferrimagnetic) metals (or insulators), in which the FM order can be enhanced by proximity effects 43,45 ." Comments: 6-4, "FM order of the CrTe2 is insensitive to the thickness" in page 6 is difficult to agree, because the judgement whether sensitive or insensitive depends on the system. The plot for Tc of film/Tc of bulk as a function of thickness for CrTe2 and Cr2Ge2Te6 seem meaningful to compare.

Reply:
We thank the reviewer for this suggestion. The normalized TC as a function of thickness is shown in Fig. R26. Compared with Fe3GeTe2 7 and Cr2Ge2Te6 2 , the TC of CrTe2 displays a weaker dependence on the number of layers. Revision: According to reviewer's suggestions, we have changed this sentence into "In order to investigate the dimensionality effect of the ferromagnetism in CrTe2 stemming from thermal fluctuation, we plot the thickness dependent TC (Fig. 4d). The TC of CrTe2 decreases slightly with reducing the film thickness compared with other commonly investigated 2D magnets, such as Cr2Ge2Te6 2 and Fe3GeTe2 7 ( Supplementary Fig. 8), demonstrating the robustness of ferromagnetism in the epitaxially gown CrTe2 thin films." Comments: 6-5, What does "quantum thickness regime" in page 7 mean? How did the authors define and evaluate the quantum feature?
Reply: Here, we want to express "few atomic layers". We agree that using "quantum thickness regime" may be not appropriate, and have replaced it with "atomic layers".
Comments: 6-6, "large magnetic moments" in page 12 is not discussed with the exact values for the films in main text. It is difficult to judge the large or small moment. Revision: Based on reviewer's suggestion, we have added the discussion of large magnetic moment in the revised manuscript on page 10.
"Notably, the atomic magnetic moment of CrTe2 is determined to be ~3 B/atom with the half-filled t2g orbital. It is the largest possible moment of Cr according to the Hund's rule." Comments: 6-7, "the thickness down to 3 ML due to the strong magnetic anisotropy" in page 12 is not supported by experimental results, because the M-H curves of in-plane and out-of-plane for 3 and 5 ML films are not provided in the present manuscript. PMA should be judged by comparison of M-H curves of in-plane and out-of-plane.

Reply:
We thank the reviewer for suggesting the additional experiments. In order to clarify the PMA in ultrathin CrTe2 thin films, we did field dependent magnetization curves of 3 ML and 5 ML CrTe2 thin films under out-of-plane and in-plane configuration (Fig. R27). The nearly square-shaped FM hysteresis loops under out-ofplane magnetic field suggest the robust FM order with the easy axis perpendicular to the thin films. The PMA constants ( = 2 ) of 3 ML and 5 ML CrTe2 films at 10 K are determined to be 6.6×10 6 erg/cm 3 and 6.5×10 6 erg/cm 3 , respectively.  loops of 3 ML and 5 ML CrTe2 thin films as supplementary materials (Fig. S5). "In order to clarify the thickness dependence of the magnetic properties, we have measured the field dependent magnetization curves of 3 ML and 5 ML CrTe2 thin films under out-of-plane and in-plane configuration ( Supplementary Fig. 5 Comments: 6-9, There is a paper not referred in this manuscript, Room temperature ferromagnetism in ultra-thin van der Waals crystals of 1T-CrTe2, Nano Research. Doi.org/10.1007/s12274-020-3021-4.

Reply:
We thank the reviewer for pointing out this interesting paper. When we submit this manuscript, the paper (Nano Research. Doi.org/10.1007/s12274-020-3021-4) 16 hasn't been published online and we only refer it in the format of arXiv as ref.22 in our first submitted manuscript.

Revision:
The paper of Nano Research 16 has now been referenced as a published one (Nano Research. Doi.org/10.1007/s12274-020-3021-4) in our revised manuscript on page 5 and 8.
In addition to the above responses to all three reviewers' comments, we also have made the following revisions.
1. The figures and references have been updated. 2. Author Prof. Jun Du is included in the author list. He provided us with further SQUID measurements and valuable suggestions.
In Fig. R20a, 20b, and 20c, Ryx-H curves at T = 10 K is missing, although the data point is plotted in Fig. R20d, 20e, and 20f. Considering from Ryx-H curves in Figs. R20 at high temperature T = 30 K and 70 K, the coercive field in Ryx-H curves at T = 10 K is likely much larger than that in M-H curves in Fig. 2b  In the revised description in page 6, line 20.
[c = 6.13 for the film and c = 5.94 for the bulk] is added. Roughly 3 % mismatch of c-axis length is rather large. In-plane lattice of the film agrees well with the bulk value, which is discussed by STM image in page 6, line 4. This in-plane value indicates small effect of in-plane strain in the film. The Authors have to discuss the origin why the c-axis length is so large. If the a-axis length is elongated 3 %, band structure is dramatically varied from bulk. In addition, is this elongation of caxis length relating on the PMA? Because the magnetic exchange coupling between two layers strongly depends on the length, the magnetic property of CrTe2, CrSe2, and CrS2 are completely different. I recommend to the authors do not overlook the large elongation of c-axis length.

Reply to the referees' comments
We thank the referees for the helpful and positive comments and have revised the paper accordingly to address the points raised. We show reviewers' reports in black typeface and answers in light blue typeface for easy identification. Major changes have been highlighted in blue in the revised main text and the supplementary information.

Comments:
The Authors have carefully taken my suggestions and comments into account. They have provided convincing answers and adequately modified their manuscript. I have nothing to oppose to the publication of the paper.

Reply:
We thank the reviewer for his/her positive appraisal and publication recommendation.

Reviewer #2 (Remarks to the Author):
Comments: It seems that authors answered all the questions appropriately and improved the manuscript by adding new discussion. I would like to confirm one additional point about the perpendicular magnetic anisotropy (related to the question 7, 8, 9, and 10 in the previous report). In Fig. 2 c and d, we can see hysteresis even for H//ab data, which looks inconsistent with the perpendicular magnetic anisotropy. Could you explain the possible origin of this hysteresis in case of H//ab?

Reply:
We thank the reviewer for his/her positive comments and he/she thinks that we have answered all the questions appropriately and improved the manuscript. The magnetic anisotropy generally originates from a combination of three factors: shape anisotropy 1,2 , magneto-crystalline anisotropy 3 and anisotropy of exchange interactions 1 .
The shape anisotropy favors in-plane magnetic anisotropy in thin films 1,2 . The magnetocrystalline anisotropy and exchange anisotropy lead to the PMA in CrTe2 films. However, the in-plane shape anisotropy is also present in the thin films, which gives rise to the in-plane hysteresis. Similar in-plane magnetic hysteresis loops have also been reported in the ferromagnetic vdW Cr2Ge2Te6 thin films 4 and typical PMA systems such as Mn2.5Ga 5 and Co/Pt 6 .
Revision: According to the reviewer's suggestions, we have included a brief discussion of the in-plane magnetic hysteresis loops in the revised manuscript on page 7. "The in-plane magnetic hysteresis loops, similar to those reported in the FM vdW Cr2Ge2Te6 thin films 4 and typical PMA systems such as Mn2.5Ga 5 and Co/Pt 6 , can be attributed to the shape anisotropy favoring in-plane easy axis for thin films 1,2

Comments:
Dear Authors, I appreciate the Authors for the revisions and responses. I agree with the significance of this study, which is clearly raised in the response. Two experimental observations are pronounced in the revised manuscript; 1) discussion about the PMA and 2) observation of ferromagnetic behavior in monolayer CrTe2. The responses to my comments and revisions are basically reasonable.
Reply: First of all, we are grateful to the reviewer for pointing out the significance of this study and the revisions we made. We also thank the reviewer for the detailed comments and constructive suggestions, which help us to further improve our manuscript.
Comments: Please check again following remained points, which should be clarified.

Reply:
We thank the reviewer for this valuable comment. In the revised manuscript, the title has been modified to: "Room-temperature intrinsic ferromagnetism in epitaxial CrTe2 ultrathin films." Comments: Relating on previous comment 2, Regarding with Fig. R17. Does the magnetization reach zero at high temperature for the data shown in Fig. R17? How did the Authors define Curie temperature for the data H//ab and H//c in Fig. R17? As I pointed out the two-step like transition of M-T curves in previous comment, the data in Fig. R17 also shows two-step and saturation at finite value around 300 K. This behavior is completely different from the data in Fig. R16, which reaches zero. In addition, are Curie temperatures estimated from the data H//ab and H//c consistently comparable in the identical sample?
The Fig. R17 corresponds to Supplementary Fig. 3 so that the above points should be clarified. I recommend to add the discussion and response to the above comment in Supplementary file.

Reply:
We appreciate the reviewer's comments and suggestions. Previously we plotted the magnetization curves only up to 300K in Fig.R17. Here we have revised the figure to show the out-of-plane and in-plane magnetization curves up to 320 K, as exhibited in Fig. R1. Both magnetization curves show a smaller slope near TC and reach zero at ~320 K.

Fig. R1
Zero-field and field cooled temperature dependence of the magnetization of 7 ML CrTe2 with an applied in-plane and out-of-plane magnetic field of 0.1 T.
The TC has been obtained by using a critical power-law function α(1−T/TC) β to fit M-T curves without the inclusion of the paramagnetic tail. This method had been used to study ferromagnetism in atomically-thin Cr2Ge2Te6 7 and Fe3GeTe2 nanoflakes 8 . As shown in Fig. R2, the TC of 7 ML CrTe2 thin films extracted from the temperaturedependent out-of-plane and in-plane magnetization are ~300±5 K and 268±3 K with β of 0.13±0.03 and 0.11±0.04, respectively, which is comparable with β = 0.125 for the 2D Ising model 8 . The TC calculated along the hard axis is lower than that of the easy axis. The theoretical work by Callen 9 shows that for an anisotropic ferromagnet, the TC depends on the direction of the magnetization. The TC is high along the easy directions, and can drop quite low in hard directions, for an anisotropy energy comparable to the exchange energy. Distinct with 3D materials in which the typical value of exchange interaction is orders of magnitudes larger than magnetic anisotropy, the TC in 2D ferromagnets is determined primarily by the excitation gap that results from the magnetic anisotropy 7 . Therefore, the dominant magnetic anisotropy in 2D magnetic materials gives rise to the variation of TC along different magnetic directions. Similar behaviors were also observed in Fe3GeTe2 (201 K along the easy axis and 196 K along the hard axis) 10 and Fe7S8 single crystals (603 K along the easy axis and 225 K along the hard axis) 11 .

Revision:
Per the reviewer's advice, we have replaced the M-T curve in Fig. S3 with the new one with temperature up to 320 K and discussed the definition of the TC in the manuscript as follows. "The TC has been obtained by using a critical power-law function α(1−T/TC) β to fit M-T curves without the inclusion of the paramagnetic tail 8 .
In the supplementary, we have added the following paragraph. "The TC of 7 ML CrTe2 thin films extracted from the temperature-dependent out-ofplane and in-plane magnetization are ~300±5 K and 268±3 K with β of 0.13±0.03 and 0.11±0.04, respectively, which is comparable with β = 0.125 for the 2D Ising model 8 . The TC calculated along the hard axis is lower than that of the easy axis. The theoretical work by Callen 9 shows that for an anisotropic ferromagnet, the TC depends on the direction of the magnetization for an anisotropy energy comparable to the exchange energy. Distinct with 3D materials in which the typical value of exchange interaction is orders of magnitudes larger than magnetic anisotropy, the TC in 2D ferromagnets is determined primarily by the excitation gap that results from the magnetic anisotropy 7 . Therefore, the dominant magnetic anisotropy in 2D magnetic materials gives rise to the variation of TC along different magnetic directions. Similar behaviors were also observed in Fe3GeTe2 (201 K along the easy axis and 196 K along the hard axis) 10 and Fe7S8 single crystals (603 K along the easy axis and 225 K along the hard axis) 11 ." Comments: In Fig.2a, the measurement configuration of film, direction of magnetic field, and the value of magnetic field are confusing. Therefore, the schematic of the measurement configuration should be added in Fig. 2a as like Fig. 2b and Fig. 2c for removing the confusion.

Revision:
Per the reviewer's suggestion, we have added the schematic of the measurement configuration to Fig. 2a and the description of the direction and The magnetic field is applied along the out-of-plane direction with a magnitude of 1000 Oe. The high TC is preserved with thickness decreasing to 3 ML. b, c Magnetic hysteresis loops of 7 ML CrTe2 at different temperatures with external fields along both the perpendicular (b) and parallel orientation (c) with respect to sample plane, indicating a strong out-of-plane magnetic anisotropy. d Enlarged hysteresis loops of 7 ML CrTe2 at 300 K, in which the intrinsic ferromagnetism and PMA still maintains. Top inset: temperature dependence of Ku for 7 ML CrTe2, where the Ku is preserved at 300 K, despite the lower intensity with the increase of temperature.
Comments: Relating on previous comment 3, Fig. 2b, Fig. R20, and Fig. R21. It is difficult to agree with the claim in Fig. R20. The authors have to provide fair comparison with coercive field in M-H and Ryx-H curves at identical temperature. For example, Rxy-H and M-H curve at 10 K or 100 K should be directly compared within one figure, which enables understanding the comparable coercive field easily. This figure can be individually made for 3ML, 5ML, and 7ML. In Fig. R20a, 20b, and 20c, Ryx-H curves at T = 10 K is missing, although the data point is plotted in Fig. R20d, 20e, and 20f. Considering from Ryx-H curves in Figs. R20 at high temperature T = 30 K and 70 K, the coercive field in Ryx-H curves at T = 10 K is likely much larger than that in M-H curves in Fig. 2b and Fig. R21. In addition, the number of data points in Figs Figures 5 and 6 so that the above point should be clarified. I recommend to add the discussion and response to the above comment in Supplementary file.

Reply:
We thank the reviewer for the helpful comments. Per the reviewer's suggestions, we have provided a complete set of Hall resistance plots for a comparison with the coercive field in M-H curves at each temperature. The field dependent magnetic moment and Hall resistance of CrTe2 thin films of 3 ML, 5 ML and 7 ML at various temperatures are plotted in Fig. R4. The Hall responses share a similar temperature dependence of the coercive field with magnetic hysteresis loops, see Figure R5.