Distinct skyrmion phases at room temperature in two-dimensional ferromagnet Fe3GaTe2

Distinct skyrmion phases at room temperature hosted by one material offer additional degree of freedom for the design of topology-based compact and energetically-efficient spintronic devices. The field has been extended to low-dimensional magnets with the discovery of magnetism in two-dimensional van der Waals magnets. However, creating multiple skyrmion phases in 2D magnets, especially above room temperature, remains a major challenge. Here, we report the experimental observation of mixed-type skyrmions, exhibiting both Bloch and hybrid characteristics, in a room-temperature ferromagnet Fe3GaTe2. Analysis of the magnetic intensities under varied imaging conditions coupled with complementary simulations reveal that spontaneous Bloch skyrmions exist as the magnetic ground state with the coexistence of hybrid stripes domain, on account of the interplay between the dipolar interaction and the Dzyaloshinskii-Moriya interaction. Moreover, hybrid skyrmions are created and their coexisting phases with Bloch skyrmions exhibit considerably high thermostability, enduring up to 328 K. The findings open perspectives for 2D spintronic devices incorporating distinct skyrmion phases at room temperature.

In this manuscript, the authors reported the experimental observation of mixed-type skyrmions in a room-temperature ferromagnet Fe3GaTe2 (FGT).They considered that the mixed-type skyrmions with both Bloch and hybrid characteristics exhibited high thermostability up to 328 K.This is an interesting finding and may be useful for the further experimental exploration of distinct skyrmion phases in 2D ferromagnets.However, there are some key issues that need to be further clarified.My detailed comments are given below.
1.The experimental results in Fig. (f-h) exhibit a visible deviation from the fitting results depicted in Fig. (i-k), particularly evident in the intensity peaks ranging from 150 nm to 200 nm.In my opinions, it is recommended to appropriately incorporate additional data point into Fig.2(f-g) to ensure consistency with the fitting outcomes in Fig. 2(i-j).
3.Dzyaloshinsky-Moriya interaction (DMI) is commonly observed in magnets with a space inversion symmetry breaking (Phys.Rev. B 2022, 106, 094403).However, the question remains: what is the underlying origin of the DMI that is necessary for generating hybrid skyrmion in this centrosymmetric Fe3GaTe2 magnet?4.In previous laws, the number of skyrmions generally increases, then decreases, and eventually disappears when a perpendicular magnetic field is applied (Appl.Phys.Lett.2022, 121, 202402).However, it is intriguing to note that in Figure 3(a-f), the addition of a vertical magnetic field leads to a gradual decrease in the number of skyrmions.Furthermore, in Figure S6, there is an initial increase followed by a subsequent decrease.Therefore, what could be the inner reason for this discrepancy between these two samples?5.The micromagnetic simulations are widely used to probe the topological magnetic texture of magnetic materials.In Fig. 3(a-f), a phase diagram should be provided to explore the potential trend of the skyrmion number of the two samples and determine an boundary among the different magnetic phases.
6.The observation of both Bloch and hybrid skyrmions is interesting.However, what cause the mixing of a skyrmion with two compounds?Could it be attributed to crystal defects or impurity adsorption in the material?7.The experimental results and micromagnetic simulation results exhibit excellent agreement, indicating a strong correlation between the data.How are the parameters of micromagnetic simulations derived from the experiments, and what is their underlying basis?If possible, the authors can make some relevant first-principle calculations.
8.Can the authors provide magnetotransport measurements of 2D room-temperature ferromagnet Fe3GaTe2 to understand the transport characteristics of mixed-type skyrmions?9.The scale bars of the graphs, such Fig.2(k,l), are not illustrated.

Dear Editor and Reviewers:
We really appreciate your letter and the reviewers' valuable comments about this paper, which have helped us tremendously to improve this revised manuscript.We have carefully considered the reviewers' comments and revised our manuscript.The main corrections in the paper and the point-by-point responses to the reviewers' comments are listed below.

Reviewer 1:
The manuscript entitled "Observation of Distinct Skyrmion Phases at Room Temperature in 2D Ferromagnet Fe3GaTe2" by the authors of X. Lv et al. presents significant findings on the identification of multiple topological phases in a twodimensional magnet Fe3GaTe2 at room temperature.The combination of Lorentz TEM (L-TEM) measurements and micromagnetic simulations to uncover the mixed Bloch-Neel character of magnetic domains in Fe3GaTe2 is commendable.Importantly, this study introduces an unprecedented type of topological structures, termed hybrid skyrmions, and demonstrates their coexistence with spontaneously formed Bloch skyrmions, exhibiting remarkable thermal stability even above room temperature.I find the present findings novel and interesting, and the experimental work is of good quality.
The implications of this research for the development of room-temperature 2D spintronic devices utilizing skyrmions are substantial.Thus, I recommend this manuscript to be published in Nature Communications as a VIP article if the authors address the following questions in revision.

Response:
We sincerely thank the reviewer for careful reading of our manuscript and for recommending our manuscript to be published in Nature Communications.In the following we have thoroughly addressed all the comments raised by the reviewer.
1.The manuscript states the presence of Dzyaloshinskii-Moriya interaction (DMI) in the FGT lamella, crucial for the mixed Bloch-Neel spin textures.However, this seems inconsistent with FGT's centrosymmetric crystal structure.Could the authors clarify the origin of DMI in this context?Is it related to the natural oxidation at the O-FGT/FGT interface, or are there other factors at play?Additional evidence to support this claim would greatly strengthen your argument.

Response:
We sincerely thank the reviewer for the valuable comments.It is indeed that the presence of DMI is not consistent with Fe3GaTe2's centrosymmetric crystal structure.Actually, Fe3GaTe2 has a similar crystal structure with Fe3GeTe2, in which the Fe content plays a key role in many properties, including the Saturation magnetization (Ms), Curie temperature (Tc), crystal structure, space group, etc.As for the Fe3+xGaTe2 in this work, the Fe content is about 3.35 and the extra Fe atoms may contribute to the non-centrosymmetric crystals.Furthermore, recent studies claimed that the displacement deviation of Fe atom in FGT can induce the DMI [Nat.Commun.15, 1017, (2024)] [Adv.Sci. 10, 2303443, (2023)], as shown in Fig. R1a.To confirm the hypothesis, we have further acquired an improved HAADF-STEM image, as shown in Fig. R1b-c.Subsequently, for a quantitative determination of the displacement of the Fe atom, we vertically integrated the corresponding imaging intensity line profile (Fig. R1d).By referencing the center of the two Te atoms, the deviation of the Fe atom towards the c axis was determined to be 0.09Å.Therefore, it is reasonable to believe that the FGT in this work is not an ideally centrosymmetric crystal structure.
To further investigated the relationship between the deviation of the Fe atom and DMI constant d, density functional theory (DFT) based first-principles calculations were employed, as shown in Fig. R2.Detailed about the calculations have been incorporated in revised supplementary information on page 12.It is evident that the absence of Fe atom deviation yields D = 0 mJ/m 2 , indicating an ideally centrosymmetric crystal structure of FGT, as shown in Fig. R2c.With the increment of Fe atom deviation, the value of D increases monotonously and reach to 0.94 mJ/m 2 at 0.1 Å deviation.It should be noted that the estimated value of D (< 0.6 mJ/m 2 ) obtained by micromagnetic simulations also falls within the range of DFT-calculated values, demonstrating the credibility of our results.Indeed, a O-FGT/FGT interface could induce a interfacial DMI, which is capable of the formation of Neel-type skyrmions, as reported in a recent work (see reference 35).
However, the value of DMI arising from the O-FGT/FGT interface (7.354 or 2.301 mJ/m 2 ) is significantly higher than that in this work (≤ 0.6 mJ/m 2 ).Furthermore, each FGT lamella that prepared by focused ion beam (FIB) system were put into the lens cone of TEM without delay for the LTEM observation.Therefore, we propose that negligible surface oxidation did not affect the domain structure in our experiments."Recent studies have asserted that the displacement deviation of Fe atom in FGT can induce the DMI, 2,3 as illustrated in Fig. S14a.To validate the hypothesis, we have further acquired an improved HAADF-STEM image, as depicted in Fig. S14b-c.
Subsequently, for a quantitative determination of the displacement of the Fe atom, we performed a vertical integration of the corresponding imaging intensity line profile (Fig. S14d).By referencing the midpoint of the two Te atoms, the deviation of the Fe atom towards the c-axis was determined to be 0.09Å." "To further investigated the relationship between the deviation of the Fe atom and DMI constant D, density functional theory (DFT)-based first-principles calculations were employed, as depicted in Fig. S15.The calculation of the DMI vector occurred in two steps.Initially, structural relaxations were performed with a fixed δ(Fe) using Gaussian smearing until the forces diminished to less than 0.001 eV/Å.Subsequently, spin-orbit coupling was integrated into the calculation, and the system's total energy was determined based on the spin configuration, as illustrated in Fig. S15b.The parameter d was determined as (ECCW-ECW)/12, where ECCW denotes the energy of the counter-clockwise configuration and ECW denotes the energy of the clockwise configuration. 4 The DMI constant D was then derived using the equation  = 3√2/(   2 ), where NF represents the number of atomic layers, a is the lattice constant, and d represents the DMI strength.In the second step, the EDIFF parameter was set to 10^-6 eV, and the tetrahedron method was employed to obtain an accurate total energy.2. On page 5, line 19, the statement "the lamella was initially zero-field cooled (ZFC) from 347 to 290 K" is confusing.It may raise doubts about whether the presence of Bloch skyrmions and hybrid stripes domains must go through the ZFC process, or if these structures are naturally present at room temperature without requiring ZFC.Could the authors provide clarification on this matter?
Response: We thank the reviewer's comments on ZFC process.Actually, the presence of Bloch skyrmions and hybrid stripes is spontaneous at room temperature and zero magnetic field without requiring ZFC process.However, for Lorentz experiments, the FGT lamella is easy to be magnetized by the residual field of objective lens when the sample holder is inserted, though the objective lens is turned off.Therefore, to ensure the observation of magnetic ground state, rather than the metastable state, we initially raised the sample temperature above Curie temperature (347 K), then cooled it to the target temperature (290 K).
3. There seems to be a discrepancy between the appearance of hybrid skyrmions in Fig. 3j and those in Fig. 4 (3a-3c).Could you explain the differences observed?Additionally, the presence of stripe domains in FGT after the field-cooled (FC) process, as shown in Fig. 4a, warrants further discussion.How does the FC process affect these magnetic domains?
Response: We sincerely thank the reviewer for the valuable comments.We agree with the reviewer that there is a discrepancy between the appearance of hybrid skyrmions in Fig. 3j and those in Fig. 4 (3a-3c).However, the difference is only about the size of hybrid skyrmions, rather than the skyrmions type.For a precise comparison of magnetic domain in Fig. 3j and Fig. 4a, several skyrmions are marked and enlarged, as shown in the Fig. R3.It is obvious that all skyrmions possess a half-dark and half-light contrast.
More importantly, the skyrmion marked as 1 has a comparable size with the skyrmions marked as 2 and 3, all of which are smaller than the skyrmion marked as 4. The reason about different-sized skyrmions can be attributed to the competition between magnetic dipole-dipole interaction energy and DMI energy, as reported in recent studies (see [Nat. Commun.15, 1017, (2024)] and [Adv.Mater.2311022, (2024)].
Following the reviewer's comments, we have supplemented the experiments about the FC process-dependent magnetic domain (Fig. R4) and some discussion in both the revised main text (refer to Page 11, Lines 6-8) and Supplementary information (refer to Page 6, Lines 10-17, as also shown below: "It is necessary to mention that neither too small nor large magnetic field in fieldcooling process is conducive to produce hybrid skyrmions, as presented in Fig. S8." "The results of FC-dependent magnetic domain are presented in Fig. S8.It is evident that only Bloch skyrmions and hybrid stripes were observed in FGT after a zero magnetic field cooled (ZFC), as shown in Fig. S8a.With the increment of magnetic field in FC process (see Fig. S8b-c), more hybrid skyrmions were observed and the zero-field hybrid skyrmions lattice were created after the 512 mT-FC process.Notably, increasing the magnetic field further would be not conducive to the formation of skyrmions, and it came in being a ferromagnetic state nearly after the 896 mT-FC process, as presented in Fig. S8d.Below are a few minor points: Figures 2f and 2g in the revised manuscript to ensure consistency with the fitting outcomes depicted in Figures 2i and 2j, as illustrated in Fig. R6.

Fig. R6
The new version of Fig. 2 in the revised manuscript.
Response: We agree with the reviewer in identifying significant differences between Fe3GaTe2 and Fe3GeTe2 in terms of their Curie temperature (Tc), magnetic anisotropy (Ku), saturation magnetization (Ms), and the conditions for skyrmions formation, among others.To the best of our knowledge, these differences can be attributed to the distinctions in their crystal structure, electronic configuration, and the specific interactions occurring within these materials, as illustrated in Table R1.For instance, the magnetism is strongly dependent on the spacing between layers and the interactions between Fe, Ge (Ga) and Te atoms.The substitution of Ge by Ga in these compounds can significantly alter the crystal field environment and the magnetic exchange interaction, leading to different magnetic behaviors.More importantly, the electronic configuration and the density of states near the Fermi level play crucial roles in determining the magnetic properties of materials.The presence of Ga instead of Ge can lead to a different band structure, affecting the magnetic exchange interactions between the Fe moments, as evidenced by [Nature 2018, 563, 94-99] and Ref. 29.These interactions are critical for the establishment of magnetic order and Tc.Besides, the nature of magnetic exchange interactions, such as direct exchange, super-exchange, and RKKY (Ruderman-Kittel-Kasuya-Yosida) interactions, can vary significantly between Fe3GaTe2 and Fe3GeTe2 due to the differences in their electronic structures and crystal geometries, as evidenced by [arXiv:2402.14618(2024).].These interactions determine the strength and nature of the magnetic ordering, contributing to the high Curie temperature in Fe3GaTe2.
As for the stabilization of skyrmions, the key factors are the Ku and Ms of the magnets.
It was reported that appropriately increasing Ms could promote the formation of magnetic bubbles, and too large or small Ku is destructive to the stability of bubbles, see Ref. Table R1.Comparison of critical parameters between Fe3GaTe2 and Fe3GeTe2.
3.Dzyaloshinsky-Moriya interaction (DMI) is commonly observed in magnets with a space inversion symmetry breaking (Phys.Rev. B 2022, 106, 094403).However, the question remains: what is the underlying origin of the DMI that is necessary for generating hybrid skyrmion in this centrosymmetric Fe3GaTe2 magnet?
Response: We sincerely thank the reviewer for the valuable comments.Recent studies claimed that the displacement deviation of Fe atom in FGT can induce the DMI [Nat.
To confirm the hypothesis, we have further acquired an improved HAADF-STEM image, as shown in Fig. R7b-c.Subsequently, for a quantitative determination of the displacement of the Fe atom, we vertically integrated the corresponding imaging intensity line profile (Fig. R7d).By referencing the center of the two Te atoms, the deviation of the Fe atom towards the c axis was determined to be 0.09Å.Therefore, it is reasonable to believe that the FGT in this work is not an ideally centrosymmetric crystal structure.
To further investigated the relationship between the deviation of the "Recent studies have asserted that the displacement deviation of Fe atom in FGT can induce the DMI, 2,3 as illustrated in Fig. S14a.To validate the hypothesis, we have further acquired an improved HAADF-STEM image, as depicted in Fig. S14b-c.
Subsequently, for a quantitative determination of the displacement of the Fe atom, we performed a vertical integration of the corresponding imaging intensity line profile (Fig. S14d).By referencing the midpoint of the two Te atoms, the deviation of the Fe atom towards the c-axis was determined to be 0.09Å." "To further investigated the relationship between the deviation of the Fe atom and DMI constant D, density functional theory (DFT)-based first-principles calculations were employed, as depicted in Fig. S15.The calculation of the DMI vector occurred in two steps.Initially, structural relaxations were performed with a fixed δ(Fe) using Gaussian smearing until the forces diminished to less than 0.001 eV/Å.Subsequently, spin-orbit coupling was integrated into the calculation, and the system's total energy was determined based on the spin configuration, as illustrated in Fig. S15b.The parameter d was determined as (ECCW-ECW)/12, where ECCW denotes the energy of the counter-clockwise configuration and ECW denotes the energy of the clockwise configuration. 4 The DMI constant D was then derived using the equation  = 3√2/(   2 ), where NF represents the number of atomic layers, a is the lattice constant, and d represents the DMI strength.In the second step, the EDIFF parameter was set to 10^-6 eV, and the tetrahedron method was employed to obtain an accurate total energy.4.In previous laws, the number of skyrmions generally increases, then decreases, and eventually disappears when a perpendicular magnetic field is applied (Appl.Phys.Lett. 2022, 121, 202402).However, it is intriguing to note that in Figure 3(a-f), the addition of a vertical magnetic field leads to a gradual decrease in the number of skyrmions.
Furthermore, in Figure S6, there is an initial increase followed by a subsequent decrease.
Therefore, what could be the inner reason for this discrepancy between these two samples?
Response: We sincerely thank the reviewer for careful reading of our manuscript.We agree with the reviewer that, in most cases, the number of skyrmions typically increases, subsequently decreases, and ultimately vanishes under the influence of the magnetic field.However, these observations are predicated on the premise that stripe domains constitute the magnetic ground state.This means that with an increase in the magnetic field, magnetic skyrmions gradually emerge from stripe domains and eventually annihilate, transitioning to the ferromagnetic state.In instances where the skyrmion domain constitutes the ground state, the number of skyrmions demonstrates a monotonically decreasing trend as a function of the magnetic field, as illustrated in Fig. Response: We sincerely thank the reviewer for catching these mistakes.All the scale bars of the graphs have been checked and illustrated in revised manuscript now.
Once again, we would like to thank the reviewers for their time spent preparing their valuable feedback on our work.We hope that our responses to their comments and updates to the manuscript and well received.
In addition, we have added the following general description about the DMI calculations in the revised version (refer to Page 15, Lines 2-6 in the main text and Page 12-13 in the supplementary information) and Supplementary Fig.S14-15, as also shown below:"Crucially, the parameter D estimated by simulations also aligns within the range of DFT-calculated results (see Fig.S14-S15 in SI for details), emphasizing the pivotal role of the deviation in Fe atoms.This could elucidate the physical origin of DMI in FGT, 49,50 thereby encouraging further exploration in this area." Fig. R1 The analysis of crystal structure of FGT. a Schematic of atom arrangements in centrosymmetric and asymmetric FGT along c axis.b Observation of Fe atom deviation.The region is selected from a atomic-resolution HAADF-STEM image (c).d Line profie of the image intensity shown in (b).The blue and red lines represent the central position of two Te atoms and Fe atom, and their distance is estimated at 0.09 Å, respectively.

Fig. R2
Fig. R2 The results of first-principles calculations.a Schematic of DMI in FGT.The orange arrow D1 shows the direction of DMI vector induced by Fe and top Te atoms, while the green arrow D2 represents the opposite direction of DMI vector induced by Fe and bottom Te atoms.D1 is not equal to D2, leading to a net DMI Deff.b Spin configurations of counter-clockwise (CCW) (left column) and clockwise (CW) (right column).c Fe atom deviation-dependent D obtained by first-principles calculations.

Fig. R3
Fig. R3 The comparison between the skyrmions under a magnetic field of 102 mT (a) and after the FC process (b).c Enlarged images of skyrmions in the boxed regions in (a) and (b).

Fig. R4
Fig. R4 Magnetic skyrmions in FGT observed at 290 K and zero magnetic field after the FC process with a magnetic field of 0 mT (a), 256 mT (b), 512 mT (c) and 896 mT (d).The tilt angle is 0° (a), and 10° (b-d).The scale bar is 1 μm.
26 and [ACS Appl.Mater.Interfaces 11, 12098 (2019)].Therefore, the discrepancies on the Ku and Ms between Fe3GaTe2 and Fe3GeTe2 attribute to the distinct skyrmions condition.Furthermore, the existence of DMI or not in systems and its magnitude would impact the formation of skyrmions, as evidenced by the observations of Neel-or Bloch-type skyrmions as well as the unconventional polarization in different FGT studies (see Ref. 25).
Fig.S14-15, as also shown below: Fig. R7 The analysis of crystal structure of FGT. a Schematic of atom arrangements in centrosymmetric and asymmetric FGT along c axis.b Observation of Fe atom deviation.The region is selected from a atomic-resolution HAADF-STEM image (c).d Line profie of the image intensity shown in (b).The blue and red lines represent the central position of two Te atoms and Fe atom, and their distance is estimated at 0.09 Fig. R13 Transport properties of FGT nanoflake.a Schematic of the FGT Hall device with I // ab plane and B // c axis.b Temperature-dependent Hall resistivity ρxy.c Representative extraction of topological Hall resistivity ρ T xy at 300 K. ρ N xy and ρ A xy shows the ordinary and anomalous Hall resistivity.d Temperature-dependent topological Hall resistivity ρ T xy.Blue and red curves were measured with decreasing and increasing magnetic field, respectively.