Strongly exchange-coupled and surface-state-modulated magnetization dynamics in Bi2Se3/yttrium iron garnet heterostructures

Harnessing the spin–momentum locking of topological surface states in conjunction with magnetic materials is the first step to realize novel topological insulator-based devices. Here, we report strong interfacial coupling in Bi2Se3/yttrium iron garnet (YIG) bilayers manifested as large interfacial in-plane magnetic anisotropy (IMA) and enhancement of damping probed by ferromagnetic resonance. The interfacial IMA and damping enhancement reaches a maximum when the Bi2Se3 film approaches its two-dimensional limit, indicating that topological surface states play an important role in the magnetization dynamics of YIG. Temperature-dependent ferromagnetic resonance of Bi2Se3/YIG reveals signatures of the magnetic proximity effect of TC as high as 180 K, an emerging low-temperature perpendicular magnetic anisotropy competing the high-temperature IMA, and an increasing exchange effective field of YIG steadily increasing toward low temperature. Our study sheds light on the effects of topological insulators on magnetization dynamics, essential for the development of topological insulator-based spintronic devices.

1. To confirm that the induced in-plane magnetic anisotropy and damping enhancement are due to interfacial exchange coupling, not other effects such as inter-diffusion at the interface, more XRD results should be presented. For example, a comparison of the Laue oscillations of the YIG (444) peak and small-angle x-ray reflectivity scans between a single YIG film and after a Bi2Se3 layer deposited on that same YIG film will tell valuable information about the TI/YIG interface. Also, what is the peak in the inset of Supplementary Fig. 3d? what is the shoulder? The XRD for a single YIG film should also be provided (in the Supplementary Materials).
2. Supplementary Fig. 6 shows SQUID hystereis loops for the bilayers, from which the authors should be able to extract saturation magnetization. Then combining with the effective magnetization obtained from FMR measurements, they should be able to get the anisotropy. This is an independent method to measurement anisotropy and will strengthen the argument made in this manuscript.
3. The authors attribute the kinks in Fig. 3c and 3d to the Tc of magnetic proximity effect. This is only a possible reason for the behavior and it should not be taken as a sure conclusion. 4. Some experimental parameters, such as the microwave power for FMR measurements, are not given.
Reviewer #2 (Remarks to the Author): In this work the authors report an extensive ferromagnetic resonance (FMR) study on Bi2Se3 films of varying thickness grown on the magnetic insulator, YIG. The authors compare their measurements to normal YIG films and find enhanced damping like effects as well as a new inplane magnetic anisotropy at room temperature. They also report some potential indirect evidence of perpendicular induced proximity magnetism at low temperatures. Overall, I find the experimental FMR characterization as being very complete. The authors have measured frequency dependence, angular dependence, and temperature dependence. They also were very thorough in studying films of varying thickness The three physical effects examined in this work are: spin pumping effects, low temperature perpendicular magnetic anisotropy (PMA) effects, and the (to my knowledge) more novel high temperature in-plane magnetic anisotropy (IMA). The latter effect has special emphasis in the text.
Spin pumping effects (ref. 7) and PMA effects (ref.14, 41) have already been reported in TI/YIG bilayers, and although the dataset that the authors report here is very useful for the community it is probably better suited for a more specialized audience. It is my opinion that the potential impact of this work hinges on the newly reported IMA effect. I find this effect interesting but it's origin goes largely unexplained and I think that this overall hurts the paper. The authors do rule out strain effects as being a potential culprit for IMA, and the thickness dependent study does suggest that the effect is interfacial in origin. Still, this is not strong enough to leave topological surface state physics as the only plausible explanation left for the IMA.
I want to re-emphasize to the authors that I believe the experimental work to be of good quality and believe that the data presented overall is relevant to a specialized audience. However, I cannot recommend publication in Nature Communications because I am not overall convinced that the main novelty of this work (IMA) actually originates from a topological surface state. By way of analogy, theoretical support similar to how ref. 41 supported the direct experimental observation of perpendicular magnetism a TI (ref 14) would greatly benefit this work. A more clear mechanism would be especially useful in this work because the magnetization dynamics in YIG are more of an indirect probe. I do believe that the paper in the current form is in good shape and is close to being suitable for publication, but my opinion is that the authors should consider a more targeted journal.
In order to improve the manuscript for any future (re)submissions I would also suggest that the authors address the following list of concerns. 1) To my eye, the linewidth broadening effects reported in this work are appreciably larger than in spin pumping studies (ref.7) and . The latter study involved a ferromagnetic metal as opposed to the insulator YIG. Can the authors comment on differences here between studies?
2) At low temperatures the analysis suggests that in the YIG/TI samples an in-plane effective field is present leading to even potentially a zero-applied field resonance. This is another effect that has a somewhat unclear origin as written. As the authors discuss, perpendicular magnetic anisotropy effects are expected to emerge from proximity induced magnetism at low temperature. It is unclear how the in-plane field, phenomonogically added into the Kittel equation, is related to this effect. In fact, the authors have a statement in line 330 that seems to be linking a perpendicularly magnetized layer to the in-plane effective field. I think the authors need to clear this confusing item up in any revision.
3) Related to the second point: Have the authors performed any out-of-plane angular FMR measurements as low temperature to compare with RT data as seen in Figure 1? I imagine that this type of measurement could be beneficial as a way to explore the phenomenology.

More Minor Comments:
Unless I missed it the acronym, TSS, is not defined anywhere in the manuscript. The authors should define this (I think) as topological surface state.
In line 173 the authors state that they are plotting the spin mixing conductance but they are plotting a damping parameter which the mixing conductance is proportional to.
In line 193 the authors state that the data "exhibited negative intercepts at Hres". The data plot is clear but I am not sure what the authors are intending to say with this sentence. Clarification on what the negative intercepts are is needed.
The authors state in line 211 that they are unable to detect lineshapes beyond 100 Oe due to instrumental limits. I'm not sure if this is what they intended to say as they do have field sweeps shown in Figure 1 that presumably would allow for detection of a lineshape of 100 Oe.

Reply to reviewer #1 of Manuscript-17-21884
We would like to thank the reviewers very much for the pertinent comments and important suggestions that have helped improve the content and the quality of our paper a great deal. Here we reply to each question and comment, point by point, in the following: 1) "To confirm that the induced in-plane magnetic anisotropy and damping enhancement are due to interfacial exchange coupling, not other effects such as inter-diffusion at the interface, more XRD results should be presented. For example, a comparison of the Laue oscillations of the YIG (444) peak and small-angle x-ray reflectivity scans between a single YIG film and after a Bi 2 Se 3 layer deposited on that same YIG film will tell valuable information about the TI/YIG interface. Also, what is the peak in the inset of Supplementary Fig. 3d? what is the shoulder? The XRD for a single YIG film should also be provided (in the Supplementary Materials)."

Our reply
Yes, we agree with the reviewer. To demonstrate that the induced in-plane magnetic anisotropy and damping enhancement are not due to the other effects such as strain or inter-diffusion at the interface, we have modified the presentation of our XRD results more clearly. indicates excellent crystallinity. (e) In-plane radial scan of YIG(12) and Bi 2 Se 3 (25)/YIG(12). The peak at 23.44° is attributed to , whereas the shoulder to YIG(22-4). (f) XRR results of Bi 2 Se 3 (6)/YIG(50) and the fit for the extraction of surface and interface roughness." 2) " Supplementary Fig. 6 shows SQUID hysteresis loops for the bilayers, from which the authors should be able to extract saturation magnetization. Then combining with the effective magnetization obtained from FMR measurements, they should be able to get the anisotropy. This is an independent method to measurement anisotropy and will strengthen the argument made in this manuscript."

Our reply
We thank the reviewer for an excellent suggestion. In principle, the method suggested by the reviewer should allow us to calculate the effective anisotropy constant using . However, the major difficulty came from the large paramagnetic signals from the GGG substrates that prevented us from accurately determining the of our samples. Here we present the raw data of our SQUID measurement in the inset of Supplementary Fig. 6. We estimate the errors to be as large as 10 % and conclude that it is not accurate enough for us to further extract reliably.
Instead, we can calculate the interfacial anisotropy field 4 / − 4 without involving . The temperature dependence of and should qualitatively agree as we expect the monotonically increases at low T by no more than 40 % of the RT value.
Hence we added the new data of and show its T dependence in the inset of Fig. 3(e). We can see a turning of the curves for both samples at a temperature range of 150-180 K, that was attributed to the interfacial PMA resulting from the magnetic proximity effect (MPE) in Bi 2 Se 3 /YIG. We interpret this as the emergence of an interfacial perpendicular magnetic anisotropy (PMA) that competes with the in-plane magnetic anisotropy (IMA). In addition, to independently show the effect of interfacial exchange coupling, we have appended our low T magnetoresistance (MR) data to strengthen our claim  (17), specifically, leads to interfacial perpendicular magnetic anisotropy (PMA) ( > 0) below 40 K. The turning of curves around 150 K implied that a competing magnetic anisotropy was emerging, which favored perpendicular direction and effectively diminished the IMA that persisted up to room temperature. Observing that the turning of curves were in vicinity of the individual hump temperature, we thus attribute the interfacial PMA to MPE in Bi 2 Se 3 /YIG. Our scenario is further supported by a theoretical model that considers direct the exchange coupling of TSS and an adjacent magnetic layer 31,42 . In this model, the calculated total electronic energy in the system with MPE indicates that perpendicular anisotropy is in favor.
To independently show the effect of strong interfacial exchange coupling in Bi 2 Se 3 /YIG, we performed electrical transport measurements at low T. As shown in Supplementary Fig. 7 samples, which might be obscured by the bulk conduction of Bi 2 Se 3 in the transport measurements." 3) "The authors attribute the kinks in Fig. 3c and 3d to the T c of magnetic proximity effect. This is only a possible reason for the behavior and it should not be taken as a sure conclusion."

Our reply
We agree with the reviewer that the kinks are the possible reason of MPE. We have tuned down our statement in the conclusion by rephrasing the feature to be "possible signatures of MPE". 4) "Some experimental parameters, such as the microwave power for FMR measurements, are not given."

Our reply
The microwave power of our microwave source was set to be no larger than 5 dBm. We have added a sentence in the Method section: "The microwave source power was no larger than 5 dBm."

Reply to reviewer #2 of Manuscript-17-21884
We would like to thank the reviewers very much for the pertinent comments and insightful suggestions that have helped improve the content and the quality of our paper a great deal. Before formally answering the questions of reviewer #2, we would like to respond first to his/her concerns of the origin of the interfacial IMA, which was stated in the preface of the response letter: "I want to re-emphasize to the authors that I believe the experimental work to be of good quality and believe that the data presented overall is relevant to a specialized audience. However, I cannot recommend publication in Nature Communications because I am not overall convinced that the main novelty of this work (IMA) actually originates from a topological surface state. By way of analogy, theoretical support similar to how ref. 41 supported the direct experimental observation of perpendicular magnetism a TI (ref. 14) would greatly benefit this work. A more clear mechanism would be especially useful in this work because the magnetization dynamics in YIG are more of an indirect probe."

Our reply
We understand the concerns of the reviewer that it seems to be lack of convincing evidence in our work  Fig. 2(c), the interfacial IMA is inferred to be a plausible consequence of TSS modulation. Hence, we revised the relevant paragraph starting from line 131 as follows: "The sizable interfacial IMA can be expected given the large SOC of Bi 2 Se 3 . One possible mechanism is that the electrons at the interface re-distribute upon the hybridization between the Fe d-orbital of YIG and the Dirac surface state of Bi 2 Se 3 . Recent theoretical study on EuS/Bi 2 Se 3 bilayers indicate that in additional to the strong SOC, TSS play a crucial role in mediating the exchange coupling of the ions in the magnetic layer 31 . The hybridization between TSS and the magnetic layer can overall enhance the magnetic anisotropy energy that is inherent at the interface 31 ." , and added a paragraph in the Discussion section (line 340): "We attribute the high temperature interfacial IMA to the enhanced exchange coupling of Fe 3+ ions in YIG mediated by TSS based on the dependence of in Fig. 2(c). We emphasize that, although the model in ref. 42 predicts a PMA originated from direct exchange coupling between TSS and a magnetic layer, in reality, other contributions of magnetic anisotropy dependent on the detailed interfacial atomic structure can arise. As illustrated in ref. 31, in addition to the PMA from MPE, the stress anisotropy energy of EuS can also be magnified by the strong SOC of Bi 2 Se 3 , which would not necessarily be PMA for a material system other than EuS/Bi 2 Se 3 . Other factors such as the Fermi energy of Bi 2 Se 3 can have pronounced effects on the exchange coupling constant and total anisotropy energy 31 . Given the multiple sources of magnetic anisotropy that are possibly influenced by TSS, an in-depth theoretical study will be needed to precisely describe the high T interfacial IMA and the emerging low T PMA of Bi 2 Se 3 /YIG." (the low T PMA will be discussed below) Indeed, a precise description of the interfacial magnetic anisotropy of Bi 2 Se 3 /YIG calls for further theoretical understanding, which would probably invoke first-principle calculations. However, the complicated crystal structure of YIG has long been hampering the progress. Therefore, our experimental results provide exceptionally valuable information on this important yet difficult-to-model TI/YIG system. Secondly, as requested by reviewer #1, we have calculated the interfacial anisotropy field for various T. The result is shown in the inset of Fig. 3(e). Clearly, there exhibits a peak around 150 K for both samples. We interpret the feature as an emerging low T PMA that competes with the high T IMA. The interpretation is simultaneously based on the fact that temperature of the peak position is right below that of the "hump" position, which we has identified as Observing that the turning of curves were in vicinity of the individual hump temperature, we thus attribute the interfacial PMA to MPE in Bi 2 Se 3 /YIG. Our scenario is further supported by a theoretical model that considers direct the exchange coupling of TSS and an adjacent magnetic layer 31,42 . In this model, the calculated total electronic energy in the system with MPE indicates that perpendicular anisotropy is in favor.
To independently show the effect of strong interfacial exchange coupling in Bi 2 Se 3 /YIG, we performed electrical transport measurements at low T. As shown in Supplementary Fig. 7, we observed a clear negative magnetoresistance (MR) of Bi 2 Se 3 /YIG, which is distinct from weak antilocalization (WAL) effect typical of Bi 2 Se 3 films without magnetic perturbation. Detailed analyses show that the MR data can be well-reproduced if we assume that the TRS is broken and electrons are magnetically scattered at the bottom Bi 2 Se 3 surface (See Supplementary Note 4), which may be indication for the presence of MPE in our Bi 2 Se 3 /YIG sample. However, we did not detect anomalous Hall effect in our samples, which might be obscured by the bulk conduction of Bi 2 Se 3 in the transport measurements." For the MR data and analyses, please refer to Supplementary Fig. 7 and Note 4.
Finally, we would like to emphasize the impact of this work to the reviewer. From the technical aspect, we agree that FMR is a somewhat indirect probe, compared to other direct techniques such as polarized neutron reflectivity (PNR). However, allow us to point out that, it would be difficult, if possible, to probe the interfacial magnetism using conventional techniques such as VSM or SQUID magnetometer. As we have shown in the revised Supplementary Fig. 6, the dramatically increased low T paramagnetic signals from the GGG substrates overwhelmed the YIG signals. We estimate the GGG signals to be at least 3 order of magnitude larger than that of YIG at the saturation field below 100 K. The proximity-induced magnetic moment is even harder to detect. It is not easy to circumvent the difficulty because GGG is the only substrate currently known for fabricating high quality YIG film. Hence, FMR or spin pumping is a very suitable table-top technique readily available to many researchers worldwide, and that can reliably probe the interfacial magnetic properties without resorting to large facility such as XMCD or neutron scattering.
Moreover, although a number of work has focused on MPE of TI/YIG, to our knowledge, this is the first work to study the interfacial magnetic anisotropy of TI/YIG. Although MPE-induced PMA in EuS/Bi 2 Se 3 has been reported 15 , the magnetic anisotropy of TI/YIG caused by TSS remains largely unknown for the community. We believe the interfacial magnetic anisotropy of TI/YIG is at least as important as that of EuS/Bi 2 Se 3 because YIG has even broader applications. It is the technical difficulties that hampers the progress on this topic. Therefore, we chose FMR, a standard technique to accurately determine magnetic anisotropy of materials. To emphasize these points we have re-written the introduction paragraph accordingly from line 54 to 61. Furthermore, there have been disputes in spin pumping results reported so far with large variations from group to group. With the rapid growth of the exciting field, we believe that our work will benefit all researchers in general, who are interested and eager to know the important magnetic feature such as interfacial magnetic anisotropy of TI/YIG, and its technological implications to viable applications of this quantum materials for spintronics in future. Hence our work is not targeted at a specialized audience only. Now, we reply to each question and comment of the reviewer, point by point, in the following: 1) "To my eye, the linewidth broadening effects reported in this work are appreciably larger than in spin pumping studies (ref.7) and . The latter study involved a ferromagnetic metal as opposed to the insulator YIG. Can the authors comment on differences here between studies?"

Our reply
The linewidth broadening of our samples is overall larger mainly because we intentionally choose thinner YIG films to magnify the and linewidth broadening, based on macrospin model. This would ensure adequately larger changes of Δ and for more accurate determination of the damping enhancement Δα and 4 . Hence, it would be fairer to compare the damping enhancement Δα or spin mixing conductance, in which the effect of YIG thickness has been incorporated. The main difference of Δα between ref. 7 (now ref. 8 of the revised manuscript) and our work is that we observed a large enhancement of damping around the 2D limit of Bi 2 Se 3 , while the Δα shown in Fig. 4(b) of ref.
7 had weak dependence. As described in line 358, we think that the discrepancy could come from different quality of Bi 2 Se 3 thin films. For example, the surface of our 7 nm Bi 2 Se 3 shows step-like feature that indicates layer-by-layer growth (roughness ~ 0.28 nm), which is shown in Supplementary   Fig. 3(b). For comparison, the surface of 6 nm Bi 2 Se 3 shown in Fig. 1(b) of ref. 7 doesn't clearly exhibit the step-like feature (roughness ~ 0.71 nm), and pinholes spreading throughout the image can be easily seen. To be more specific in describing the difference of Δα, we added some sentences starting from line 361: "Specifically, our samples show larger Δα when was approaching the 2D limit. Note that the linewidth broadening observed in this work is overall larger than that reported in ref. 8 mainly because we have chosen thinner YIG films." As for ref. 8 (now ref. 9), we think that it would be inappropriate to directly compare the linewidth broadening or Δα of ferromagnetic metal (FM)/TI and TI/FI heterostructures side by side. From the material aspect, the much cleaner interface of TI/FI has minimized the damping that can potentially arise from the interdiffusion or surface roughness common in FM/TI (see Gupta et al. AIP Adv. 7, 055919 (2017), for example). On the other hand, spin backflow in FM has also been considered to be a correction of damping enhancement (Jiao et al. Phys. Rev. Lett. 110, 217602 (2013)). The two side effects are believed to be minor in spin pumping from YIG to TI.
2) "At low temperatures the analysis suggests that in the YIG/TI samples an in-plane effective field is present leading to even potentially a zero-applied field resonance. This is another effect that has a somewhat unclear origin as written. As the authors discuss, perpendicular magnetic anisotropy effects are expected to emerge from proximity induced magnetism at low temperature. It is unclear how the in-plane field, phenomonogically added into the Kittel equation, is related to this effect. In fact, the authors have a statement in line 330 (original version) that seems to be linking a perpendicularly magnetized layer to the in-plane effective field. I think the authors need to clear this confusing item up in any revision." We would like to split this question into three parts (a-c) for easy to discuss step by step. a) "At low temperatures the analysis suggests that in the YIG/TI samples an in-plane effective field is present leading to even potentially a zero-applied field resonance. This is another effect that has a somewhat unclear origin as written."

Our reply
We have discussed the origin of the in the manuscript starting from line 276. To describe the origin and physical mechanism of more clearly, we would like to begin with comparing the experimental observations of our spin pumping in Bi 2 Se 3 /YIG and ST-FMR measurement on Py/Bi 2 Se 3 in ref. 9. In our experiment, we have observed a shift of resonance field at all frequencies shown in Fig. 3(b), and based on the observation we quantify the shifts using the effective field . Similarly, in Extended Fig. 1 of ref. 9, there is also a shift, which the authors attributed to the exchange effective field due to the field-like spin torque from the current-induced spin accumulation at TSS. Note that one of the main feature of ref. 9 is the observation of large field-like torque comparable to damp like torque. This is the first clue suggesting that the is related to TSS.
The second clue is revealed by comparing our T dependence of with the T dependence of field-like torque of another ST-FMR measurement reported in ref. 46. The striking similarity can be seen in Fig. 4  , and revised the relevant paragraph starting from line 294: "Moreover, we noticed that the T dependence of in Fig. 3 increased at low T. The unique T dependence of suggests that it is likely originated from TSS." b) "As the authors discuss, perpendicular magnetic anisotropy effects are expected to emerge from proximity induced magnetism at low temperature. It is unclear how the in-plane field, phenomonogically added into the Kittel equation, is related to this effect."

Our reply
Following the train of thought of the previous part, the is a non-equilibrium phenomenon due to spin pumping. As we have discussed in the manuscript, is phenomonogically similar to exchange bias effective field, which is a static and equilibrium effect, and we have precluded the possibility by showing hysteresis loops without exchange bias ( Supplementary Fig. 6). The main point to clarify here is that, the magnetic anisotropy discussed in this work, high T IMA and low T PMA, are static and equilibrium magnetic properties. In contrast, spin pumping effect involves dynamical exchange at interface and further induces a non-equilibrium spin density that manifests as . Therefore, the two types of effects may not be treated on equal footings. The two types of effects surely can have some kind of mutual interaction, but at this stage, we tend to emphasize the different nature of these effects and not to describe their interaction as it would require advanced modeling.
c) "In fact, the authors have a statement in line 330 that seems to be linking a perpendicularly magnetized layer to the in-plane effective field. I think the authors need to clear this confusing item up in any revision." Our reply Actually, we did not intend to link the PMA to . The purpose of this paragraph was to highlight that the strongly modulated magnetic properties can be viewed as good signs for future study on the magnetization dynamics of a PMA films modulated by TIs. Here, we have revised the paragraph to express our point more clearly in line 380: "Despite the fact that an interfacial PMA showed up at low T in Bi 2 Se 3 /YIG, the bilayer sample still exhibited a gross in-plane anisotropy due to the shape anisotropy of YIG. However, the notable modulation of the YIG properties presented in this work is a promising start to examine these models." 3) "Related to the second point: Have the authors performed any out-of-plane angular FMR measurements as low temperature to compare with RT data as seen in Figure 1? I imagine that this type of measurement could be beneficial as a way to explore the phenomenology."

Our reply
Unfortunately, our equipment does not allow us to perform out-of-plane FMR at low T unless we make a major modification. We believe that the measurements will give valuable information to explore the origin of . As for 4 , the in-plane frequency-dependent FMR data presented in this paper should provide equivalent information to that provided by angle-dependent FMR (see Supplementary Note 2). To bring up the future work, we revised the conclusion part starting from line 394: "Moreover, the TSS-modulated dynamics is a cornerstone for future investigation on novel physics such as topological inverse spin galvanic effect, and further raises several interesting topics. For example, how the , a quantity that comes from the non-equilibrium process of spin pumping, depends on the spin texture of TSS and the interfacial magnetic anisotropy will be an important question to answer.
Temperature-dependent FMR with out-of-plane setup should provide us with valuable information." More Minor Comments: "Unless I missed it the acronym, TSS, is not defined anywhere in the manuscript. The authors should define this (I think) as topological surface state."

Our reply
Yes, TSS stands for topological surface state. We have added the definition of the acronym in line 56.
"In line 173 the authors state that they are plotting the spin mixing conductance but they are plotting a damping parameter which the mixing conductance is proportional to." Our reply This is a typo. We have removed the sentence in this revision.
"In line 193 the authors state that the data "exhibited negative intercepts at H res ". The data plot is clear but I am not sure what the authors are intending to say with this sentence. Clarification on what the negative intercepts are is needed."

Our reply
By observing Eq.
(2), the magnitude of the negative intercepts equal . We specifically point out the feature to convince readers that it is necessary to add the term in the Kittel equation to fit the data in Fig. 3(b). It is clear that the original Kittel equation without the is unable to produce an intercept. To clarify, we have added a sentence in line 203: "Note that the Kittel equation in its original form cannot produce an intercept." "The authors state in line 211 that they are unable to detect lineshapes beyond 100 Oe due to instrumental limits. I'm not sure if this is what they intended to say as they do have field sweeps shown in Figure 1 that presumably would allow for detection of a lineshape of 100 Oe."

Our reply
Here we are indicating the limit of our FMR measurement using co-planar waveguide. Fig. 1(c) is the data taken with a microwave cavity, which has much better sensitivity. To avoid the confusion, we have revised the sentence in line 219: "We were not able to detect FMR signals with ∆ beyond 100 Oe due to the limited sensitivity of our co-planar waveguide." Reviewer #1 (Remarks to the Author): The authors have addressed my questions and comments, and added new data in the manuscripts as well as in the supplementary materials. I recommend its acceptance by Nature Communications.
Reviewer #2 (Remarks to the Author): I have received and read the response letter from Fanchiang et al. on "Strongly exchange-coupled and surface-states-modulated magnetization dynamics in Be2Se3/YIG heterostructures".
My concern with the original manuscript was centered around the fact that the IMA the authors can extract from FMR measurements was tied to a coupling between the topological surface state and the magnetic insulator. With most of the related literature showing PMA effects in these same systems (from proximity exchange interaction), I did not feel that the authors effectively argued why the IMA was also a possibility. So, while I felt that the experiment was thorough and well executed with interesting data, I believed that the conclusion was not supported and that the conflicts with literature were not addressed.
I appreciate the efforts that the authors went through in their attempt to better contextualize and interpret their results. I think that the authors now have been able to argue to their audience that the PMA seen in a TI/EuS system is not universal and that IMA in the TI/YIG system could be an example of other interfacial induced anisotropies. To support this, the authors have based an argument on recent theoretical work in TI/EuS where indeed, changes in the lattice parameter of the EuS can change PMA to IMA. In their response I think the following two points are wellemphasized: 1. I do agree with the authors that studying the magnetic anisotropy of the TI/YIG "is at least as important" as the TI/EuS system. The authors are correct to note that YIG is a material that is of broad interest in the field of spintronics, magnonics, etc. I do appreciate the fact that this is an FMR study in the first place is largely due to the YIG being an excellent material for this type of study.
2. I think that the authors have successfully argued in their rebuttal that the audience should not be so quick to immediately equivocate the magnetic proximity effect with what they call interfacial magnetic anisotropy. Essentially, the authors remind us that it is in EuS/Bi2Se3 where PMA was observed and that "the magnetic anisotropy of TI/YIG…remains largely unknown." The other concerns and comments I had suggested to the authors in my first review have been addressed and I am satisfied with the changes that were made. I can now recommend publication of this manuscript and feel the authors have done a commendable job improving their original submission.