Engineering polar vortex from topologically trivial domain architecture

Topologically nontrivial polar structures are not only attractive for high-density data storage, but also for ultralow power microelectronics thanks to their exotic negative capacitance. The vast majority of polar structures emerging naturally in ferroelectrics, however, are topologically trivial, and there are enormous interests in artificially engineered polar structures possessing nontrivial topology. Here we demonstrate reconstruction of topologically trivial strip-like domain architecture into arrays of polar vortex in (PbTiO3)10/(SrTiO3)10 superlattice, accomplished by fabricating a cross-sectional lamella from the superlattice film. Using a combination of techniques for polarization mapping, atomic imaging, and three-dimensional structure visualization supported by phase field simulations, we reveal that the reconstruction relieves biaxial epitaxial strain in thin film into a uniaxial one in lamella, changing the subtle electrostatic and elastostatic energetics and providing the driving force for the polar vortex formation. The work establishes a realistic strategy for engineering polar topologies in otherwise ordinary ferroelectric superlattices.

) are actually created by the reconstruction from a topologically trivial strip domain structure in the as-deposited film on a substrate. The reconstruction is induced by the thin plate fabrication for TEM observations.
As my first impression, the present manuscript could have been submitted to Nature as a Comment on "Observation of polar vortices in oxide superlattices." by Yadav, A. K. et al. Nature 530, 198-201 (2016) rather than an independent publication. It appears, however, that the authors chose the latter option. They wrote a manuscript claiming that the reconstruction is useful as an artificial engineering technique of topologically non-trivial polar vortices from topologically trivial stripe domain, instead of criticizing the previous publication. I would like to leave the editor to choose the best way to publish their findings. Overall, their manuscript is well written based on technically sound experimental data with scientific rigor. Of course, the contents would attract a majority of professional and general readers as was proved by the previous Nature publication. So I recommend the manuscript to be published on a high-impact journal. However, their manuscript must be brushed up further by supplementing additional data to complement their analysis on this fascinating ferroelectric structure at the nanometer length-scale. As a conclusion, I would like to reconsider the manuscript for a publication in Nature Communications after major and minor revisions as I describe in the following paragraphs.
Major revisions (1) A plan-view DF-TEM image as shown in Fig. 3b in Ref. 1 must be presented. The data is significant to discuss how the two orthogonal thin plate fabrication processes reconstruct the original stripe domain.
(2) PFM measurements reveal the period of stripe domain is 68.2±2.6 nm, which is much different from the period of vortices (8.6 nm) as well as their phase-field simulations (also 8.6 nm?). The authors must explain the discrepancy in the main text. In addition, the orientation of the stripe domain (a-c domain) is different from the stripe (a-a domain) as shown in Fig. 3b and Fig. 4 22356-0 (2021). A typical Introduction is composed of three paragraphs. It would be a good idea to include this latest publication in Introduction as it appears closely related with the present work. (4) Also, Discussion is too short (only 122 words). It would be a good idea to add a discussion on the difference between the plan-view lamella and the cross-sectional lamella. The readers must be interested in how the two engineering processes reconstruct the original stripe domain.
Minor Revisions (0) Throughout the manuscript: "topological trivial "-> "topologically trivial" (1) Title: "Reconstruction of polar vortex from topological trivial domain architecture"-> What is reconstructed is not the polar vortex but the topologically trivial domain. "Reconstruction (or Engineering) of topologically trivial stripe domain into topologically non-trivial polar vortex " would be better.

End of Review
Reviewer #3 (Remarks to the Author): This manuscript shows that a (PbTiO<sub>3</sub>)<sub>10</sub>/(SrTiO<sub>3</sub>)<sub>10</sub> superlattice sample comprises "topologically trivial" strip-like polarisation domains as fabricated but that a thin lamella prepared from this sample comprises an array of polarization vortices. As regards the electron microscopy, the analysis uses standard techniques for such systems but is thorough in showing that multiple forms of evidence point to a common conclusion. I leave any critique warranted on the details of the piezo-response force microscopy, X-ray 3D reciprocal space mapping and phase field simulations to reviewers better qualified to make it, observing only that I found the description of these analyses to be clear.
The point of novelty of the manuscript seems to me somewhat subtle. It is not that (PbTiO<sub>3</sub>)<sub>10</sub>/(SrTiO<sub>3</sub>)<sub>10</sub> superlattice thin films may contain an array of polarization vortices: as the authors acknowledge, these have been observed via atomic-resolution electron microscopy before (e.g. Ref. [1], and by some of the present authors in Ref. [29]) and explained by phase field simulations (e.g. Ref. [25] using thin-film -i.e. stress-free -boundary conditions). Rather, because these vortices are demonstrated not to be present in the original specimen (i.e. prior to the lamella preparation needed to produce an electrontransparent sample), the point of novelty is that such specimen preparation process is therefore a route to producing topologically non-trivial polarization configurations, with potentially significant practical applications. I am not able to judge to what extent film thickness may implicitly have been appreciated to be a governing factor in earlier work on these materials, and the present manuscript does not explore where the transition region between the two endpoint regimes might be. Nevertheless, the case is clearly made, so if this insight is indeed novel then I think the manuscript would be of wide significance and interest and thus very suitable for publication in Nature Communications.
Important point for clarification: * The lamella preparation in the methods section gives ~30 µm as the thickness after mechanical polishing. Presumably this is not the specimen thickness for STEM imaging -the analysis of Fig. 2(d) especially would be questionable for a sample of thickness much beyond a few tens of nanometers.
Since the evidence presented only demonstrated the presence of arrays of polarization vortices in the area of sample on which the EM data is obtained, can the authors please give a more concrete thickness estimate for the region(s) imaged in Fig. 2?
Minor points for the authors' consideration: * The caption to Fig. 1(a) refers to a "yellow arrow line", but all the arrows I can see are black. (Also on Fig. 1(a), the significance of the blue obelisk-shaped graphic element in the bottom left eluded me for a while, but from Supplementary Fig. 2 I tentatively guess it to denote the PFM tip. May I assume this is a standard convention in the PFM literature for denoting scan orientation?) * It is asserted in line 131 of the manuscript that the interface between the PTO and STO layers is "sharp and coherent". The latter I agree with. The former is relative. I'd not expect sharpness to be evident at the magnification at which Fig. 2(a) is shown. Supplementary Fig. 5 is more convincing, but it seems to me that in the STO layer at the bottom of that image the Sr map shows a weak Sr signal in the first Pb plane in the PTO layer above, and likewise that the Pb map shows a weak Pb signal in the first Sr plane in several of the STO layers adjacent to the PTO layers. This has little bearing on the thrust of the authors' argument, but may warrant adding a little nuance to the statements about "atomically sharp"? * With a convergence semi-angle of 30 mrad, the quoted collection inner angle of 39 mrad seems to me uncharacteristically low to qualify being called "high-angle" ADF. If that inner angle is not simply a typographical error, it's relatively low value may complicate the interpretation of Fig. 2(d) because there may be an appreciably contribution from elastically-scattered electrons (although since the analysis presented is qualitative rather than quantitative it is quite difficult to imagine imaging artefacts giving rise to such clear topological features in the displacement maps). Can the authors offer any qualification or comment on this point? * The manuscript largely reads very well, but the second sentence of Supplementary Fig. 2 is a bit off: "The scanangle will be seted to be 90°". Consider making "scan angle" two words, and replacing "will be seted" with "was set"? 1 Engineering polar vortex from topologically trivial domain architecture

Response to referees' comments
We would like to thank all the three referees for their thoughtful and highly constructive reviews that help us to improve our manuscript further. In response to their comments and suggestions, we have carried out additional experiments and analysis, with which we have revised our manuscript carefully to address all the concerns made by the referees. These revisions are detailed in our point-to-point responses below, and key revisions are also highlighted in the revised manuscript.

Response
We appreciate the reviewer's careful examination. We agree with the reviewer that the slight variation in thickness dose exist in our sample, for example as shown in Fig

Comment #2
It is known that DSO substrate features anisotropy and usually it has significant effects on the domain structures of ferroelectric films grown on it, I suggest the authors make some discussions on how the vortex phase looks like if the sample is cut from the perpendicular direction.

Response
We appreciate this important suggestion and we have carried out additional experiments to verify it. As shown in Fig. R2, cross-sectional DF-TEM of the same STO 10 /PTO 10 superlattice sample taken along the orthogonal [100] pc zone axis also 3 shows periodic contrast modulation along [010] pc direction, suggesting the presence of periodic clockwise-anticlockwise vortex pairs in PTO layers 1   The corresponding SAED pattern of (a) with enlarged (001) pc spots in the inset.

Comment #3
In Page 6, the authors describe that "……the in-plane lattice parameter a and out-of-plane lattice parameter c are calculated to be ~3.93 Å and ~4.02 Å". I suggest that such a statement should be rearranged, since electron diffraction cannot provide such a high precision for determination of lattice parameters. 4

Response
We appreciate this important point, and we have revised the statement on page 5 as "It reveals superlattice reflections both in-plane and out-of-plane, from which the in-plane lattice parameter a and out-of-plane lattice parameter c are calculated to be ~3.9 Å and ~4.0 Å, similar to those observed in reference 40 40 ", given the precision of the selected area electron diffraction in TEM.

Comment # 4
Some of the description in the text should be tuned down, such as "From application point of view, it is highly desirable if we can engineer nontrivial polar topologies from the ordinary ferroelectrics with topological trivial domain architecture, yet this has not been accomplished to our best knowledge". Actually, observation of a 1 /a 2 to flux-closure domain transformations induced by e-beam was reported recently (Acta Materialia 193 (2020) 311).

Response
We appreciate this important reference, and we have added the corresponding discussion on page 2 and 3 with this reference:

Response:
We thank the reviewer for the valuable comment, and we apologize for the oversight.
We have revised this part as suggested, overviewing experimental observation on topological ferroelectric domains in a chronological order.

General Comment
As my first impression, the present manuscript could have been submitted to Nature as a Comment on "Observation of polar vortices in oxide superlattices." by Yadav, A.
K. et al. Nature 530, 198-201 (2016) rather than an independent publication. It appears, however, that the authors chose the latter option. They wrote a manuscript 6 claiming that the reconstruction is useful as an artificial engineering technique of topologically non-trivial polar vortices from topologically trivial stripe domain, instead of criticizing the previous publication. I would like to leave the editor to choose the best way to publish their findings. Overall, their manuscript is well written based on technically sound experimental data with scientific rigor. Of course, the contents would attract a majority of professional and general readers as was proved by the previous Nature publication.

Response
We appreciate the referee's assessment of this work, and we choose to publish this finding as an independent paper instead of as a comment, which we feel more comfortable.

Comment #1
A plane-view DF-TEM image as shown in Fig. 3b in Ref. 1 must be presented. The data is significant to discuss how the two orthogonal thin plate fabrication processes reconstruct the original stripe domain.

Response:
We appreciate this important point and have carried out additional experiments. We acquired the plane-view DF-TEM image ( Figure R3) of the PTO 10 /STO 10 superlattices, from which the period of the strip-like domain is estimated to be ~69 nm, in good agreement with the PFM and RSM results in Figure 1f and 3f. In combination with the cross-sectional DF-TEM image taken along the orthogonal [100] pc zone axis, as shown in Figure R1, the reconstruction into topologically non-trivial polar vortex from topologically trivial stripe domains is confirmed. We have added this point on page 7 with additional data (Fig. R3 as Supplementary Fig. 10) of plan-view DF-TEM image: "We also acquired the planar-view DF-TEM image of the PTO 10 /STO 10 superlattice film as shown in Supplementary Fig. 10, which exhibits long-range strip-like domain 7 along [110] pc direction with the period estimated to be ~69 nm consistent with both PFM and 3D-RSM data. These set of data thus reconfirms the topologically trivial strip-like domain structure in PTO 10 /STO 10 superlattice before reconstruction."

Response:
We apologize for not making it clear that PFM maps strip domains before reconstruction, with a period of 68.2±2.6 nm in good agreement with the ~70 nm periodicity determined from 3D-RSM measurement. After reconstruction, the period for vortex array is determined from DF-TEM to be ~8.6 nm, so PFM data also support our conclusion of reconstruction and there is no discrepancy.
Furthermore, as demonstrated in Figure 1 and Figure 3f, the stripe domain in the as-grown PTO 10 /STO 10 superlattice is ~70 nm-wide planar a-a domain (instead of a-c domain) with the orientation of domain walls along [11 0] pc direction, which is also demonstrated by the planar-view DF-TEM imaging in Figure R2. The stripe domain in Fig. 3b and Fig. 4 of the reference revealed by planar-view TEM is regarded as vortex array by the authors there, which we believe is due to different thickness of PTO layer, PTO 10 /STO 10 versus PTO 16 /STO 16 .
We clarified these points on page 4 that: "Domain widths for both a 1 and a 2 domains can be estimated from the LPFM mapping over a larger area in Supplementary Fig. 3 along the line profile shown, as presented in Fig. 1f, from which the period of the strip-like domain is estimated to be 68.2 ± 2.6 nm. Such domain pattern is quite common in ferroelectrics, for example in strained Pb x Sr 1-x TiO 3 35 and PbTiO 3 thin films 36 , yet it is different from vortex array seen in PTO 16 /STO 16 superlattice 8 , which we believe arises from different thickness.
It will be exciting, however, if we can engineer such topologically trivial domain architecture into more interesting topologies, such as polar vortex" And reemphasize the reconstruction on page 7 that: "We also acquired the planar-view DF-TEM image of the PTO 10 /STO 10 superlattice film as shown in Supplementary Fig. 10, which exhibits long-range strip-like domain 9 along [110] pc direction with the period estimated to be ~69 nm consistent with both PFM and 3D-RSM data. These set of data thus reconfirms the topologically trivial strip-like domain structure in PTO 10 /STO 10 superlattice before reconstruction."

Response
We appreciate this important point. As suggested, we have rewritten the Introduction section, which now has two paragraphs, and we added the latest publication on vortex-antivortex pair as the reference.

Comment #4
Also, Discussion is too short (only 122 words). It would be a good idea to add a discussion on the difference between the plan-view lamella and the cross-sectional lamella. The readers must be interested in how the two engineering processes reconstruct the original stripe domain.

Response
We appreciate this important point. As suggested, we have rewritten the Discussion part. In particular, we added discussion on page 8 regarding planar lamella: "Such understanding can guide us exploring as well as engineering new polar topologies further. For example, we can explore planar instead of cross-sectional lamella that may modify the magnitude of biaxial misfit strain and thus change the energy landscape, which is currently under investigation."

Response
We have corrected as suggested.

Comment #2
Title: "Reconstruction of polar vortex from topological trivial domain architecture"-> What is reconstructed is not the polar vortex but the topologically trivial domain.
"Reconstruction (or Engineering) of topologically trivial stripe domain into topologically non-trivial polar vortex " would be better.

Response:
Thank the reviewer for the valuable comment. We have revised the title as (10) Line 76: "Guided by previous report on strip-like domain configuration"-> A citation to the "previous report" is necessary.
(11) Figure 2, caption, line 112: "scanning transmission electron microscopy (STEM) image"->"ADF-STEM image or ADF-STEM image", All acronyms must be defined in the main text when they appear first.
(12) Figure 2, caption, line 113: "Dark field TEM image"->"DF-TEM image", All acronyms must be defined once in the main text when they appear first.
(13) Figure 2, caption, line 115: "A selected-area electron diffraction (SAED) pattern"->"SAED pattern", All acronyms must be defined once in the main text when they appear first.

Response
We have made all these correction as suggested.

Important point for clarification
The lamella preparation in the methods section gives ~30 µm as the thickness after mechanical polishing. Presumably this is not the specimen thickness for STEM imaging -the analysis of Fig. 2(d)  image. Line profile extracted at the white arrow showing that the thickness ranges from ~20 to ~40 nm.
14 Minor points for the authors' consideration:

Comment #1
The caption to Fig. 1(a) refers to a "yellow arrow line", but all the arrows I can see are black. (Also on Fig. 1(a), the significance of the blue obelisk-shaped graphic element in the bottom left eluded me for a while, but from Supplementary Fig. 2 I tentatively guess it to denote the PFM tip. May I assume this is a standard convention in the PFM literature for denoting scan orientation?)

Response:
Thank the reviewer to point out these issues. We have revised and added the related descriptions in the caption of Fig. 1 as "The blue obelisk-shaped marker denotes the orientation of PFM cantilever. c, d Amplitude and phase profiles along the black arrow line in (a, b).". Furthermore, the cartoon-like tip denoting scan orientation is commonly adopted in PFM literature 6,7 .

Comment #2
It is asserted in line 131 of the manuscript that the interface between the PTO and STO layers is "sharp and coherent". The latter I agree with. The former is relative. I'd not expect sharpness to be evident at the magnification at which Fig. 2(a) is shown. Supplementary Fig. 5 is more convincing, but it seems to me that in the STO layer at the bottom of that image the Sr map shows a weak Sr signal in the first Pb plane in the PTO layer above, and likewise that the Pb map shows a weak Pb signal in the first Sr plane in several of the STO layers adjacent to the PTO layers. This has little bearing on the thrust of the authors' argument, but may warrant adding a little nuance to the statements about "atomically sharp"?

Response:
We appreciate this point and revised it on page 5 as "relatively sharp and coherent".

Comment #3
With a convergence semi-angle of 30 mrad, the quoted collection inner angle of 39 mrad seems to me uncharacteristically low to qualify being called "high-angle" ADF.
If that inner angle is not simply a typographical error, it's relatively low value may complicate the interpretation of Fig. 2(d) because there may be an appreciably contribution from elastically-scattered electrons (although since the analysis presented is qualitative rather than quantitative it is quite difficult to imagine imaging artefacts giving rise to such clear topological features in the displacement maps). Can the authors offer any qualification or comment on this point?

Response
Thank the reviewer for the valuable comment. To increase the contrast of the vortex array structure, we acquired the ADF-STEM images with a smaller convergence semi-angle for enhancing the stress contrast in the strained PTO layer. Different convergence semi-angle will only affect the relative intensity of the atomic column, not the position of the atom columns. So, it does not affect our conclusion. To avoid confusion, we changed HAADF to ADF in the revised manuscript and added the related descriptions in methods on page 10.

Comment #4
The manuscript largely reads very well, but the second sentence of Supplementary Fig.   2 is a bit off: "The scanangle will be seted to be 90°". Consider making "scan angle" two words, and replacing "will be seted" with "was set"?

Response
Thank the reviewer for the valuable comment and suggestion. We have revised this.
Review of revised Nature Communications manuscript "Engineering polar vortex from topologically trivial domain architecture" by Congbing Tan et al. Manuscript ID: NCOMMS-21-11782A I am pleased to find that their one-by-one responses to my previous comments are almost satisfactory. However, I would like to ask the authors to make the last revisions, which I believe are significant to deepen their findings. I would recommend the manuscript for a publication in Nature Communications after they respond to the major and minor revisions as described in the following paragraphs.
Major revision (1) A plan-view DF-TEM image as shown in Supplementary Fig. 10c has to be replaced by a new image having the same magnification and orientation with that of Fig. 3b as shown in Ref. 8. See Fig. R1 below, which shows a comparison between the two images. In my opinion, it appears that a narrower periodicity than 69 nm (indicated by red arrows in Fig. R1b) exists. I hope a higher magnification image could deepen their understanding of the reconstruction (engineering). Please add a comment on the discrepancy of the two images in Discussion. Minor Revisions (1) Line 38: "Topologically nontrivial polar structures are not only attractive for highdensity data storage, but may also enable ultralow power microelectronics thanks to their exotic negative capacitance"->"Topologically nontrivial polar structures are attractive not only for high-density data storage but also for ultralow power microelectronics thanks to their exotic negative capacitance" (2) Line 48: "tipping the subtle electrostatic and elastostatic energetics and providing the driving force for the polar vortex formation"-> The meaning of "tipping" is vague for non-native English readers. Use a more plain word.

End of Review
Reviewer #3 (Remarks to the Author): The authors have addressed the points I raised.
I reiterate that the electron microscopy analysis seems to me to be thorough in showing that multiple forms of evidence point to a common conclusion, and that if the insight that controlling cross-sectional lamella thickness is a route to producing topologically non-trivial polarization configurations in such materials is indeed novel (something I am not sufficiently familiar with this class of materials to judge) then I highly recommend the manuscript for publication in Nature Communications. 1

Engineering polar vortex from topologically trivial domain architecture Response to referees' comments
We would like to thank all the three referees for their thoughtful reviews and positive recommendations. For the remaining issues raised by the second referee, we have carried out additional experiments and analysis, with which we have revised our manuscript accordingly. These revisions are detailed in our point-to-point responses below, and key revisions are also highlighted in the revised manuscript.

Referee #1
Comment I find the authors have well addressed the concerns that I raised when reading the initial submission. In the meanwhile, I also find the responses by the authors to the concerns raised by the other reviewers are acceptable. Therefore, I am happy to recommend the paper for publication in Nature Communications.

Response
We appreciate the positive recommendation of the referee.

Comment #1
I am pleased to find that their one-by-one responses to my previous comments are almost satisfactory. However, I would like to ask the authors to make the last revisions, which I believe are significant to deepen their findings. I would recommend the manuscript for a publication in Nature Communications after they respond to the major and minor revisions as described in the following paragraphs.

Major revision
A plan-view DF-TEM image as shown in Supplementary Fig. 10c has to be replaced by a new image having the same magnification and orientation with that of Fig. 3b as   2 shown in Ref. 8. See Fig. R1 below, which shows a comparison between the two images. In my opinion, it appears that a narrower periodicity than 69 nm (indicated by red arrows in Fig. R1b) exists. I hope a higher magnification image could deepen their understanding of the reconstruction (engineering). Please add a comment on the discrepancy of the two images in Discussion.

Response:
We appreciate this important suggestion and we have acquired additional plane-view DF-TEM images with different magnifications, as shown in Figure R1. As the reviewer pointed out, there exist a few strip-like domains with narrower periodicity (indicated by red arrows), and there are a small number of strip-like domains with perpendicular orientation as well, which can also be observed by PFM over a larger area ( Figure R2). The orientations of these domain walls are fully consistent with continuum analysis based on strain and polarization compatibilities, and it is distinct from the orientations and period of vortex array reported in Ref. 8 ( Figure R3). In other words, these are still topologically trivial domain pattern.
To clarify this point, we have updated Supplementary Figure 10 (combining DF-TEM and PFM) as Figure R4, and added the following discussions on page 7: "We also acquired the planar-view DF-TEM image of the (PTO) 10 /(STO) 10 superlattice film as shown in Supplementary Fig. 10 Fig. 10d), which can also be observed by PFM over a larger area (Supplementary Fig. 10e). These  Comment #2 6 Minor Revisions (1) Line 38: "Topologically nontrivial polar structures are not only attractive for highdensity data storage, but may also enable ultralow power microelectronics thanks to their exotic negative capacitance"->"Topologically nontrivial polar structures are attractive not only for high-density data storage but also for ultralow power microelectronics thanks to their exotic negative capacitance" (2) Line 48: "tipping the subtle electrostatic and elastostatic energetics and providing the driving force for the polar vortex formation"-> The meaning of "tipping" is vague for non-native English readers. Use a more plain word.

Response
We appreciate these important suggestions and we have made all these correction as suggested.

Comment
The authors have addressed the points I raised.
I reiterate that the electron microscopy analysis seems to me to be thorough in showing that multiple forms of evidence point to a common conclusion, and that if the insight that controlling cross-sectional lamella thickness is a route to producing topologically non-trivial polarization configurations in such materials is indeed novel (something I am not sufficiently familiar with this class of materials to judge) then I highly recommend the manuscript for publication in Nature Communications.

Response
We appreciate the positive recommendation of the referee.