Manipulating topological transformations of polar structures through real-time observation of the dynamic polarization evolution

Topological structures based on controllable ferroelectric or ferromagnetic domain configurations offer the opportunity to develop microelectronic devices such as high-density memories. Despite the increasing experimental and theoretical insights into various domain structures (such as polar spirals, polar wave, polar vortex) over the past decade, manipulating the topological transformations of polar structures and comprehensively understanding its underlying mechanism remains lacking. By conducting an in-situ non-contact bias technique, here we systematically investigate the real-time topological transformations of polar structures in PbTiO3/SrTiO3 multilayers at an atomic level. The procedure of vortex pair splitting and the transformation from polar vortex to polar wave and out-of-plane polarization are observed step by step. Furthermore, the redistribution of charge in various topological structures has been demonstrated under an external bias. This provides new insights for the symbiosis of polar and charge and offers an opportunity for a new generation of microelectronic devices.

counterparts? Is the conclusion drawn from Figs. 3 and 4 still robust? A quantitative estimation of a diverging potential and the screening charges required would be helpful for interpreting the EELS results. 4. STEM-EELS is indeed capable of probing screening charges to ferroelectric dipoles but unable for tackling the bound charges of given dipoles. In this regard, the authors' interpretation of unveiling the ferroelectric-bound charges in a down-pointing film region (Figs. 4c-e) becomes puzzling. Again, comparisons to the bulk-PTO spectra are indispensable in order to clarify the issue. In summary, the structural characterization part of this work is decent. In comparison, the electronic interpretation part is unsatisfactory and, in some places, contradicting to the established wisdom. Indeed, this electronic part is essential for the titled subject and extensive revisions would be required before further considerations of this manuscript.
Minor point: The ABF imaging does not require extremely thin specimens according to this referee's hand-on experience. Therefore, it would be important for the authors to be specific about the specimenthickness requirements of the respective iDPC and ABF techniques for the merit of potential interest parties.
Reviewer #3 (Remarks to the Author): The manuscript reports atomic scale structure and evolution of topological textures in a PbTiO3/SrTiO3 (PTO/STO) superlattice. By using the advanced TEM techniques such as iDPC-STEM, EELS, and in-situ non-contact bias, as well as high-resolution STEM, the authors successfully reveal the delicate ferrolectric structures emerging in the thickness-controlled PTO sub-layers of the superlattice. The image quality looks excellent and convincing. One of the main findings is observation of negative charge accumulation at the core of the topological vortices and the EELS measurement results provide useful hints on the electronic structures at the local areas. Since the topological textures in ferrolectrics are an emerging field attracting a lot of attentions recently, the findings in a hot topological system have potential merits to be published. But, the paper still has room for improvement and raises the following questions and concerns as listed.
1) The correct topological terminologies should have used to describe the chiral vortices. Vorticity is a different concept from chirality. In the caption of Fig. 1(c), the phrase of "The red and blue regions indicate the vortex-antivortex pairs." is not correct. According to 2D winding number calculation, two singular points in the red and blue regions appear to have a topological charge of +1, respectively. And thus, they both should be called vortices rather than using the antivortex. Since they can be distinguished in aspect of chirality, "clockwise or counterclockwise chiral vortices" are topologically meaningful expressions to indicate the two regions. More rigorous description of the topological charges in ferroelectrics can be found in recently published references [Kim, K. E. et al. Nature Communications 9, 403 (2018), Li, Y. et al., npj Quantum Materials 2, 43 (2017), Seidel, J. (Ed.) Topological structures in ferroic materials. (Springer, 2016)], which are necessary to be cited in addressing the topological structures.
2) Specify where the biased voltage is applied during the in-situ bias experiment. Regardless of the explanation in the Methods section, the experimental geometry of non-contact electric bias experiment is still unclear. Is it possible to quantify the electric field across the corresponding layer of PTO?
3) In Figs. 2b-d, the white dots indicating negative charges are displayed on the experimentally obtained polarization maps. Is this charge distribution also experimentally confirmed or just guessed from polarization discontinuity? As in the Fig. 2d, one can easily imagine the bottom interface of polarization down region has a negative bound charge density. But, it would not seem simple to predict the singularities have negative charges in the vortex and wave configurations. The Figs. 2b-d have three columnar sub-panels consisting of two experiments and one simulation. What does the first column in the experimental part mean? 4) In the following EELS experiments, the t2g-eg splitting in the L3 or L2 peaks is used as an indicator of electron doping. As argued by the authors, the decrease in the splitting can be attributed to the existence of Ti3+ along with Ti4+. But, this may not be the unique reason. Basically, the t2g-eg level splitting is due to the crystal field from the neighboring anions. The vortex areas have non-collinear arrangements of polarizations, which can result in complex octahedral deformations. Exact electronic structure in the situation is not disclosed yet. Without exclusion of the possible concern or minimal warning, such innocent interpretation can fall into error. 5) How can the authors quantify the ratio of Ti3+ and Ti4+ concentrations in Fig. 4e? Is it proportional to the ratio of integrated intensities of t2g peak relative to the eg peak because the Ti3+ partially occupies the t2g orbitals? If so, the physical meaning of the spectroscopic results should be more kindly and strictly described in the main text related to the figure.

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2) We measured the a/c ratio and provided a detailed analysis of the diffraction patterns.

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The energy of a PTO layer as a function of PTO thickness obtained from phase field 50 modeling is also attached here (see response to comment 2 by referee 2). We modified 51 the statement about strain. 52 We also rewrote the main text to improve the readability of the work. In addition, some 53 terminologies and presentations are clarified.   ii) The polarization rotating region seems like a 90° domain wall, as shown in Fig.R2 (orange-C 88 region). The EELS results reveal that the t2g-eg energy splitting in such regions show no distinct 89 variation compared with the vertical or horizontal polarization regions (marked as green), which 90 is consistent with common understanding.

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iii) We systematically studied the regions where polarization is suppressed that we called "vortex 92 core" and included the results in our revised manuscript and the response to comment 3 of 93 referee 2. The vector maps of electric and polarization fields in the vortex layer and domain wall energy have previously been presented in [Nature 565, 468-471 (2019)], and it was shown that 95 these walls are also the regions where the energy density is larger than in the bulk of the domains. 96 We included the above discussions in the main text together with Fig. 3.    How would the authors reconcile this puzzle? Moreover, the GPA method demands for a 111 reference lattice. What was the reference-lattice frame exploited and was it statistically 112 meaningful enough? Is the non-uniform in-plane strain that implies a lifting of the generally 113 applicable pseudomorphic strain real or rather an artifact? The physical origin underlining the topological transformation of the domain patterns as a function of the PTO thickness is not clear 115 to this referee.

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Response: According to our experimental results, not only the out-of-plane strain but also the in-117 plane strains exhibit periodicity, while the magnitude of in-plane strain is relatively small thus 118 the periodicity is not as clearly seen as that for the out-of-plane strain. Following the referee's 119 suggestion, we added some marker lines in the in-plane strain images to make the periodicity 120 more visible, and updated the related images in the supplementary material. In the in-plane strain   out-of-plane strain exhibit a sinusoidal array, which is in accordance with a/c ratio.

Response:
We totally agree that electron carriers in ferroelectrics are fundamental for screening the diverging electrostatic potential of relevant head-to-head dipoles. While the trapped electrons 190 in vortex/wave layers are mainly distributed in core-region where polarization is near zero (as 191 shown in Fig. 3c), but not at the head-to-tail region as shown in Fig. R2. 192 Considering the origin of the electron concentrations: 1) for out-of-plane polarization, our 193 experimental evidence supports that it is driven by the demand of a screening mechanism as 194 discussed in the main text and in response to comment 1; 2) for vortex and wave layers, their   For a more rigorous statement, we also updated the manuscript .   In summary, the structural characterization part of this work is decent. In comparison, the 259 electronic interpretation part is unsatisfactory and, in some places, contradicting to the 260 established wisdom. Indeed, this electronic part is essential for the titled subject and extensive 261 revisions would be required before further considerations of this manuscript.   To clarify this, we modified the statement "ABF-STEM requires an extreme thin sample to 280 image light elements" in the main text.  Response: We'd like to thank the referee for his/her careful reading, valuable comments, and 303 positive evaluation. We are delighted to see that Referee#3 speaks highly of our work. We took 304 the remarks of the referee very seriously and improved our manuscript accordingly. Below we 305 will respond to the specific comments and better clarify our results.  Actually, we also tried the contact bias mode, in which the needle directly contacts with the top 333 of multilayer at the initial state. The shaking needle brought enormous difficulties to the subtle 334 STEM experiment, and the lamella is easily broken in this mode.

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For the non-contact bias mode, the distance between the tungsten probe and the lamella can be 336 technically controlled to be less than 3 nm, according to our hand-on experience, when applying 337 a bias voltage, the lamella will be attracted to the tungsten probe, and the final distance between 338 them will be shortened to even less. The thickness of the multilayer used for the in-situ bias 339 experiment is ~60 nm. Although in our experiment the situation is complex (the irregular shape 340 of the tungsten probe and the lamella will influence the precision of the evaluation), using the  in main text Fig. 3d and supplementary Fig. S11) and wave structure (as shown in main text Fig.  4a-b).

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To map the polarization in the whole 10-uc-PTO region (second question), the STEM images 368 would include too many arrows in our initial version. For the sake of readability, we added some 369 schematic diagrams as shown in the first column to make the corresponding topological structure 370 visually clearer. Following the referee's comment, we updated the figure caption and modified 371 the annotation of first column into a "schematic diagram".  We further checked the elongation and rotation of the oxygen octahedra, and found that both of 404 them are limited to minimal degrees, and no obvious distinction between vortex core and other 405 regions is seen. The wave structure reveals the same results.

List of main changes
In general, we rewrote the texts discussing the electron distributions with added series of Reviewers' comments:

Reviewer #2 (Remarks to the Author):
This referee deeply appreciates the tremendous experimental and theoretical efforts put by the authors to improve the work. The rewriting of the manuscript, however, brought up several selfinconsistencies (elucidated below), which are inadequate for an active consideration of the work in its present form.
1. As indicated by the new title of the manuscript, the most important exploration of the work is the rich evolution of the domain patterns upon increasing electric biases (Fig. 2). In this revision, the authors raised the issue of an electron concentration at the vortex core, assisted by the oxygenvacancy formation. Hence, the field-dependent domain evolution is also to be entangled with the fielddriven redistribution of oxygen vacancies, as suggested in Figs. R1 and R2 though not thus argued. An electric-field driven redistribution of oxygen vacancies has been a well-known phenomenon, while this is not the concern of this referee. The profound concern of this reviewer is rather that the energetics proposed in Fig. R5 would then need to incorporate this additional term, not to mention that none of each contributing term in Fig. R5 has been clearly defined in the Methods section. More seriously, Fig.  R5 and the corresponding Fig. S8 show totally different energy-density scales. The physics behind Fig.  R5 and the corresponding Fig. S8 readily become questionable and all related paragraphs added to the revised manuscript are equally problematic. 2. Significant efforts have been paid to the spectral interpretation of Ti-L and O-K edges. However, the authors' argument on Ti3+ throughout the manuscript should be accompanied with an estimated ratio from the corresponding spectral fitting. None of such a quantitative estimation of the Ti3+ fraction has been described in the work. Take Fig. 3d for example, if the Ti3+ ratio is indeed large or larger as suggested by the authors, the t2g-eg splitting shall then be washed out considering the characteristic Ti L-edge spectrum of Ti3+ does not show the t2g-eg splitting. However, Fig. 3d does not reveal such a corresponding spectral signature. 3. What is the EELS detection limit of the authors' apparatus? On page 11 (line 187), the discussed "high concentration of electrons (~1020 cm-3) or oxygen vacancies" would nonetheless correspond to a detection limit below 1 atomic percent, the probing of which is unlikely even for state-of-the-art EELS facility, and renders the spectral argument on oxygen vacancies largely uncertain. In PTO, an oxygen vacancy can pair up with a lead vacancy, casting an overall charge neutrality. This referee is conservative about the authors' argument on an electron doping by oxygen vacancies considering also that the EELS spectra in Figs. 3 and 4 are indeed too noisy (summing up more spectra of a comparable quality can resolve the problem). It is, however, true that an oxygen vacancy can indeed lead to a lattice dilation and should then lead to a positive pressure around the vortex cores (Fig. R6). Why it is indicated as a negative pressure in Fig. R6? 4. Many typos appear in this revision package.
It is this referee's general impression that the authors may have rushed to the writing of the revised manuscript after extensive additional experimental and theoretical tasks, thus leading to the above inconsistencies that are not supposed to appear at the present stage. Indeed, this is a good work from the structural-characterization aspect, while the corresponding electronic part still does not reach the minimum requirement of a self-consistency. This referee could not recommend the publication of the work at this moment.
Since the questions are reasonably answered and the requests are reflected in the revised manuscript, I would like to recommend acceptance for publication in Nature Communications.

Point-by-Point Response to Referees
Response to Referee #2 General comment: This referee deeply appreciates the tremendous experimental and theoretical efforts put by the authors to improve the work. The rewriting of the manuscript, however, brought up several self-inconsistencies (elucidated below), which are inadequate for an active consideration of the work in its present form.

Response:
We thank the referee for the positive comments about the new results we provided in the revised paper. While after carefully checking the manuscript, we agree with that some description may be not clear or accurate enough, but respectfully disagree with the comment of "self-inconsistencies". The point-by-point response to the referee's suggestions is in the following, the points which may mislead the referee are clarified one by one.
Comment 1: As indicated by the new title of the manuscript, the most important exploration of the work is the rich evolution of the domain patterns upon increasing electric biases (Fig. 2). In this revision, the authors raised the issue of an electron concentration at the vortex core, assisted by the oxygen-vacancy formation. Hence, the field-dependent domain evolution is also to be entangled with the field-driven redistribution of oxygen vacancies, as suggested in Figs. R1 and R2 though not thus argued. An electric-field driven redistribution of oxygen vacancies has been a wellknown phenomenon, while this is not the concern of this referee. The profound concern of this reviewer is rather that the energetics proposed in Fig. R5 would then need to incorporate this additional term, not to mention that none of each contributing term in

Response:
We thank the referee for his/her careful reading of our response. Our experimental evidences point towards the existence of oxygen vacancies which could give a reasonable explanation for the Ti valence changes, and they play a key role in the polarization screening mechanism.
Actually, the detailed definition of each contributing term in the energy evolution graph has been raised in the Methods section in the form of references . We are glad to put those equations into the method part, the expression for each energy density have been added.
The evolution of energy components is presented to reveal the phase transition sequence with the increase in the PTO thickness from an energy aspect. We apologize for providing two graphs about energy evolution which misled the referee. These two graphs are both from phase field modeling, the result shown in Fig. S8 is set up with a more accurate dielectric constant in the calculation initial conditions, and its corresponding calculated domain morphology fit our experimental results in a better degree (thus the results shown in the supplementary materials Fig. S8 should be preserved). We mistakenly put both of them in the previous revision package, while this does not change any discussion or summary of this part, just showing the same trend of energy evolution with different initial conditions.
We are happy to give a more detailed introduction here to explain the physical meaning underlying this energy evolution graph as shown in Fig. S8, besides the figure caption mentioned in the supplementary materials. According to [Damodaran, A. R., et al. Nat. Mater. 16,1003-1009(2017], the analysis of energy change is effective to describe the phase transition. The decrease of the average elastic energy density could be understood since the vortex state has a higher ratio of elastically favorable out-of-plane polarization, and the flux-closure state has the highest ratio of out-of-plane polarization [Hsu S. L. et al. Adv. Mater., 1901014, (2019)]. The landau energy density decreases owning to increasing out-of-plane polarization. Meanwhile, electric and gradient energy density increase owing to the phase transition from the wave-like state, to rotational vortex state smoothly, and to flux-closure state gradually with more distinct domain wall [Hong, Z., et al. Nano Lett. 17, 2246-2252(2017]. From an energetic point of view, the film thickness-driven phase transition is a result of the competition between the individual energies-elastic, electric, Landau, and gradient. More details about this theoretical part about the domain evolution and corresponding energy evolution could be found in Ref. 3 [Nano Lett. 17, 2246-2252(2017] and Ref [Adv. Mater., 1901014, (2019)].
Comment 2: Significant efforts have been paid to the spectral interpretation of Ti-L and O-K edges. However, the authors' argument on Ti3+ throughout the manuscript should be accompanied with an estimated ratio from the corresponding spectral fitting.
None of such a quantitative estimation of the Ti3+ fraction has been described in the work. Take Fig. 3d for example, if the Ti3+ ratio is indeed large or larger as suggested by the authors, the t2g-eg splitting shall then be washed out considering the characteristic Ti L-edge spectrum of Ti3+ does not show the t2g-eg splitting. However, Fig. 3d does not reveal such a corresponding spectral signature.

Response:
We thank the referee for reminding us of this point. We totally agree that it's important to present an estimated ratio. Actually, we have given such a quantitative estimation of Ti 3+ fraction in the main text and supplementary materials. Using modelbased quantification of the EELS spectra, the relative concentrations of Ti 4+ and Ti 3+ were estimated.
Such as: 1) Fig. 3c is the superposition of the Ti 4+ and Ti 3+ signal based on EELS analysis, color here represents the distribution and fraction contribution of Ti 4+ and Ti 3+ component.
2) Fig. S13c shows the Ti 3+ /Ti 4+ ratio in the PTO and STO layers across the multilayer.
The value of Ti 3+ /Ti 4+ ratio is given on the left vertical coordinate axis.
The hint of splitting could be observed even at a higher Ti 3+ fraction of ~ 0.536 (x=0.20).
According to our estimated Ti 3+ fraction in the vortex layer shown in Fig. R1b, the average value of Ti 3+ fraction in core-region is ~ 0.19, which means the t2g-eg splitting should be quite clear rather than "be washed out". Comparing our spectrum with the reference spectrums of x=0.10 and x=0.02, a high degree of consistency could be found.
For the out-of-plane polarization as shown in Fig. S13a, the Ti 3+ fraction would be less than 0.5 (for 8-uc PTO layer) based on our estimation as shown in Fig. S13c, compared with that in Fig. R1 (x=0.20, Ti 3+ fraction is ~ 0.536), the Ti edge would contain a clear L3-splitting and an obscure L2-splitting, which also shows a high degree of consistency with our experimental results as presented in Fig. S13b (the bottom spectrum). Actually, there are the other two common methods which are widely used to measure the Ti valence changes: the L2,3 intensity ratio and the energy splitting; while the L2,3

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intensity ratio has some shortcomings for high energy resolution data as discussed in Ref. [Ultramicroscopy 110, 1014[Ultramicroscopy 110, -1019[Ultramicroscopy 110, (2010], thus it is the more suitable choice to use the t2g-eg splitting to measure the proportion of the Ti 4+ and Ti 3+ components as used in our work.
Meanwhile, the high-end EELS equipment with a monochromator was used in our work, in which the energy resolution could be significantly improved to ~ 0.3 eV as shown in  In the revised main text, we have added "According to the model-based quantification, the average Ti 3+ fraction in a typical core-region is calculated to be ~ 0.19" besides the mapping of Ti valence fraction in Fig. 3c.
Comment 3: What is the EELS detection limit of the authors' apparatus? On page 11 (line 187), the discussed "high concentration of electrons (~ 1020 cm-3) or oxygen vacancies" would nonetheless correspond to a detection limit below 1 atomic percent, the probing of which is unlikely even for state-of-the-art EELS facility, and renders the spectral argument on oxygen vacancies largely uncertain.

Response:
We thank the referee for his/her careful reading. I. I. Ivanchik raised that the electrons/vacancies could accumulate and play a role in screening in the bulk density of the order of 10 20 cm -3 in Ref. [Ferroelectrics, 145(1), 149-161 (1993)]. While considering that in single domain, most of the electrons/vacancies concentrated in the extremely narrow surface/interface layer, the charge density in this local area would be rather higher than 10 20 cm -3 . Taking  To make our claim more accurate, we have added the statement of "with bulk density of the order of" in front of ~10 20 cm −3 in the main text.
In PTO, an oxygen vacancy can pair up with a lead vacancy, casting an overall charge neutrality. This referee is conservative about the authors' argument on an electron doping by oxygen vacancies considering also that the EELS spectra in Figs. 3 and 4 are indeed too noisy (summing up more spectra of a comparable quality can resolve the problem). It is, however, true that an oxygen vacancy can indeed lead to a lattice dilation and should then lead to a positive pressure around the vortex cores (Fig. R6). Why it is indicated as a negative pressure in For the EELS spectrum presented in Fig. 3 and Fig.4, they have already been processed through summing up aimed at reducing the noise. While the EELS spectrum could not be as smooth as the optical spectrum (such as XAS) due to the limit of the instrument and beam sensitivity of the sample to a greater or lesser extent. Increasing acquiring time and dose could further promote the spectrum quality while this would cause larger beam damage to the sample, in which the crystal lattice would be destroyed and severe carbon deposition would happen. Different experiment parameters had been considered

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and compared when we acquired these data. For example, the EELS data in this article required a high energy resolution, thus the monochromated EELS equipment was used, which would reduce the spatial resolution, we have to seek the balance between these parameters and we have tried our best to increase the spectrum quality through many methods.
We totally agree with your saying that the lattice dilation and positive pressure are led by oxygen vacancies. Actually, we are talking about the same phenomena. Here, awe use the hydrostatics pressure with the form: -(sigma11+sigma22+sigma33)/3, where sigma11, sigma22 and sigma33 are the local stress components. The hydrostatics pressure, thus, can be considered as the reaction force of the pressure that vortices are given. Response: According to the referee's advice, we have carefully checked all the submitted files again, and the discovered typos have been corrected.
Such as, in line 14 the "offer" have been corrected to "offers", in line 94 the "a" have been added, and so on.
It is this referee's general impression that the authors may have rushed to the writing of the revised manuscript after extensive additional experimental and theoretical tasks, thus leading to the above inconsistencies that are not supposed to appear at the present stage. Indeed, this is a good work from the structural-characterization aspect, while the corresponding electronic part still does not reach the minimum requirement of a self-consistency. This referee could not recommend the publication of the work at this moment.

Response:
We sincerely thank the referee for his/her positive view on our work from the structural-characterization aspect, indeed the main focus of this article is using highend structural-characterization methods to explore the topological structures.
With the added theoretical and experimental work above, we believed the referee's concerns have been well addressed. As quoted from the other two referees, our present work is of high quality and have the original achievements.
Referee #1:"…the electric field control of the vortices and associated changes in chemical structure (EELS) in my opinion make this an interesting and original study…" Referee #3:"…The image quality looks excellent and convincing…the topological textures in ferroelectrics are an emerging field attracting a lot of attentions recently…" We hope now the referee can be satisfied with our revised manuscript and agrees with the publication in Nature Communications