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Vortex states in a ferroelectric cylinder
by Svitlana Kondovych, Maksim Pavlenko, Yurii Tikhonov, Anna Razumnaya, Igor Lukyanchuk
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Submission summary
| Authors (as registered SciPost users): | Svitlana Kondovych |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2112.10129v1 (pdf) |
| Date submitted: | 2021-12-21 10:28 |
| Submitted by: | Kondovych, Svitlana |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational, Phenomenological |
Abstract
The past decade's discovery of topological excitations in nanoscale ferroelectrics has turned the prevailing view that the polar ground state in these materials is uniform. However, the systematic understanding of the topological polar structures in ferroelectrics is still on track. Here we study stable vortex-like textures of polarization in the nanocylinders of ferroelectric PbTiO$_3$, arising due to the competition of the elastic and electrostatic interactions. Using the phase-field numerical modeling and analytical calculations, we show that the orientation of the vortex core with respect to the cylinder axis is tuned by the geometrical parameters and temperature of the system.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2022-7-7 (Contributed Report)
- Cite as: Anonymous, Report on arXiv:2112.10129v1, delivered 2022-07-07, doi: 10.21468/SciPost.Report.5353
Strengths
1- interest and timeliness in view of current attention to topological defects in ferroelectrics
2-Usefulness for analysis of experimental data
Weaknesses
1-no particular weaknesses identified, some changes are requested, see below
Report
In view or recent developments in the field the proposed manuscript is topical and timely. It offers a detailed analytical and numerical description of vortex structures that may appear in ferroelectric cylindrical nanodots and nanowires due to depolarization effects. The authors take into account elastic and electrostatic energy contributions and demonstrate their role in the formation of polar structures, revealing non-trivial features in polarization distribution.
Employing phenomenological approach together with numerical phase-field simulations, the authors classify a variety of vortex-like textures in nanoscale cylinders and build the corresponding phase diagram as a function of the radius and height of cylinders, as well as of the temperature. The resulting systematic description is of practical use in the experimental design of ferroelectric-based nanoelectronic elements. Overall, the manuscript is well-written, and clearly presents the results and relevant discussions. I do recommend the manuscript for publication in SciPost Physics after addressing several technical issues. Specifically:
1) Equation (5) gives the polarization distribution of an isotropic vortex in the cylindrical nanodot. However, this expression would not fulfill the natural boundary condition of zero polarization derivatives at r=R. Comment on this would be useful in the manuscript.
2) In numerical simulations, the ferroelectric cylinders are surrounded by non-ferroelectric medium as shown in Fig.5. In the text, the cylinders are described as free-standing particles. I think it would be practical to mention the requirements for this surrounding media needed to consider the cylinders as free-standing, as well as to discuss the possible technological realizations of such free-standing nanostructures.
Requested changes
1- Equation (5) gives the polarization distribution of an isotropic vortex in the cylindrical nanodot. However, this expression would not fulfill the natural boundary condition of zero polarization derivatives at r=R. Comment on this would be useful in the manuscript.
2- In numerical simulations, the ferroelectric cylinders are surrounded by non-ferroelectric medium as shown in Fig.5. In the text, the cylinders are described as free-standing particles. I think it would be practical to mention the requirements for this surrounding media needed to consider the cylinders as free-standing, as well as to discuss the possible technological realizations of such free-standing nanostructures.
Anonymous on 2022-05-18 [id 2492]
In this paper, the authors report that the orientation of the vortex core in PbTiO3 cylinder could be tuned by the geometrical parameters and temperature using phase-field simulations. This work is systematic and would provide the guidance for designing the polar topological states experimentally in ferroelectric nanostructures. Following are the comments and questions.
1. The authors stated that the basic idea of the polarization vortices formation is sketched in Fig. 1. Under short-circuited boundary conditions, the uniform polarization occurs in the PbTiO3 cylinder, while the vortex states are observed in the PbTiO3 cylinder under open-circuited boundary conditions. However, as reported by Li S. et al. (Appl. Phys. Lett. 111, 052901 (2017)), the symmetry of the electrical boundary conditions played more crucial influences on the formation of flux-closure domains. Thus, additional theoretical results or discussions are suggested to be included in this paper to illuminate the formation and transition of vortex states in ferroelectric cylinders.
2. Figure 7 is suggested to be included in the main text, which would facilitate to understand the transition between a-vortex states and c-vortex states displayed in the phase diagram in Fig. 2.
3. About the title, “in a ferroelectric cylinder” is suggested to be more specific, as in the manuscript, only PbTiO3 cylinder was discussed.