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The skyrmion-bubble transition in a ferromagnetic thin film
by Anne Bernand-Mantel, Lorenzo Camosi, Alexis Wartelle, Nicolas Rougemaille, Michaël Darques, Laurent Ranno
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|Anne Bernand-Mantel · Laurent Ranno · Nicolas Rougemaille
Magnetic skyrmions and bubbles, observed in ferromagnetic thin films with perpendicular magnetic anisotropy, are topological solitons which differ by their characteristic size and the balance in the energies at the origin of their stabilisation. However, these two spin textures have the same topology and a continuous transformation between them is allowed. In the present work, we derive an analytical model to explore the skyrmion-bubble transition. We evidence a region in the parameter space where both topological soliton solutions coexist and close to which transformations between skyrmion and bubbles are observed as a function of the magnetic field. Above a critical point, at which the energy barrier separating both solutions vanishes, only one topological soliton solution remains, which size can be continuously tuned from micrometer to nanometer with applied magnetic field.
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- Cite as: Anonymous, Report on arXiv:1712.03154v2, delivered 2018-01-08, doi: 10.21468/SciPost.Report.318
1. If the weak points could be addressed, the paper would be useful to the experimental community in their search for skyrmions in DM materials, and in guiding the fabrication of new such materials.
2. The presentation is clear and detailed.
1. Expression (9) is usually a good approximation for the energy, but it is not easy to know when this could break down. Despite the detailed explanations in the paper on the limitations of the approximation, there may be further unexpected cases that this breaks down.
2. Α weak point of the paper is that the results are not compared against simulations. It would be desirable that the subtle regions of the phase diagram (the region of skyrmion and bubble having similar radii or merging, and the regions of skyrmion bursting, or bubble collapsing) be confirmed by simulations.
For example, it appears, in the phase diagram in Fig. 3f, that the bubble exist almost down to external field H=0. As far as I know, existing numerical simulations do not confirm this.
Another example is zone 0 in Fig. 3b. It should be easy to check numerically whether this approximate result carries over to the full model.
3. Apart of all the above comments, the relation of the present paper to previous works should be clarified. (Indeed, a very good presentation of the literature is provided). Specifically, Ref.  claims to provide a "Full phase diagram of isolated skyrmions". Apart from differences in the presentation of the phase diagram, I cannot see what is the additional information provided in the present paper compared to the results presented in Ref. .
I would ask the authors to clarify this.
Magnetic skyrmions in Dzyaloshinskii-Moriya (DM) materials is a very active field of research in the last years and the perspectives for applications is supporting research activity. Despite the quantity of related research papers the understanding of a skyrmion configuration is not yet complete. Specifically, the community is not yet confident about the relation of a skyrmion (in DM materials) to a magnetic bubble (in perpendicular anisotropy materials, known since the 1960s).
The present paper is a contribution towards a quantitative understanding of the relation between skyrmions and bubbles and it provides a phase diagram for the two states.
The theoretical model for the energy of an axially symmetric skyrmion in a DM material is given in Eq. (9). The terms come from obvious approximations of the (a) exchange and anisotropy energy for a domain wall, (b) DM interaction, and (c) Zeeman energy, while the magnetostatic energy is given by an approximation that appears in Ref. .
The rest of the paper is a study of this expression as a function of the skyrmion radius, while the DM parameter D and the external field H are parameters that may be varied.
Based on previous work on skyrmions and on work on bubbles, it can easily be anticipated that this function may have two minima.
It is interesting to follow these minima. The paper explains the cases that these are well separated and the cases that they merge to a single minimum. In the later case a skyrmion and a bubble is one and the same thing.
1. Eq. (5) is claimed to give a good fit "without adding any fitting parameters". Actually all numbers appearing in Eq. (5) are fitting parameters, that have already been given appropriate values.
2. Eq. (8) is explained to give "demagnetising energy difference between a magnetic cylinder with uniform magnetisation pointing in one direction and the uniform ferromagnetic state". This is not a precise expression. What is probably meant by "cylinder" is a uniformly magnetized film with a cylindrical domain with inverted magnetization?
3. In the beginning of Sec. 3 it is stated that "changes in the fixed parameters do not modify qualitatively the results presented here but rather shift the main features to different D values." This result would probably follow trivially if one would work in a nondimensional form of the equation.
4. All the information in Figs. 1a,b,d,e seems to be contained in Fig. 1f. What is there in a,b,d,e that is not contained in Fig. 1f?
All the information in Figs. 1c seems to be contained in Fig. 1g.
If this is correct then Fig. 3 need to contain only entries f and g.
5. In the figure captions (e.g., Fig. 3 and 4) it is, in same cases, not clear which entry the description is referred to. It would be clearer if each entry is explained separately.
6. In many places the expression "spin rotation energy" is used. This expression is not a clear one.
7. In Sec. 4.1.1 (and in various other places) there is the expression "a blue dot in Fig. 3b above which...". Referring to a "region" above a "point" is not a clear specification.
8. In Sec. 4.1.2 we read "Zone 1 starts along the blue line". It is not clear what is meant.
9. In Sec 2.4.4 and 4.3.2 it is claimed that errors are negligible because some energy term is small compared to other terms. But, comparing energies is not safe. What matters is rather compare variations of energies.