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Stability and asymptotic interactions of chiral magnetic skyrmions in a tilted magnetic field

by Bruno Barton-Singer, Bernd J Schroers

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Bruno Barton-Singer
Submission information
Preprint Link: scipost_202212_00011v2  (pdf)
Date accepted: 2023-05-22
Date submitted: 2023-03-08 21:52
Submitted by: Barton-Singer, Bruno
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


Using a general framework, interaction potentials between chiral magnetic solitons in a planar system with a tilted external magnetic field are calculated analytically in the limit of large separation. The results are compared to previous numerical results for solitons with topological charge $\pm 1$. A key feature of the calculation is the interpretation of Dzyaloshinskii-Moriya interaction (DMI) as a background $SO(3)$ gauge field. In a tilted field, this leads to a $U(1)$-gauged version of the usual equation for spin excitations, leading to a distinctive oscillating interaction profile. We also obtain predictions for skyrmion stability in a tilted field which closely match numerical observations.

Published as SciPost Phys. 15, 011 (2023)

Author comments upon resubmission

We thank the reviewers for their clearly careful consideration of the paper, and a number of useful comments. We have followed all of them.

List of changes

Reference to PRB 99, 064437 (2019) was added in the introduction.

A comment was added in the caption to Figure 8, explaining what is happening in more detail and to what extent this reflects the behaviour of the interaction potential.

All figure captions were revised to improve clarity, and in particular to allow them to stand alone from the text more.

The points 0 and R were added to Figure 4.

The paragraph involving the phrase 'the integral of the gauge connection between the two sources' was re-worded - the concept is referred to more clearly in the previous paragraph.

At the first introduction of the notion of soliton centre, the reasoning for using -e3 rather than -n0 is given. This was previously a comment in the appendix, which has been amended accordingly.

Reports on this Submission

Anonymous Report 2 on 2023-5-3 (Invited Report)


As 1st report




The authors have adequately addressed the issues I raised. I recommend publication of the revised version.

Requested changes


  • validity: top
  • significance: high
  • originality: good
  • clarity: high
  • formatting: excellent
  • grammar: perfect

Anonymous Report 1 on 2023-4-4 (Invited Report)


After minor revisions and corrections made by the authors, the manuscript is now ready for publication.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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