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PreprintCC BY 4.0arXiv

Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets

  • Glal Bacho
  • Christof Melcher
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Abstract

We study a continuum model of frustrated magnetism that supports particle-like field configurations with nontrivial Hopf index. The energy functional combines competing second and first order exchange interactions with a stabilizing external magnetic field and gives rise to a variational problem for maps from three-dimensional space into the two-sphere. We prove the existence of energy minimizers in infinitely many nontrivial homotopy classes. We further establish the existence of a unit-charge Hopfion in the regime of strong external fields. Finally, we analyze the corresponding large-field limit, identify the natural concentration scale, and prove strong convergence of suitably rescaled minimizers to a minimizer of a limiting variational problem.

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Cite

BibTeXRIS
BibTeX
@misc{bacho2026existence,
  title = {{Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets}},
  author = {Glal Bacho and Christof Melcher},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13883},
  eprint = {2610.13883},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13883},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Existence and large-field asymptotics of Hopfions in a continuum model of frustrated magnets
AU  - Glal Bacho
AU  - Christof Melcher
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13883
UR  - https://arxiv.org/abs/2610.13883
AB  - We study a continuum model of frustrated magnetism that supports particle-like field configurations with nontrivial Hopf index. The energy functional combines competing second and first order exchange interactions with a stabilizing external magnetic field and gives rise to a variational problem for maps from three-dimensional space into the two-sphere. We prove the existence of energy minimizers in infinitely many nontrivial homotopy classes. We further establish the existence of a unit-charge Hopfion in the regime of strong external fields. Finally, we analyze the corresponding large-field limit, identify the natural concentration scale, and prove strong convergence of suitably rescaled minimizers to a minimizer of a limiting variational problem.
ER  -