Existence and strong-field asymptotics of skyrmions in a fourth-order model of frustrated ferromagnets
Abstract
We study a fourth-order variational model for two-dimensional frustrated ferromagnets with competing exchange interactions and an applied magnetic field of strength H>0. For every H>1/4, we prove that the energy admits minimizers in the topological classes Q=±1 and that every minimizing sequence is precompact in H2 modulo translations. The main difficulty is that spectral coercivity degenerates as H↓1/4. Using a Helmholtz circle-mean identity, we prove that the residual energy of every nonzero-degree configuration has a uniform positive lower bound, even at the degenerate endpoint. Together with a sphere-valued H2-splitting construction, this provides a threshold-stable binding inequality and yields compactness throughout the coercive regime. We also identify H=1/4 as the sharp spectral threshold. Below it the energy is unbounded from below, whereas at the threshold nonzero-degree configurations retain a positive energy barrier and degree-zero Weyl sequences lose compactness. Finally, in the strong-field regime, rescaled minimizers approach those minimizers of the limiting functional that maximize the Dirichlet energy, while topological-charge and normalized-energy measures concentrate on the H−1/4-scale.
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BibTeX
@misc{li2026existence,
title = {{Existence and strong-field asymptotics of skyrmions in a fourth-order model of frustrated ferromagnets}},
author = {Xinye Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08255},
eprint = {2609.08255},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08255},
}
RIS
TY - UNPB
TI - Existence and strong-field asymptotics of skyrmions in a fourth-order model of frustrated ferromagnets
AU - Xinye Li
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08255
UR - https://arxiv.org/abs/2609.08255
AB - We study a fourth-order variational model for two-dimensional frustrated ferromagnets with competing exchange interactions and an applied magnetic field of strength H>0. For every H>1/4, we prove that the energy admits minimizers in the topological classes Q=±1 and that every minimizing sequence is precompact in H^2 modulo translations. The main difficulty is that spectral coercivity degenerates as H↓1/4. Using a Helmholtz circle-mean identity, we prove that the residual energy of every nonzero-degree configuration has a uniform positive lower bound, even at the degenerate endpoint. Together with a sphere-valued H^2-splitting construction, this provides a threshold-stable binding inequality and yields compactness throughout the coercive regime. We also identify H=1/4 as the sharp spectral threshold. Below it the energy is unbounded from below, whereas at the threshold nonzero-degree configurations retain a positive energy barrier and degree-zero Weyl sequences lose compactness. Finally, in the strong-field regime, rescaled minimizers approach those minimizers of the limiting functional that maximize the Dirichlet energy, while topological-charge and normalized-energy measures concentrate on the H^−1/4-scale.
ER -