---
_id: '14884'
abstract:
- lang: eng
  text: We perform a stochastic homogenization analysis for composite materials exhibiting
    a random microstructure. Under the assumptions of stationarity and ergodicity,
    we characterize the Gamma-limit of a micromagnetic energy functional defined on
    magnetizations taking value in the unit sphere and including both symmetric and
    antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic
    energy functional with homogeneous coefficients. We provide explicit formulas
    for the effective magnetic properties of the composite material in terms of homogenization
    correctors. Additionally, the variational analysis of the two exchange energy
    terms is performed in the more general setting of functionals defined on manifold-valued
    maps with Sobolev regularity, in the case in which the target manifold is a bounded,
    orientable smooth surface with tubular neighborhood of uniform thickness. Eventually,
    we present an explicit characterization of minimizers of the effective exchange
    in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s
    predictions on the emergence of helical structures in composite ferromagnetic
    materials with stochastic microstructure.
acknowledgement: All authors acknowledge support of the Austrian Science Fund (FWF)
  through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally
  been supported by the FWF through grants V662, Y1292, and P35359, as well as from
  OeAD through the WTZ grant CZ09/2023.
article_number: '30'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Elisa
  full_name: Davoli, Elisa
  last_name: Davoli
- first_name: Lorenza
  full_name: D’Elia, Lorenza
  last_name: D’Elia
- first_name: Jonas
  full_name: Ingmanns, Jonas
  id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
  last_name: Ingmanns
citation:
  ama: Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic
    energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>.
    2024;34(2). doi:<a href="https://doi.org/10.1007/s00332-023-10005-3">10.1007/s00332-023-10005-3</a>
  apa: Davoli, E., D’Elia, L., &#38; Ingmanns, J. (2024). Stochastic homogenization
    of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear
    Science</i>. Springer Nature. <a href="https://doi.org/10.1007/s00332-023-10005-3">https://doi.org/10.1007/s00332-023-10005-3</a>
  chicago: Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization
    of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of
    Nonlinear Science</i>. Springer Nature, 2024. <a href="https://doi.org/10.1007/s00332-023-10005-3">https://doi.org/10.1007/s00332-023-10005-3</a>.
  ieee: E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic
    energies and emergence of magnetic skyrmions,” <i>Journal of Nonlinear Science</i>,
    vol. 34, no. 2. Springer Nature, 2024.
  ista: Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic
    energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2),
    30.
  mla: Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies
    and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>, vol.
    34, no. 2, 30, Springer Nature, 2024, doi:<a href="https://doi.org/10.1007/s00332-023-10005-3">10.1007/s00332-023-10005-3</a>.
  short: E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).
date_created: 2024-01-28T23:01:42Z
date_published: 2024-01-23T00:00:00Z
date_updated: 2024-02-05T08:54:44Z
day: '23'
department:
- _id: JuFi
doi: 10.1007/s00332-023-10005-3
external_id:
  arxiv:
  - '2306.05151'
intvolume: '        34'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2306.05151
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
publication: Journal of Nonlinear Science
publication_identifier:
  eissn:
  - 1432-1467
  issn:
  - 0938-8974
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stochastic homogenization of micromagnetic energies and emergence of magnetic
  skyrmions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2024'
...