@article{cd6b740b27b8420cbe341c23006029b4,
title = "Magnetic Domains in Thin Ferromagnetic Films with Strong Perpendicular Anisotropy",
abstract = "We investigate the scaling of the ground state energy and optimal domain patterns in thin ferromagnetic films with strong uniaxial anisotropy and the easy axis perpendicular to the film plane. Starting from the full three-dimensional micromagnetic model, we identify the critical scaling for which the transition from single domain to multidomain ground states such as bubble or maze patterns occurs as the film thickness goes to zero and the lateral extent goes to infinity. Furthermore, we analyze the asymptotic behavior of the energy in these two asymptotic regimes. In the single domain regime, the energy Γ-converges towards a much simpler two-dimensional and local model. In the multidomain regime, we derive the scaling of the minimal energy and deduce a scaling law for the typical domain size.",
author = "Hans Kn{\"u}pfer and Muratov, {Cyrill B.} and Florian Nolte",
note = "Funding Information: The work of Cyrill B. Muratov was supported, in part, by NSF via Grants DMS-1313687 and DMS-1614948. Florian Nolte wishes to thank NJIT for its hospitality. Hans Kn{\"u}pfer acknowledges support by German Research Foundation (DFG) via the Grant 392124319. The authors also thank C. Melcher for stimulating questions, P. Bousquet for pointing us to [29], and B. Brietzke and T. Simon for a careful reading of the manuscript. Funding Information: Acknowledgements. The work of CYRILL B. MURATOV was supported, in part, by NSF via Grants DMS-1313687 and DMS-1614948. FLORIAN NOLTE wishes to thank NJIT for its hospitality. HANS KN{\"u}PFER acknowledges support by German Research Foundation (DFG) via the Grant 392124319. The authors also thank C. Melcher for stimulating questions, P. Bousquet for pointing us to [29], and B. BRIETZKE and T. SIMON for a careful reading of the manuscript. Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2019",
month = may,
day = "2",
doi = "10.1007/s00205-018-1332-3",
language = "English (US)",
volume = "232",
pages = "727--761",
journal = "Archive for Rational Mechanics and Analysis",
issn = "0003-9527",
publisher = "Springer New York",
number = "2",
}