Variational principles of micromagnetics revisited
Analysis of PDEs
2020-11-03 v1 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Pattern Formation and Solitons
Abstract
We revisit the basic variational formulation of the minimization problem associated with the micromagnetic energy, with an emphasis on the treatment of the stray field contribution to the energy, which is intrinsically non-local. Under minimal assumptions, we establish three distinct variational principles for the stray field energy: a minimax principle involving magnetic scalar potential and two minimization principles involving magnetic vector potential. We then apply our formulations to the dimension reduction problem for thin ferromagnetic shells of arbitrary shapes.
Keywords
Cite
@article{arxiv.1905.04568,
title = {Variational principles of micromagnetics revisited},
author = {Giovanni Di Fratta and Cyrill B. Muratov and Filipp N. Rybakov and Valeriy V. Slastikov},
journal= {arXiv preprint arXiv:1905.04568},
year = {2020}
}