BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hans Knüpfer (University of Heidelberg) DTSTART:20210511T170000Z DTEND:20210511T180000Z DTSTAMP:20260423T021045Z UID:OSGA/60 DESCRIPTION:Title: Ga mma-limit for zigzag walls in thin ferromagnetic films\nby Hans Knüpf er (University of Heidelberg) as part of Online Seminar "Geometric Analysi s"\n\n\nAbstract\nIn the continuum theory\, the magnetization of a ferroma gnetic sample $\\Omega \\subset \\R^3$ is described by a unit vector field $m \\in H^1(\\Omega\,S^2)$. The minimization of the underlying micromagne tic energy leads to the formation of extended magnetic domains with unifo rm magnetization\, separated by thin transition layers. One type of such t ransition layers\, observed in thin ferromagnetic films are the so called zigzag walls. We consider the family of energies\n$$E_\\varepsilon[m] \\ = \\ \\frac{\\epsilon}{2}\\|\\nabla m\\|_{L^2(\\Omega)}^2 + \\frac 1{2\\var epsilon} \\|m \\cdot e_2\\|_{L^2(\\Omega)}^2 %\n + \\frac{\\pi\\lambda} {2|\\ln \\varepsilon|} \\|\\nabla \\cdot (m-M)\\|_{\\dot H^{-\\frac 12}}^2 \, \n$$\nvalid for thin ferromagnetic films. We consider a material in the form a thin strip and\n enforce a charged domain wall by suitable bo undary conditions on $m$. Here\, $M$ is an arbitrary fixed background fie ld to ensure global neutrality of magnetic charges. In the\n limit $\\var epsilon \\to 0$ and for fixed $\\lambda > 0$\, corresponding to the macros copic\n limit\, we show that the energy $\\Gamma$--converges to a limit e nergy where jump\n discontinuities of the magnetization are penalized ani sotropically. In\n particular\, in the subcritical regime $\\lambda \\leq 1$ one--dimensional charged\n domain walls are favorable\, in the superc ritical regime $\\lambda > 1$ the limit\n model allows for zigzaging two- -dimensional domain walls.\n LOCATION:https://researchseminars.org/talk/OSGA/60/ END:VEVENT END:VCALENDAR