Variational Principles of Micromagnetics Revisited
Giovanni Di Fratta, Cyrill B. Muratov, Filipp N. Rybakov, Valeriy V. Slastikov
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 nonlocal. 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.
Topics & Concepts
MicromagneticsMinificationMathematicsMinimaxDimension (graph theory)Scalar potentialVariational principleMagnetic fieldMathematical analysisScalar (mathematics)Calculus of variationsField (mathematics)Magnetic potentialScalar fieldApplied mathematicsFerromagnetismVector potentialMagnetizationVariational methodReduction (mathematics)Demagnetizing fieldMagnetic domainMaxwell's equationsWork (physics)Variational analysisClassical mechanicsEnergy minimizationDomain (mathematical analysis)PhysicsVector fieldAdvanced Mathematical Modeling in EngineeringNonlocal and gradient elasticity in micro/nano structuresComposite Material Mechanics