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Numerical Micromagnetics: Finite Difference Methods



J. Miltat, Michael J. Donahue


Micromagnetics is based on the one hand on a continuum approximation of exchange interactions, including boundary conditions, on the other hand on Maxwell equations in the non-propagative (static) limit for the evaluation of the demagnetizing field. The micromagnetic energy is most often restricted to the sum of the exchange, (self-)magnetostatic, Zeeman and anisotropy energies. When supplemented with a time evolution equation, including field induced magnetization precession, damping and possibly additional torque sources, micromagnetics allows for a precise description of magnetization distributions within finite bodies both in space and time. Analytical solutions are, however, rarely available. Numerical micromagnetics enables the exploration of complexity in small size magnetic bodies. Finite difference methods are here applied to numerical micromagnetics in two variants for the description of both exchange interactions/boundary conditions and demagnetizing field evaluation. Accuracy in the time domain is also discussed and a simple tool provided in order to monitor time integration accuracy. A specific, yet demanding, example allows for a fine comparison between two discretization schemes with as a net result, the necessity for mesh sizes well below the exchange length in order to reach adequate convergence.
Numerical Micromagnetics: Finite Difference Methods
Publisher Info


approximation order, boundary conditions, finite differences, Landau-Lifshitz-Gilbert, magnetization dynamics, micromagnetics


Miltat, J. and Donahue, M. (2007), Numerical Micromagnetics: Finite Difference Methods, , , [online], (Accessed June 17, 2024)


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Created August 31, 2007, Updated October 12, 2021