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A Variational Approach to Exchange Energy Calculations in Micromagnetics



Michael J. Donahue


This paper presents a magnetization interpolation method for micromagnetic exchange energy calculations using a variational procedure to relax spins on a supplemental (refined) lattice. The approximations implicit in standard micromagnetic discretization schemes fail when angles between neighboring spins in the model become large, but the described interpolation effectively reduces the angle between neighboring spins, alleviating many of the associated problems. Moreover, this method does not introduce excessive discretization-induced vortex pinning observed with some large angle exchange energy formulations. This paper includes details on proper post-interpolation exchange torque calculation, bounds on nearest neighbor angles for interpolated lattices, a simple model predicting discretization induced Neel wall collapse, and an example of an apparently collapsed (1 cell wide) domain wall that can be restored by the proposed technique.
Journal of Applied Physics
No. 11


energy minimization, exchange energy, interpolation, micromagnetics, Neel domain walls


Donahue, M. (1998), A Variational Approach to Exchange Energy Calculations in Micromagnetics, Journal of Applied Physics, [online], (Accessed February 28, 2024)
Created June 1, 1998, Updated February 17, 2017