µMAG Standard Problem #3

Standard Problem #3 Diagram

Problem proposed by Alex Hubert, University of Erlangen-Nuremberg.

Please send comments to rmcmichael@nist.gov and join the µMAG discussion e-mail list for ongoing discussion.

A set of solutions have been submitted.


This problem is to calculate the single domain limit of a cubic magnetic particle. This is the size L of equal energy for the so-called flower state (which one may also call a splayed state or a modified single-domain state) on the one hand, and the vortex or curling state on the other hand.


A cube with edge length, L, expressed in units of the intrinsic length scale, lex = (A/Km)1/2, where Km is a magnetostatic energy density, Km = 1/2µ0Ms2 (SI) or 2piMs2 (cgs emu).

Material parameters:

Uniaxial anisotropy Ku with Ku = 0.1 Km, and with the easy axis directed parallel to a principal axis of the cube.

Desired output for comparison:

All these values should be given for both configurations (flower and vortex) at the single domain size. The results should be shown to be independent of the discretization size.

Please see the µMAG standard problem strategy page for information on publicizing your results.


The transition is expected to be found in the neighborhood of L = 8 lex.

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