µMAG Standard Problem #4

Standard problem #4 diagram

Problem brainstormed by Bob McMichael, Roger Koch and Thomas Schrefl; developed by Jason Eicke and Bob McMichael.

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

Sets of solutions are available.


Standard problem #4 is focused on dynamic aspects of micromagnetic computations.  The initial state is an equilibrium  s-state  such as is obtained after applying and slowly reducing a saturating field along the [1,1,1] direction to zero.  Fields of magnitude sufficient to reverse the magnetization of the rectangle  are applied to this initial state and the time evolution of the magnetization as the system moves towards equilibrium in the new fields are examined.  The problem will be run for two different applied fields.


A film of thickness, t=3 nm, length, L=500 nm and width, d=125 nm will be used.

Material parameters:

Similar to  Permalloy:
       A = 1.3e-11 J/m (1.3e-6 erg/cm)
       Ms = 8.0e5 A/m (800 emu/cc)
       K = 0.0
The dynamics, calculated either using the Landau-Lifshitz equation,
Landau-Lifshitz equation
or the Gilbert equation,

Landau-Lifshitz-Gilbert equation
will use parameters,
alpha = 0.01, gamma prime = 221 km/As, gamma = 221.1 km/As, Lambda= 4.42 km/As

Note that these parameters are related by the equations:

Applied Fields:

Two switching events will be calculated using fields applied in the x-y plane of different  magnitude and direction.

Each field will be applied instantaneously at t=0 to the equilibrium s-state .


Two outputs are desired for comparison:

The magnetization values in the time series data should be normalized by Ms.  The time series data is desired so that a detailed comparison can be made between solutions.   The magnetization images are to check for any differences in the  reversal mechanisms  if the time data between solutions is different.

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


The problem was chosen so that resolving the dynamics should easier for the 170 degree applied field  than the 190 degree applied field.   Preliminary simulations reveal that, in the case of the field applied at 170 degrees, the magnetization in the center of the rectangle rotates in the same direction as at the ends during reversal.  In the 190 degree case, however, the center rotates the opposite direction as the ends resulting in a more complicated reversal.  The field amplitudes were chosen to be about 1.5 times the coercivity in each case.

The results should be shown to be independent of the discretization size.

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29-FEB-2000 by Jason Eicke