µMAG Standard Problem #4 results

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Solution directory

• Comparisons
• G. Albuquerque, J. Miltat and A. Thiaville
• R. D. McMichael, M. J. Donahue, D. G. Porter, and J. Eicke
• Liliana Buda, Lucian Prejbeanu, Ursula Ebels and Kamel Ounadjela
• E. Martinez, L. Torres and L. Lopez-Diaz
• José L. Martins and Tania Rocha
• P.E. Roy and P. Svedlindh
• Massimiliano d’Aquino, Claudio Serpico, and Giovanni Miano
• Dmitri Berkov
• M. J. Donahue and D. G. Porter
• Rasmus Bjørk, E. B. Poulsen and A. R. Insinga

Submitted Solution: Gonçalo Albuquerque, Jaques Miltat and André Thiaville

Date:

July 18, 2000

From:

Gonçalo Albuquerque, Jaques Miltat and André Thiaville,
Laboratoire de Physique des Solides,
Bâtiment 510, Université de Paris-Sud, 91405 Orsay Cedex

Contact:

G. Albuquerque

These calculations used done using a finite difference scheme, with one cell across the thickness of the sample. Magnetostatic interactions were calculated using FFT techniques assuming constant volume charges within each cell and fields calculated at the center of each cell. Exchange interactions were calculated for the four neighbors of each cell, along each relevant axis. Boundary conditions were accurately enforced [M. Labrune and J. Miltat, J. Magn. Magn. Mater. 151, 231 (1995)]. Two meshings were used, approx. 2 nm cells and approx. 4 nm cells.

The time integration was done using a semi-implicit Crank-Nicholson scheme with accuracy feedback from monitoring of the damping coefficient, maximum torque and total energy.

For an approx. 4 nm mesh size, the results are insensitive to the time step in the range of 10-50 fs (femtoseconds). A time step of 25 fs was used to calculate the results shown below.

Results:

• For the first part of the problem, with the field applied 170° from the x-axis (Field 1):

  
  A plot of the spatially averaged magnetization calculated using 2 nm cells.

  
  Comparison of M vs. t data calculated with 2 nm cells and 4 nm cells. These results demonstrate that the results cannot be entirely independent of mesh size.
  

  
  and an image of the magnetization when M_x first crosses zero.

• For the second part of the problem, with the field applied 190° from the x-axis (Field 2):

  
  A plot of the spatially averaged magnetization calculated with a 2 nm mesh.

  
  Comparison of M vs. t data calculated with 2 nm cells and 4 nm cells.
  

  
  and an image of the magnetization when M_x first crosses zero.

Raw data:

• Field 1: Time series for 2 nm mesh, Time series for 4 nm mesh, and Vector data at M_x=0.
• Field 2: Time series for 2 nm mesh, Time series for 4 nm mesh, and Vector data at M_x=0.

References: