Standard Problem 1

[Huan Kiat Koh]

Hi, for standard problem 1 shown in Tutorial 3, why is it acceptable to set the cell size as 20nm in the z-axis when (1) it is much larger than the exchange length, (2) it is also a few times larger than the cell size in the x and y axes? Thank you very much. 

[Josh Lauzier]

Hi,

In this particular problem, everything important happens to be in the x-y plane due to the shape and magnetocrystalline anisotropies dominating. The reason to choose a smaller cell-size is so that you can accurately resolve magnetic features like a domain wall. In directions where there isn't any important variation (common in thin films), you can get away with a larger cellsize because there isn't anything important going on in that direction. You can empirically verify this. If you rerun the simulation but with a smaller z cellsize (and more cells in z to compensate, keeping the film the same), you should get functionally identical results for the hysteresis loop. Technically you may miss out in some minor details in the z-direction that won't affect the hysteresis loop itself. Using larger cells like this can be convenient because it will speed up the simulation and reduce memory requirements. Just be very careful when applying it.

For a deeper discussion, you can check this tutorial paper, in particular the section about multilayer structures. It goes into this in a bit more detail.

Best regards,
Josh L.