Domain wall motion in infinite system

[xgzsChris]

Hi, I am a new one learning Mumax3. I want to simulate the domain wall motion and the simulation window is set as 1 um*1 um. The DW was initialed in the center. But I found the Walker breakdown in simulation occurs beyond the deduced Walker field from 1D model. I suspect that the demag field has a nonnegligible effect on DW motion so I want to simulate the DW motion in an infinite system(e.g. 1 cm*1 cm) to weaken the demeg field. How can I do it?

[Josh Lauzier]

Hi,

I believe in those cases, people usually either remove the surface charges, or apply an opposite external field (which is equivalent to removing the surface charges). For an example of the former, see the 'Py Racetrack' example on the mumax examples page, which removes the charges at the ends to simulate an infinite wire. The latter approach was used by ' Current-driven domain wall mobility in polycrystalline Permalloy nanowires: A numerical study' by Leilieart et al. I believe their results had agreement with the 1D model. They also move the simulation window, keeping the domain wall at the center. 

If you still need a large system, you can look into the SetPBC() function. This allows you to set a certain number of repetitions in each direction. The number determines the cut off for the demag field.

Best,

Josh L.

[Felipe Garcia]

Hi,

Are you working in perpendicular anisotropy systems? If you do, how do you calculate the 1D Walker field? Normally, it will come from the dipolar field, unless you have created a second anisotropy, which is in-plane. If for example you remove the dipolar field and there is no transversal anisotropy then, you remove the Walker field. Also there is no preference for Bloch walls if you remove the dipolar field. Therefore, first I would check what the energy terms in my system are.

With PBC, one will have to use only PBC in one direction, the direction parallel to the wall. For obvious reasons: PBC automatically creates another wall if one uses PBC perpendicularly to the wall. On the other hand, 1cm by 1cm is out of reach. Another option is removing the charges as Josh discussed.

Felipe

On Sat, Sep 9, 2023 at 9:11 AM xgzsChris <xgzs...@gmail.com> wrote:

Hi, I am a new one learning Mumax3. I want to simulate the domain wall motion and the simulation window is set as 1 um*1 um. The DW was initialed in the center. But I found the Walker breakdown in simulation occurs beyond the deduced Walker field from 1D model. I suspect that the demag field has a nonnegligible effect on DW motion so I want to simulate the DW motion in an infinite system(e.g. 1 cm*1 cm) to weaken the demeg field. How can I do it?

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[xgzsChris]

Below are my codes. Yes, I am working in PMA system. I do not want to remove the demeg field, but want to mimic a real system because the simulation window is limited. I have set the ext_rmsurfacecharge(), but the Walker Breakdown occurs under 0.3 mT. In addition, I want to learn about the first parameter of ext_rmsurfacecharge(), the zero represents mx, and the two represents mz? Last but not least, when I keep the DW in the center of window by ext_centerwall(), the DW position recorded by ex_dwpos() is quite different from the case without keeping DW in the center. Does it mean the demeg field has a non-negligible effect on DW motion?
Thanks a lot!

Nx:=256
Ny:=256
Nz:=1
sizeX:=1e-6
sizeY:=1000e-9
sizeZ:=1e-9
SetGridSize(Nx,Ny,Nz)
SetCellSize(sizeX/Nx,sizeY/Ny,sizeZ/Nz)
cellsizeY:=sizeY/Ny

Msat = 6.23e5
anisU = vector(0, 0, 1)
Ku1 = 4.62e5
Aex = 2e-11
alpha = 0.015
//Dind = 0.03e-3

//remove edge charges
BoundaryRegion := 0
MagLeft        := 1
MagRight       := -1
ext_rmSurfaceCharge(BoundaryRegion, MagLeft, MagRight)

m = twodomain(0, 0, 1, -1, 0, 0, 0, 0, -1)
relax()
snapshot(m)
//ext_centerwall(2)

autosave(m,0.1e-9)
tableadd(ext_dwxpos)
tableadd(ext_dwspeed)
tableautosave(0.1e-9)

B_ext=vector(0,0,0.3e-3)
run(100e-9)

[Felipe Garcia]

If you are using PMA, then the instruction to remove the charges will not work. It works for in-plane systems. You can find the meaning in the API https://mumax.github.io/api.html (look for in Extensions) and also in the example https://mumax.github.io/examples.html#example11

If one sees differences from the center to one side is due to the dipolar field. Basically, it is coming from the fact that there is a difference in magnetization in both domains (one is larger than the other). To remove that one has to include the fields created from infinite domains in the right and in the left. The problem is that your field is quite small, so a small error in the calculation of such a field will be relevant.

If you are interested in the dipolar field created due to the volume charges, and that is what you consider in your model as the origin of Walker field, I would center the wall and use PBC(0,NY,0) with NY some tens or so.

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[xgzsChris]

I follow your advice, and I set PBC(0,Ny,0) with different Ny. But the DW position begins to oscillate and nearly cannot be observed move forward under 0.3 mT or 3 mT field. And the DW precesses under a quite low magnetic field below the Walker field.

[Felipe Garcia]

Hi,

What you show is a strange compensation of the torque. I don't know the reason. This does not happen if you activate centerwall. It will continue to move. Anyway, one still has the demag field coming from the volume charges that appear during motion. This will yield the Walker field. With your numbers that field is small below 0.3 mT.  I suppose you are trying to add DMI to increase that field but, what is the analytical derivation you have used for the equation of Walker field without DMI?

Regards,

Felipe

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