Inquiry Regarding Abnormal Breathing Mode Excitation of Skyrmion During Relaxation

[Wanlu Yu]

Dear All,

Thank you very much for your previous response regarding the initial size of the skyrmion. Your guidance was truly helpful.

I am now encountering a new issue in my simulations and would like to seek your advice once again.

My model setup is as follows:

1. Within a rectangular region, two magnonic waveguides are designed by modulating the saturation magnetization Ms​.

2. The waveguides are symmetrically placed on both sides of a skyrmion.

3. Two alternating magnetic fields (h1​ and h2​) are applied to the left end of the upper waveguide and the skyrmion region, respectively.

My problem is: During the relaxation process, the Néel-type skyrmion is expected to exhibit a breathing mode (periodic expansion and contraction of its radius). However, in my simulation, the skyrmion repeatedly appears and annihilates at a fixed frequency instead of forming a stable breathing oscillation.

For your reference, I have attached my initialization script. I would greatly appreciate it if you could help me identify the potential causes of this issue.

Thank you very much for your time and support.

Best regards,
Yulu

[Josh Lauzier]

Hi,

Your images don't seem to have gone through, you may need to repost those.

Based on your script, the first few things I would check:

1)  Is the amplitude of these applied fields meant to be so large? These are in Tesla, so you are applying 20T and 5T, which is quite large.

2) You may need to reduce your cellsize. Based on your previous post, you're aiming for a skyrmion around 17.5nm. At 5nm cellsize, that's only ~3-4 cells. That may make it difficult to properly resolve a skyrmion of that size.

3) Your initial magnetization is also likely not what you are expecting. When you do "m = NeelSkyrmion(1, -1).scale(0.63, 0.63, 1)", this completely overwrites "m.setInShape(a, uniform(0, 0, 1))" set previously. Also, the relax procedure erases any skyrmion you might have. I would check the image that you saved as "after" (after relaxation, but before the excitation is applied), and see if that is what you are expecting as your starting m configuration.

4) Your way you set alpha is likely not doing what you expect. You seem to be trying to set up some sort of gradient, but only 2 values are used: 0.005 and 0.1. If you plot alpha, there is basically only two regions: the two waveguides and everything else. There is no gradient or high alpha region local to the skyrmion. Probably this comes with how you are defining regions. One thing to keep in mind is that each cell can only belong to one region, so if there are overlapping regions, the newest will override the previous.

Best,
Josh L.

[Wanlu Yu]

Hello,

 I have made some adjustments based on your suggestions. As a beginner, I am still not very familiar with some of the more complex settings. This code is my attempt to reproduce a paper from the literature, which uses absorbing damping at the boundaries. I am not entirely sure how to set this up correctly.  

After modifying the code and running relaxation, the skyrmion disappears even before applying any excitation field. It also disappears after applying the field—I don’t understand why this is happening. Additionally, the magnetization directions in both waveguides, as well as between them, have changed. I am not sure whether this is normal or why it occurred.  

My goal is to couple the waveguides with the skyrmion to excite its breathing mode. How should I modify the code to achieve this? Thank you very much for your help!

Best

WanlU

[Josh Lauzier]

Hi,

There's a few things to tweak. One general piece of advice I would suggest when building complex regions like this, is to view them in the mumax GUI, each step of the way as you add a new region command. It is very helpful to see if each step is doing what you intend. You can plot things like regions,alpha or Ku1 directly in the GUI.

For the magnetization: Whether this is normal will depend on your set up. What this is telling you is that your initial configuration is not energetically stable. If I had to guess, this is likely due to Ku1 not being set correctly. Very early in the script, you set it for region 1, where region1 is the entire film. However, when you start assigning other regions on top of region1, they do not inherit the Ku1 value. You need to set it for each region. My guess is you thought Ku1 is still being applied throughout the entire film.

For the absorbing damping at the boundaries, the way you were trying to approach it originally was correct. The Xrange bumpers here:

  DefRegion(cc+10, XRange(-400e-9 + cc*2e-9, -400e-9 + (cc+1)*2e-9))
  alpha.SetRegion(cc+10, alpha_value)
  DefRegion(cc+50, XRange(400e-9 - (cc+1)*2e-9, 400e-9 - cc*2e-9))
  alpha.SetRegion(cc+50, alpha_value)

These look to be correct, to me, nothing needs to change. However, they are getting partially overwritten by the bumpers in the y direction. For the yrange bumpers, I am not sure why they start at +/-5e-9? This will start them very close to the center. Perhaps what you meant was -75e-9 and +75e-9 (your y thickness is 150 nm, and keeping in mind 0 will be in the center. So the top will start at -75e-9, and the bottom ends at +75e-9, in the y direction). However, with how thick those bumpers are currently, they will start to overlap your waveguides. So probably your simulation needs to be a big bigger to accomodate both the bumpers and waveguide, or your bumpers need to be thinner.

I've attached an updated code, where I've annotated the changes (there were a lot of small ones to fix the various regions, too long to list here)

Cheers,
Josh L.

[Wanlu Yu]

Dear  Josh Lauzier  ,

Hello,

I am writing to seek your assistance with an issue I have encountered in my micromagnetic simulations. After relaxing the system, the magnetic skyrmion expands and appears to connect with the waveguide region, similar to what is shown in the images I previously shared with you.

I would like to understand why this expansion occurs and how to stabilize the skyrmion to prevent it from growing excessively. Additionally, I have observed that the expansion of the skyrmion seems to be correlated with an increase in the saturation magnetization (Ms) of the waveguide region.

Could you please provide guidance on how to maintain a stable, compact skyrmion configuration while implementing the waveguide structure? Any suggestions regarding parameter adjustments or simulation strategies would be greatly appreciated.

Thank you for your time and support.

Best regards,
[Wanlu]