Biquadratic interlayer exchange

Feedback & Feature requests
1

Dear Lukas & Attila,

Thank you very much for your work on TetraX and its recent update with torque relaxation, which allows to simulate SAFM systems in external fields.

However, we would like to ask if it would be possible to implement both, bilinear and biquadratic interlayer coupling as described in https://doi.org/10.1103/PhysRevLett.67.3172.

If it is already possible to implement such coupling, I would be grateful for advice on how to achieve this.

Thank you very much for considering this feature,

Best,
Ondrej

2

Dear Ondrej,

Thanks for your nice feedback! We really appreciate it.

Regarding the biquadratic term in the interlayer exchange coupling: in a timescale of weeks, how urgent such an implementation would be useful for your studies?

Cheers,
Attila

3

Dear Attila,

Thanks for the quick reply!

We are not in a hurry. We would be happy to have this implemented in about 10 weeks.

Cheers,
Ondrej

4

Dear Ondrej,

Would it be enough if we implement it for films(layers) only for now?
Actually Lukas is working on it and soon we test it.

Cheer,
Attila

5

A little addon: layers here also mean multilayers.

6

Dear Lukas & Attila,

yes this would be sufficient.

Thank you very much for helping with this!

Cheers,
Ondrej

7

Hi Ondrej,

I have partial success with the comparison of the results to some results I have found in my existing literature about dispersions in IEC bilayers. Could you maybe suggest me reliable literature where there is dispersion calculation for bilayers with both the bilinear and biquadratic terms? I’m sure your knowledge is better about this research field. This would be a great help to me/us.

Cheers,
Attila

8

Hi Atilla,

I would suggest our publication https://pubs.aip.org/aip/apl/article/125/13/132401/3313695/Unidirectional-propagation-of-zero-momentum.

There is analytic model assuming one macrospin per layer (works well for thin layers) and MuMax simulation (to also validate the model).

The analytical model is available here (if you want to implement tests) GitHub - CEITECmagnonics/SpinWaveToolkit: Set of tools useful in spin wave research.

9

Also if you want any assistance with the analytical model, just tell me (i.e. prepare script for calculation of the dispersion relation for given parameters)

Cheers,
Ondrej

10

Hi Ondrej,

Thanks to Lukas the J2 is implemented into TetraX, but you need to install it from the 98-implement-interlayer-exchange-for-waveguide_axial-geometry branch. I made some quick comparisons with your SpinWaveToolkit. Attached please find the obtained dispersion for the antiparallel state using for the J1, J2 and other material parameter values from your example python script. When I apply a field perpendicular to the magnetization and is strong enough to saturate the two layers, for the lowest branch I get a slight shift, that increases with the field strength. I tried to see where this difference comes from, could not yet find the origin. Although I really compared the values of the dynamic matrix from theory with that of TetraX and I got perfect agreement.

I think would be very welcome, if you start testing it, for cases you know the results. You could compare it with simulations from some 3D softwares as mumax or oommf.

For the next couple of weeks I will not have much time for further developments, but of course if you tell us that there is a problem and you might even know where this should originate, I would be happy to check it and correct it.

Cheers,
Attila

Screenshot 2025-03-12 at 16.53.23
Screenshot 2025-03-12 at 16.53.231136×972 108 KB

11

Hi Attila,

thank you very much for such quick implementation! We will look into it and let you know.

With many thanks,
Ondrej