Thermal Field And Demag Field

[Adrien Pivano]

Hi,

I try to compute the stochastic motion of a domain wall in nanostrip and I've tried to put the temperature in my simulation. I've compared the magnitude of the Thermal Field and the Demag Field for a cellsize of 15nm3 with dt=10e-15s and dt=10e-14s using the RK4 solver.

And I would like to know if it's normal to have the thermal field 100 times larger than the demag field in both cases (dt=10e-13 and dt=10e-15) ?

Thank you.

Best Regard,

Adrien

[Felipe Garcia]

Dear Adrien, The thermal field represents the fluctuactions, which will give the ensamble averages, that is Boltzmann distribution for a single cell. It depends in temperature, damping and timestep. Therefore, from your email is not very easy to conclude which are the values for that. But it is easy to verify that mumax follow the Boltzmann distribution.

To check that one can run a cell with only uniaxial anisotropy (no exchange no dipolar field). A script like this would do that:


SetMesh(2, 2, 2, 4e-09, 4e-09, 4e-09, 0, 0, 0)

Msat = 1e6
Aex = 0
alpha = 0.01

anisU = vector(0, 0, 1)
Ku1=1e5

m = RandomMag()
FixDt = 1e-14

SetSolver(4)

EnableDemag=False

DefRegionCell(1,1,1,1)

Temp=400
tableAdd(m.Region(1))
tableAdd(B_therm)
tableautosave(1e-12)
Run(100e-09)

With this data the average value of mz for 400 K should be according to Boltzmann distribution (the ratio of Ku*V/kbT is 1.159 in that case)  0.601643. For a single run I get a value of  0.60519, which is in good agreement.  For 100 K, the theoretical value should be 0.844196 and the calculated value is 0.84482. Therefore, the fields are correctly calculated and have to be interpreted in that sense.

Regarding your cell, it is small (I guess 5x3x1nm3) and therefore it will have large fluctuations. A particle like that would be superparamagnetic if it would be an isolated nanoparticle. In the micromagnetic case exchange coupling with neighboring cells will allow to have a net magnetization in the sample but for example temperature is at the end enable to overcome the exchange beyond Curie temperature. I don't think there is anything wrong in your calculations unless you used an unrealistic value for the damping or the timestep (timesteps seem correct). The events of depinning will depended also on the depth of your pinning potential.

Best regards,

Felipe

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[Adrien Pivano]

Dear Felipe,

Thank you for your complete answer ! I will try your script. Nevertheless, the damping parameter used in my simulation was 0.02 for Ni at room temperature and my cellsize was 2x3x2.5nm. It's maybe this cellsize which is to small and increase the thermal field.

Best Regards,

Adrien

[Felipe Garcia]

Dear Adrien, evidently the cell size has also to be consistent with your micromagnetic parameters, that is the exchange length. Regarding my script I checked the value of m.region1z (single moment). The total mz with have a different average.

Best regards,

Felipe

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[Adrien Pivano]

Dear Felipe,

Did you change the cellsize in your script with a lower value ?

Unfortunatly, I can't change my cellsize because I need to compare the dynamic at zero temperature and at room temperature with exactly the same condition. My pinning potential could change if I change my cellsize.

Best Regards,

Adrien

[Felipe Garcia]

Dear Adrien, I did not change the cell size. it works independently. I just wanted to show you that mumax has correctly included temperature (at least in the traditional form). I said that your cell is small because if you include few of such a cells thermal fluctuations will be bigger that the pinning potential and the domain wall will be not very stable. And as an independent element a cell like that would be superparamagnetic. If one has plenty of such a cell the thermal field averages out and then the domain will be stable.

Best regards,

Felipe

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[Felipe Garcia]

Dear Pradeep,

Sorry for the delay. In each cell it is a different realization of the gaussian random number generator, eta in the Eq 24. So it has the same averages for Btherm but in each instant of time each cell has a different thermal field. This is true as long as they have the same properties that define the strength of the thermal fluctuations (see Eq 24. in the mumax3 paper). Those quantities can be damping and saturation magnetization. For example, if some cells have different damping the standard deviation of the field will be different for those cells. I don't know if it is clearer now.

Best regards,

Felipe

On Tue, Apr 12, 2022 at 5:32 PM PRADEEP KUMAR ROUT <pradee...@gmail.com> wrote:

Dear Felipe,

Could you please help me understand how the temperature affects the magnetization in each cell? If we set the temperature to 300 K, then is mumax adding different random thermal fields to each cell or the thermal fluctuations in every cell is the same ?

Thanks a lot.

Best wishes

Pradeep

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[PRADEEP KUMAR ROUT]

Dear Felipe,

Many thanks for the detailed explanation. It is clear to me now.

Best wishes

Pradeep