Elastic Parameter Settings

[yun shu]

Hello everyone，

When I was modeling strain gradients, I came across some parameters that mumax seemed unable to set directly， such as the magnetostriction constant and the Young's modulus. Do I need to convert them to other  parameters and set them up, or is there a way I don't know to set directly?

Thanks very much！

[Josh Lauzier]

Hi,

There are parameters B1 and B2 are material parameters that are equivalent to λ. Theorists tend to prefer B1/B2, whereas experimentalists will often report λ instead. The B's directly capture the strength of the coupling (in J/m^3) between magnetic and elastic systems, whereas  λ is closer to what you actually end up measuring. For cubic crystals, the relationship is  λ_100=-2/3*((B_1)/(c_11-c_12)) and  λ_111=-1/3*((B_2)/(c_44)). where λ_100 or λ_111 is the magnetostriction along the 100 axis and 111 axis, and c11,c12,and c44 are the elastic material parameters from the strain tensor. A good derivation is Kittel's famous paper ' Physical Theory of Ferromagnetic Domains' (1949). 

For isotropic films, B_1=B_2. (For polycrystalline films, one needs to take care. Often it is assumed λ_100=λ_111=λ , but this isn't quite right. It is generally a weighted average, since it's not truly isotropic. The book by Etienne du Trémolet de Lacheisserie has a good discussion of this).

It is similar for Young's modulus- it (along with other things like Poisson ratio) are equivalent to the C_i's in the strain tensor, although I don't recall the relationship offhand. But the magnetoelastic extension uses the strain tensor values (C11, C12, C44), as well as the density rho. You should be able to find those directly in the literature for whatever material you're studying.

Which ones you need depends whether you're using the magnetoelatic fork/module (which requires being compiled separately), or just the effective magnetoelastic field term that comes with base mumax. For the fork, you'll need B1/B2 (for the magnetoelastic coupling), as well as C11,C12,C44 and rho (elastic parameters) for material parameters. For the effective field term, it just needs B1/B2 for material parameters. Both assume cubic or higher symmetry

Best,

Josh L.

[yun shu]

Hi，

Thank you very much for your reply. I have found the magnetic parameters of the relevant materials. But now there is a problem that I have not been able to solve. When I used mumax3 (including the magnetoelastic module) to simulate, I found that the elastic strain exx or eyy ... (no matter how large or small) I set did not have any effect on the system. Is it because I ignored something? My script is attached here:

// skyrmion racetrack

N1 := 400
N2 := 75
setGridSize(N1, N2, 1)

c := 2e-9
setCellSize(c, c, 0.4e-9)

Msat=580e3
Aex=15e-12
Dind=3.0e-3
Ku1=0.8e6
AnisU=vector(0,0,1)
alpha=0.04

m=neelskyrmion(1,-1).transl(-100e-9,0,0)
minimize()

//Elastics
C11 = 307e9
C12 = 165e9
C44 = 75.5e9
rho = 8.836e3
eta = 0
B1 = -2.24e6
B2 = -2.24e6

for i:=0; i<80; i++{
          dx := 10e-9
          de := 0.01e-3
          e0 := -0.4e-3
    defregion(i, xrange(i*dx, (i+1)*dx))
          exx.setregion(i, e0+i*de)
}        
save(regions)

eyy = 0
ezz = 0

Pol=0.5
xi=0.04
j=vector(-5e10,0,0)

SetSolver(9)
dtt := 1e-13
fixdt= dtt

autosave(m,5e-10)
tableAutosave(1e-11)
tableAdd(ext_bubblepos )

run(40e-9)

[yun shu]

Supplement:

The strain gradient set for ezz also had no effect. What I want to simulate is that the strain gradient perpendicular to the film surface can lead to the transverse displacement of the skyrmion, but the  perpendicular strain gradient I set does not make the effect of the skyrmion.

for i:=0; i<80; i++{
          dx := 10e-9
          de := 0.01e-3
          e0 := -0.4e-3
    defregion(i, xrange(i*dx, (i+1)*dx))

          ezz.setregion(i, e0+i*de)
}        
save(regions)

eyy = 0
exx = 0

[YL M]

Hi，

Have you solved the problem of strain setting?

Recently， I have been using the extension module to reproduce other work and have found some problems.