On 07/21/2014 08:22 PM, Joseph Batley wrote:

Thanks for the response, here goes

Charge:

$\int_{\Omega} (\sigma_{\uparrow} \nabla \mu_{\uparrow} \nabla \nu + \sigma_{\downarrow} \nabla \mu_{\downarrow} \nabla \delta ) - \int_{\Gamma} (\sigma_{\uparrow} \nu (\nabla \mu_{\uparrow} \cdot n) + \sigma_{\downarrow} \delta (\nabla \mu_{\downarrow} \cdot n) = 0$

This is just conservation of charge. I think I have implimented the weak form correctly by choosing a different test function for each variable $\mu_{\uparrow/\downarrow}$?

By using two different test functions you solve in fact:

$\Delta(\sigma_{up} \mu_{up}) = 0$ $\Delta(\sigma_{down} \mu_{down}) = 0$

• two independent equations - probably not what you want. It is not the same as your original system.

Spin:

$\int_{\Omega} (\nabla \mu_{\uparrow} \nabla \nu + \nabla \mu_{\downarrow} \nabla \delta ) - \int_{\Gamma}(\nu (\nabla \mu_{\uparrow} \cdot n) + \delta (\nabla \mu_{\downarrow} \cdot n) = \frac{1}{\lambda} \int_{\Omega} (\mu_{\uparrow} \nu + \mu_{\downarrow} \delta )$

Same here. You have two equations in strong form, so use one test function of the first one and another for the second one.

I do not really know how to implement the surface terms here. I can define a current for each spin as: $j_{\uparrow} = \sigma_{\uparrow}(\nabla \mu_{\uparrow} \cdot n)$, $j_{\downarrow} = \sigma_{\downarrow}(\nabla \mu_{\downarrow} \cdot n)$

but the BCs are combinations of these. charge current $j_c = j_{\uparrow} + j_{\downarrow}$ spin current $j_s = j_{\uparrow} - j_{\downarrow}$

I want to make sure these are continuous at the interface between the magnet and non-magnetic metals and I want to be able to set the charge current at one side to be $j_c = 1e^{-8}$

Do the two domains have the same equations? They differ in material parameters only, right?

I have attached the problem file I have come up with. I took the surface terms out of the two PDEs and have created two new equations for the BCs. Unfortunately this hasn't worked.

I hope I have given you the information you wanted.

Pretty much, yes. Could you try reformulating the equations/problem file as recommended above (if you agree with my interpretation of what you wrote :))? I will then try running the file.

Cheers, r.

On 07/22/2014 08:08 PM, Joseph Batley wrote:

Ah, thanks you Robert, It appears I did not quite understand the conversion from strong to weak. I have made the changes and attached the problem file.

I have found a thesis "THEORY BASED DESIGN AND OPTIMIZATION OF MATERIALS FOR SPINTRONICS APPLICATIONS", where the same equations are solved by FEM, and it seems to me that what is in the attached file (*) is ok. Have a look at it as well, please.

(*) updates:

• fixed dw_surface_flux material parameter shape (needs a tensor - compile sfepy with -DDEBUG_FMF in site_cfg.py to catch that)
• fixed the Jc boundary condition (not sure about sign...)
• fixed/simplified interface_FM, interface_NM region definitions - now their faces have opposite normals (is that ok?)
• added more things to output for debugging

It looks promising, the post process shows \mu_{c} = \mu_{\uparrow} + \mu_{\downarrow} looks correct so the normal charge current side works, the \mu_{s} = \mu_{\uparrow} - \mu_{\downarrow} which is the spin accumulation however should simply show a peak around the interface which decays with different lengths in each domain.

After the above changes I still do not see a peak. Instead, mu_up and mu_down are the same, so \mu_{s} is zero.

You have more debugging ahead :)

r. PS: you may need to tweak the mesh filename. PPS: one.val material is not needed, you can use simply dw_laplace.i.Omega(d, mu_up)...

And yes you're correct, the equations oars the same in both domains, it is only the material parameters that change.