Simulate the tensor form of conductivity with respect to magnetic moments

[wenchang sun]

Hello everyone,I'm a bit confused about  how to simulate the tensor form of conductivity with respect to magnetic moments in mumax3?

[Josh Lauzier]

Hi,

Mumax3 right now only simulates the magnetics. To investigate the conductivity, you'd need to save the magnetization data into an OVF, and put it into another piece of software like Comsol.

Mumaxplus, an extension of mumax3, might be able to do this. You can find it here. It does have features to set things like the conductivity (including a conductivity tensor). You might find this example helpful: https://github.com/mumax/plus/blob/5763c2793f18275ca9ab917b9ab6207f77097ef6/test/test_conductivitytensor.py#L23 . I don't know how developed the feature is (it is not in the paper, but it is in the public branch), so perhaps a member of the mumaxplus team can comment.

Best,
Josh L.

[Ian Lateur]

Hi,

In mumax+ you can set the conductivity as a simple parameter. The conductivity_tensor is a quantity which can be calculated by mumax+ and as far as I can tell it uses exactly the formula of the included figure.

The feature that is indeed less developed, and thus not really mentioned, is the "electrical_potential" calculated with the conductivity(_tensor). It seems to work for simple geometries like rectangles, but it's worse for more complex geometries. It also lacks proper (physical) testing.

Although if you only want to obtain the conductivity tensor from the magnetization, it seems easiest to use mumax3 for the magnetic simulations, save the magnetization, convert it to numpy arrays, and calculate formula (4) of the figure using Python (or any other post-processing method you prefer).

Best regards,

Ian

Op di 19 aug 2025 om 09:30 schreef Josh Lauzier <joshl...@gmail.com>:

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[wenchang sun]

Thank you for your explanation!I've solved the questions above in Comsol.I am currently attempting to reproduce the anisotropic magnetoresistance (AMR) in systems containing Néel or Bloch skyrmions, as illustrated in the figure (where yellow dots represent the electrodes). 

I have questions regarding two issues.

1.I try to replicate figure 3,I cannot figure out why, even though I use the same simulation data as in the literature, the time it takes for the skyrmion to move from the edge to the target position is around 5 ns in my simulation, while it only takes 2.93 ns in the literature.

2.While I am aware that the resistivity and conductivity can be expressed in forms such as:（in the attachment）
I have encountered difficulties in translating these formulations into resistance calculations,Despite repeated attempts, I am unsure how to accurately implement these anisotropic transport relations in simulation software like COMSOL.Could you kindly provide guidance on this,best regards.