Building a magnetocrystalline anisotropy energy model, attempt 1

Like our work on Curie temperature, the effort here is to build a machine learning model that can take a crystal structure and predict its magnetocrystalline anisotropy energy.

Relevant for permanent magnet design and screening, MCA/MAE tells us how much energy is required to rotate the magnetization away from its preferred crystallographic direction(s). A high MAE means the magnetization is strongly "locked" to certain crystal axes, which is essential for permanent magnets to maintain their magnetization against demagnetizing fields and thermal fluctuations.

Where does it come from?

MAE originates from the spin-orbit coupling interaction, which links the electron spin (responsible for magnetism) to the orbital motion of electrons around atoms. This coupling causes the magnetic energy to depend on the orientation of magnetization relative to the crystal lattice. The strength of this effect depends on the crystal symmetry, the specific atoms involved (heavier elements typically have stronger spin-orbit coupling), and the electronic band structure near the Fermi level.

MAE is an intrinsic (comes from the crystal structure, unit cell) property, meaning it's determined by the atomic arrangement and electronic structure within a single unit cell, independent of extrinsic factors like grain boundaries, defects, or sample shape. This makes it a fundamental material parameter that can be calculated from first principles or predicted from crystal structure data.

Approach

I'm starting off with the same approach as a before. Read more about it here:

I short, we take the crystal structure, encode it with an MLIP like CHGNet or Orb, and use that feature vector as input a regression model like a boosted tree or neural network.

I'm glazing over the details because, as we'll see in a moment, we had very little success.

Dataset

Publishing the dataset here:

I'll share a more in-depth post of what we've got here but until then you can get a general picture from my posts on NovoMag and Novamag datasets.

Results

Modeling is like building a tool to find a needle in a haystack. However, in this case I think we're not even looking through the right haystack.

We need to go back to the drawing board and build a better input vector. There is practically zero signal in this feature vector from CHGNet.

I think it's exciting! It's a failure, but it tells us a lot and will push us to expand our computational understanding of materials. We already knew these MLIP latent spaces could be highly predictive for certain properties, and of course energies, forces, and stresses, which they were designed to predict.

For certain properties, like magnetic saturation and Curie temperature, we were starting to see these MLIPs struggling. The latent representation they learned did not need to account for magnetic properties so it's no surprise.

It's not surprising we had poor results. We know the mechanism for MAE well in theory. It's spin-orbit coupling. This complex interaction just was not captured but these MLIP models, and that's no surprise. It's just not relevant for predicting forces, stresses, and energies.

Going forward

Going to change up our GNN model and way of embedding the materials. It's clear the common MLIPs don't have the capacity to capture what we're looking for.

Instead, something like https://github.com/QuantumLab-ZY/HamGNN is of interest. While they haven't published any pretrained models yet, there should be a universal model soon https://arxiv.org/abs/2504.19586.