Permanent Magnet Explorations

To best summarize what we're looking for its worth outlining how the current state, (NdFeB) magnets, dominates and why an alternative is needed.

NdFeB magnets are the strongest type of permanent magnets commercially available, being 10-20 times stronger than traditional ferrite or ceramic magnets. This strength allows for powerful magnetic fields in compact sizes, enabling the miniaturization of many devices and technologies.

1. Compact Size and Lightweight
   NdFeB magnets are relatively small and lightweight. This characteristic is crucial for applications where space and weight considerations are paramount, such as in portable electronic devices and advanced industrial equipment.

2. Versatility in Applications
   NdFeB magnets find widespread use across numerous sectors:

• Electronics: Used in hard disk drives, speakers, and mobile phones

• Industrial: Employed in motors, generators, and magnetic separation equipment

• Medical: Critical components in MRI machines and certain medical implants

• Clean Energy: Essential for electric vehicle motors and wind turbine generators

• Consumer Goods: Found in various everyday items like toys and tools

4. Energy Efficiency
   The strong magnetic properties of NdFeB magnets contribute to increased energy efficiency in many applications, particularly in electric motors and generators. This aligns with global efforts towards sustainable and resource-efficient technologies.

5. Technological Advancements
   NdFeB magnets have enabled significant technological progress in fields such as microwave communication, where they are used in circulators, isolators, and other components.

6. Economic Importance
   The unique properties of NdFeB magnets have made them critical materials in many high-tech and green technologies. Their importance in electric vehicles and wind turbines, for instance, has elevated their status as strategically important materials in the global economy.

And here's why rare earths (Neodymium in this case) are problematic.

Environmental Concerns:

1. Mining operations cause extensive environmental damage, including:

   • Pollution of land, water, and air

   • Destruction of vegetation and ecosystems

   • Contamination of surface water and groundwater with heavy metals and radioactive materials

   • Soil erosion and acidification

2. Processing rare earths produces toxic waste:

   • Wastewater ponds containing acids, heavy metals, and radioactive material

   • One ton of rare earth elements generates approximately 2,000 tons of toxic waste

Health Risks:

• Exposure to pollutants from rare earth mining and processing can lead to:

  • Skeletal fluorosis and chronic arsenic toxicity

  • Potential long-term health effects including central nervous system issues, cancers, and cardiovascular and respiratory problems

Supply Chain Vulnerabilities

1. Geopolitical concentration:

   • China dominates the global supply, accounting for 63% of mining, 85% of processing, and 92% of rare earth magnet production

   • This concentration creates supply chain risks and potential national security concerns

2. Complex and opaque supply chains:

   • Difficulty in tracing material origins and ensuring sustainable sourcing

   • Challenges in achieving transparency and sustainability goals within the industry

Economic and Strategic Challenges

1. Limited production outside China:

   • Few alternative sources, with the U.S. producing about 14% and Australia 6% of rare earth elements

   • Efforts to diversify supply are ongoing but face significant hurdles

2. Critical for emerging technologies:

   • Essential for clean energy technologies, electric vehicles, and advanced military equipment

   • Increasing demand signals as the world transitions to electrification

Technological Hurdles

• Separation and refining of rare earth elements is a complex and expensive process due to their similar chemical properties

A permanent magnet that possesses rare-earth level magnetic properties has innumerable applications and making the case for a switch over to this alternative is beyond simple given the above concerns.

The problem is it seems like rare earths are the key...

I spent the week wrestling with MatterGen, property sampling where magnetic density = 1.5 (derived from a desired 1.4 Tesla for Neodymium systems):

Magnetization (MM) is related to Bohr magnetons per volume by:

M(T)=9.274×10−24A⋅m2μB×ρm(μB/A˚3)

where ρm is the magnetization density in μB/A˚3

For a strong Neodymium magnet (~1.4 T):

ρm=1.49.274×10−24≈1.51μB/A˚3

Experiments with direct property sampling fell short. Adding in an extra condition for desired chemical systems; Fe, Mn, Al, etc... only further limited the magnetic properties of the candidates.

Generated candidates were evaluated using CHGNET:

from chgnet.model.model import CHGNet
from pymatgen.core import Structure

chgnet = CHGNet.load()
structure = Structure.from_file('examples/mp-18767-LiMnO2.cif')
prediction = chgnet.predict_structure(structure)

for key, unit in [
    ("energy", "eV/atom"),
    ("forces", "eV/A"),
    ("stress", "GPa"),
    ("magmom", "mu_B"),
]:
    print(f"CHGNet-predicted {key} ({unit}):\n{prediction[key[0]]}\n")

Magnetic moment arrays were produced for each candidate. Example:

CHGNet-predicted magmom (mu_B):
[0.6684334 0.6848458 2.6759646 3.0232825 2.6717536 2.2206595 1.6731002
 2.67375   1.6724313 1.9725461 2.2248173 1.6720649 1.9724829 1.9793818
 2.6719716 1.6795249 1.6731651 2.6756277 1.6762803 2.6684768]

Already the individual moments are a decent ways off the expected 3.27 minimum that Nd contributes

Neodymium (Nd³⁺ ion in a solid) typically has an atomic magnetic moment of ~3.27 μB. In bulk Nd₂Fe₁₄B (NdFeB) magnets:

• Nd contributes ~3.27 μB per atom.

• Fe contributes ~2.2–2.3 μB per atom.

• Total bulk magnetization: ~1.5 μB/A˚3.

But we can estimate the magnetic density for the system somewhat intuitively from these measurements. Using our unit cell volume from the produced .cif file, and the sum of the magnetic moments, magnetic density is simply total magnetic moment divided by unit cell volume.

And for every sample generated, this value fell between 0.1 and 0.2, a nice 75-80% off our target strength. A deeper dive into the MatterGen paper quickly shows why this is happening. MatterGen's contributors were well aware of the problems surrounding rare earths, and as such, many were intentionally held out from the training dataset in hopes that the model would avoid using them in predictions. This means the peak DFT calculated magnetic density that exists in the dataset is the same 0.2 we saw from the predictions.

So now we're back to the problem of being able to predict out of sample. It was wishful thinking to assume that a relatively straightforward diffusion model with a small-ish dataset would be able to pull this off in one shot but if it was that easy, we'd have this magnet out in the world already.

For next steps the goal is to try and influence MatterGen's denoising with a new reward function that incentivizes creating structures with higher magnetic density. Here's how I'm thinking about it:

During each denoising step xt, we:

• Convert the structure representation into a format CHGNet can process (e.g., atomic positions, species, and lattice parameters).

• Compute magnetic density using CHGNet.

• Define a reward function based on the computed magnetic density.

Reward Function:

R(xt)=λ⋅Magnetic Density(xt) / Target Magnetic DensityR(xt​)

where:

• xt is the current noisy structure.

• λ is a scaling factor to balance the gradient updates.

MatterGen’s denoising process is typically unconditioned or conditioned on basic properties. We modify it to:

1. Evaluate Magnetic Density at Each Step:

   • After each denoising step xt→xt−1xt​, run CHGNet to estimate magnetic density.

2. Adjust the Noise Update Rule:

   • Modify the standard score function update using the reward:s^θ(xt)=sθ(xt)+α∇R(xt) where:

     • sθ(xt) is the learned score (denoising direction).

     • α controls the influence of the reward on the update.

The standard denoising loss follows:

Ldiff=Ext,t[∥ϵ−ϵθ(xt,t)∥2]

We need to modify it to include reward weighting:

Lrewarded=Ext,t[R(xt)⋅∥ϵ−ϵθ(xt,t)∥2]

where:

• Higher magnetic density samples get higher weight.

• Hopefully encouraging the model to focus more on "good" structures.

More coming soon.