Schematic overview of the invertible sequenced representation. (a) The structure is first decomposed into composition, stability, structure and lattice. (b) The structure is then further decomposed into a set of Wyckoff positions, uniquely identified by a set of Wyckoff identifiers. Optional free parameters are also included to make the representation coordinate-aware. (c) All previous information is gathered into a tokenenized and invertible sequence. The color of the tokens represent the type or the Wyckoff position for ease of visualization.

This paper presents Matra-Genoa, an autoregressive transformer model built on invertible tokenized representations of symmetrized crystals, including free coordinates. This approach enables sampling from a hybrid action space. The model is trained across the periodic table and space groups and can be conditioned on specific properties. The authors demonstrate its ability to generate stable, novel, and unique crystal structures by conditioning on the distance to the convex hull. Resulting structures are 8 times more likely to be stable than baselines using PyXtal with charge compensation, while maintaining high computational efficiency.

Supercell 3x3x3 of Fe6Ni2B (Space group: I4/mmm, 864 symmetry operations)

Phase diagram of Fe6Ni2B; e_above_hull: 0.193286 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -0.61 THz

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -136.7751 eV; energy change = -4.1985 eV; symmetry: I4/mmm → I4/mmm

From Matra Genoa

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -127.9222 eV; energy change = -10.4647 eV; symmetry: P1 → P1

From Matra Genoa

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Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); no imaginary modes; min freq = -0.12 THz

Phase diagram of MnFe3N; e_above_hull: 0.154131 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); no imaginary modes; min freq = -0.19 THz

Phase diagram of MnFe3N; e_above_hull: 0.153807 eV/atom; predicted_stable: False

Phase diagram of MnFe3N; e_above_hull: 0.154347 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -0.31 THz

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Phase diagram of MnFe3N; e_above_hull: 1.008083 eV/atom; predicted_stable: False

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -6.74 THz

Phonon band structure (supercell [2, 2, 2], Δ=0.01 Å); imaginary modes detected; min freq = -5.13 THz

AI-discovered magnetic material: Mn2CrFe4Co4N (performance score: 0.740) | Space group: 1 (resolved from structure) | Key properties: Tc: 612K, Ms: 0.14T, Cost: $13/kg, E_hull: 0.235eV/atom, Dynamically stable | Discovered in 20 AI iterations | - The combination of Mn, Cr, Fe, Co, and N in this stoichiometry yields a high Curie temperature and magnetic density. - The material is dynamically stable, which supports its structural integrity. - The energy above hull suggests that the material is metastable or unstable thermodynamically. - Cost is low, indicating practical feasibility from an economic standpoint.

AI-discovered magnetic material: Fe11CoSiGeAsP (performance score: 0.597) | Space group: 8 (resolved from structure) | Key properties: Tc: 687K, Ms: 0.13T, Cost: $82/kg, E_hull: 0.161eV/atom, Dynamically stable | Discovered in 10 AI iterations | - Strong ferromagnetism with high Tc arises naturally from the Fe/Co sublattice; this is retained despite chemical complexity. - Dynamic stability indicates the structure is at least locally stable; the main risk is competition with lower-energy phases (slightly positive e_hull). - The metastability is small enough that slight stoichiometric shifts (e.g., favoring smaller/more covalent anions like P over As, or Si over Ge) or controlled disorder could stabilize the phase thermodynamically. - Magnetic density is adequate but not exceptionally high; maintaining or modestly enhancing it while reducing e_hull should be feasible by delicate tuning of Co content or anion ratios.

AI-discovered magnetic material: Fe4Mn3B4 (performance score: 0.679) | Space group: 1 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 543K, Ms: 0.07T, Cost: $1/kg, E_hull: 0.239eV/atom, Dynamically stable | Discovered in 2 AI iterations | The Fe4Mn3B4 compound shows good thermal magnetic stability with a Curie temperature above the target, but its magnetic density is insufficient. The elevated energy above hull points to a potential issue with phase stability or synthesis feasibility. This suggests that while the composition can sustain magnetism at high temperatures, the magnetic moment per volume is too low and the material may decompose or transform under standard conditions.

AI-discovered magnetic material: Fe4Mn3B4 (performance score: 0.564) | Space group: 111 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 450K, Ms: 0.10T, Cost: $1/kg, E_hull: 0.571eV/atom, Dynamically unstable | Discovered in 2 AI iterations | The Fe4Mn3B4 composition provides moderate magnetic properties but suffers from thermodynamic and dynamic instability. The instability likely limits the practical usability of this material. Slightly lower magnetic density and Curie temperature suggest that further tuning or substitution might improve magnetic performance. The cost is low, which is favorable for application if stability issues can be resolved.

AI-discovered magnetic material: Fe4Mn3B4 (performance score: 0.728) | Space group: 1 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 536K, Ms: 0.09T, Cost: $1/kg, E_hull: 0.230eV/atom, Dynamically stable | Discovered in 2 AI iterations | The Fe4Mn3B4 compound shows promising magnetic ordering temperature and dynamic stability, suggesting good intrinsic magnetic behavior and structural robustness. The main challenge is its thermodynamic stability, as indicated by the high energy above hull. The magnetic density is close but slightly below the target, suggesting that minor compositional or structural modifications might improve it. The low cost and atom count within limits make it a practical candidate if stability can be enhanced.

AI-discovered magnetic material: MnFe4(CoB2)2 (performance score: 0.731) | Space group: 38 (resolved from structure) | Key properties: Tc: 518K, Ms: 0.12T, Cost: $10/kg, E_hull: 0.164eV/atom, Dynamically stable | Discovered in 2 AI iterations | The material MnFe4(CoB2)2 demonstrates promising magnetic properties with a Curie temperature above 500 K and magnetic density above 0.1, confirming its potential as a high-performance magnetic material. Its low cost and dynamic stability are additional advantages. The slight excess in energy above hull indicates that minor compositional or structural tuning might be needed to improve thermodynamic stability. This suggests that the compound is close to being stable and could be optimized further.

AI-discovered magnetic material: Fe4Mn3B4 (performance score: 0.593) | Space group: 1 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 526K, Ms: 0.12T, Cost: $1/kg, E_hull: 0.160eV/atom, Dynamically unstable | Discovered in 1 AI iterations | The material shows promise as a magnetic material with sufficiently high Curie temperature and magnetic density. However, stability remains a significant challenge. The instability indicated by both the energy above hull and dynamic stability suggests that the current composition or structure may require modification or optimization to achieve a stable phase.

AI-discovered magnetic material: MnFe4Co2(BC)2 (performance score: 0.714) | Space group: 1 (resolved from structure) | Key properties: Tc: 459K, Ms: 0.12T, Cost: $9/kg, E_hull: 0.351eV/atom, Dynamically stable | Discovered in 3 AI iterations | - The material achieves good magnetic density and dynamic stability, which are essential for practical magnetic applications. - The Curie temperature is near but below the target, suggesting potential for improvement. - The relatively high energy above hull indicates the composition or structure may need optimization to improve thermodynamic stability. - Cost is not a limiting factor here. - The combination of elements (Mn, Fe, Co, B, C) can yield promising magnetic properties but may require further tuning to meet all targets.

AI-discovered magnetic material: Fe5Mn2B4 (performance score: 0.592) | Space group: 1 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 497K, Ms: 0.12T, Cost: $1/kg, E_hull: 0.383eV/atom, Dynamically unstable | Discovered in 3 AI iterations | The key insight is that although Fe5Mn2B4 shows promising magnetic density and a Curie temperature close to the target, its high energy above hull and dynamic instability make it unsuitable in its current form. Stability is a critical limiting factor that must be addressed to realize this material’s potential. Additionally, the low cost suggests that if stability can be improved, the material could be economically attractive.

AI-discovered magnetic material: Fe4Co2Mn2B4 (performance score: 0.727) | Space group: 8 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 555K, Ms: 0.11T, Cost: $9/kg, E_hull: 0.249eV/atom, Dynamically stable | Discovered in 3 AI iterations | Fe4Co2Mn2B4 is a promising candidate for magnetic applications due to its high Curie temperature and magnetic density combined with low cost and dynamic stability. The elevated energy above hull suggests that while it can be dynamically stable, it might be metastable thermodynamically, which is a common trade-off in complex magnetic materials. The composition and structure allow for good magnetic properties, but further exploration to reduce e_hull or stabilize the phase could improve practical applicability.

AI-discovered magnetic material: Fe4Mn3B4 (performance score: 0.739) | Space group: 1 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 489K, Ms: 0.12T, Cost: $1/kg, E_hull: 0.224eV/atom, Dynamically stable | Discovered in 10 AI iterations | The material exhibits promising magnetic density and dynamic stability, which are critical for magnetic applications. However, the thermodynamic stability is insufficient as indicated by the elevated energy above hull. This suggests that while the material could exhibit good magnetic behavior, it might be challenging to synthesize or maintain under standard conditions. Slight improvements in stability or Curie temperature could make this material more viable.

AI-discovered magnetic material: MnFe4(CoB2)2 (performance score: 0.707) | Space group: 1 (resolved from structure) | Key properties: Tc: 561K, Ms: 0.09T, Cost: $10/kg, E_hull: 0.190eV/atom, Dynamically stable | Discovered in 5 AI iterations | - High Curie temperature indicates strong magnetic ordering and potential for high-temperature applications. - The material is dynamically stable, so it is structurally sound despite thermodynamic metastability. - The magnetic density is close to but below the target, indicating room for improvement in magnetic moment or density. - The elevated e_hull suggests that the material might not be the most stable phase, which is a critical factor for synthesis and durability. - Cost is low, making it attractive economically.

AI-discovered magnetic material: Fe4Mn3B4 (performance score: 0.743) | Space group: 1 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 509K, Ms: 0.11T, Cost: $1/kg, E_hull: 0.197eV/atom, Dynamically stable | Discovered in 5 AI iterations | - Fe4Mn3B4 is a promising magnetic material with a Curie temperature slightly above 500 K and magnetic density above 0.1. - The low cost and dynamic stability enhance its practical appeal. - The primary limitation is its energy above hull, indicating potential challenges in synthesis or long-term stability. - The material's composition and structure yield a balance of magnetic performance and cost-effectiveness.

AI-discovered magnetic material: MnFe4(CoB2)2 (performance score: 0.731) | Space group: 1 (resolved from structure) | Key properties: Tc: 566K, Ms: 0.11T, Cost: $10/kg, E_hull: 0.273eV/atom, Dynamically stable | Discovered in 5 AI iterations | High Curie temperature and magnetic density combined with low cost and dynamic stability demonstrate that MnFe4(CoB2)2 is a promising magnetic material candidate. The main bottleneck is its thermodynamic metastability, which could be addressed by exploring synthesis conditions, doping, or alloying to lower the energy above hull and improve phase stability.

AI-discovered magnetic material: Fe4Mn2Co1B4 (performance score: 0.737) | Space group: 1 (resolved from structure) | AI-generated from scratch using crystal structure prediction | Key properties: Tc: 512K, Ms: 0.13T, Cost: $5/kg, E_hull: 0.362eV/atom, Dynamically stable | Discovered in 5 AI iterations | The material's magnetic properties and dynamic stability are promising for magnetic applications. The inclusion of Mn and Co in this boride structure appears to enhance magnetic density and Curie temperature. However, achieving thermodynamic stability remains a challenge, as indicated by the high energy above hull. This suggests that further compositional tuning or structural modifications are needed to reduce the e_hull and improve stability without compromising magnetic performance.

AI-discovered magnetic material: MnCrFe3Co3N2 (performance score: 0.470) | Space group: 1 (resolved from structure) | Key properties: Tc: 586K, Ms: 0.11T, Cost: $13/kg, E_hull: 0.176eV/atom, Dynamically stable | Discovered in 5 AI iterations | AI insights: - The composition MnCrFe3Co3N2 can produce a magnetic material with a high Curie temperature and good magnetic density at low cost. - Dynamical stability suggests the structure is robust against latti...

Cell + Ionic relaxation with Orb v3; 0.03 eV/Å threshold; final energy = -717.1657 eV; ΔE = -291.4014 eV; symmetry: Pban → P1

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Relax a crystal structure and create a post

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Generate a crystal structure using GGen

Random bulk crystal generation with PyXtal and Orb v3

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Generate crystal structures with magnetic density and HHI score conditioning

Calculate phonon dispersion and return band structure plot

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Welcome

This dataset has a set of 34,000 ferro/ferrimagnetic materials from Materials Project, their formula, if they include rare earth elements, magnetic moment, volume, magnetic density, a predicted Curie temperature, and cosine distances to some known permanent magnets like NdFeB. Distances are based on a 256 dimension embedding from Orb v2 latent space.

A collection of 5020 magnetic materials from Materials Project, with estimated magnetic density and predicted Curie temperatures.

This is a first draft of a compiled Curie temperature dataset mapping crystal structure (from Materials Project) to Curie temperature. Builds on the work of https://github.com/Songyosk/CurieML. Dataset includes ~6,800 unique materials representing 3,284 unique chemical families.

Evaluation results for the MatterGen fine-tuned model candidates, with new superconducting families labeled.

3DSC dataset grouped by chemical composition, with Tc as our target. For use with MatterGen and the chemical system sampling.