Generative Diffusion Model DiffCrysGen Discovers Rare Earth-Free Magnetic Materials

TL;DR

DiffCrysGen presents a fully data-driven score-based diffusion model that unifies the generation of crystal structure components into a single end-to-end diffusion process, enabling rapid creation of complete inorganic crystals. Operated under a variance-exploding diffusion scheme with a lightweight denoiser, the model achieves throughput of roughly $308$ samples per second and yields about $1.3\times10^6$ crystals, with a large fraction being valid, unique, and diverse. A hierarchical ML and DFT-based screening pipeline identifies 28 promising rare-earth-free magnets (14 FM, 14 AFM) with high magnetization and anisotropy, validated by DFT and convex-hull proximity analyses. The work demonstrates that diffusion-based crystal generation can accelerate de novo materials discovery, including rediscovery of known compounds and proposal of novel RE-free magnets, without relying on heavy-handed inductive biases.

Abstract

Efficient exploration of the vast chemical space is a fundamental challenge in materials discovery, particularly for designing functional inorganic crystalline materials with targeted properties. Diffusion-based generative models have emerged as a powerful route, but most existing approaches require domain-specific constraints and separate diffusion processes for atom types, atomic positions, and lattice parameters, adding complexity and limiting efficiency. Here, we present DiffCrysGen, a fully data-driven, score-based diffusion model that generates complete crystal structures in a single, end-to-end diffusion process. This unified framework simplifies the model architecture and accelerates sampling by two to three orders of magnitude compared to existing methods without compromising chemical and structural diversity of the generated materials. In order to demonstrate the efficacy of DiffCrysGen in generating valid and useful materials, using density functional theory (DFT), we validate a number of newly generated rare earth-free magnetic materials that are energetically and dynamically stable, and are potentially synthesizable. These include ferromagnets with high saturation magnetization and large magnetocrystalline anisotropy, as also metallic antiferromagnets. These results establish DiffCrysGen as a general platform for accelerated functional materials discovery.

Figures (6)

• Figure 1: Generative diffusion framework in DiffCrysGen.a The diffusion process consists of two stages: forward diffusion (corruption) and reverse diffusion (denoising), both governed by the corresponding stochastic differential equations (SDEs) with a time-dependent noise level $\sigma(t)$. Here, $p_{data}({\bf x}_0)$ and $p_{T}({\bf x}_T)$ denote initial data distribution and prior distribution, respectively. The reverse diffusion is guided by the score function $\nabla_{\bm x} \log p_t({\bm x})$ of the marginal probability density $p_t(\bm x)$ at each time step $t$. b Schematic of the denoising process implemented by a noise-conditional UNet as the denoising neural network. It takes as input a noisy data ($\bm{x_t}$) and corresponding noise level ($\sigma_t$), and predicts the ground truth denoised structure ($\bm{x_0}$).
• Figure 2: Generating diverse inorganic crystalline materials. a Visualization of four randomly selected V.U.N. materials generated by DiffCrysGen, with corresponding reduced formula and space group. b Distribution of space groups among V.U.N. materials in the triclinic and monoclinic crystal systems. c Distribution of space groups among V.U.N. materials in high-symmetry crystal systems (space group number $\ge$ 16). d Distribution of different chemical compositions within the RE-free subset of V.U.N. materials containing transition metal (TM) elements.
• Figure 3: Materials design pipeline and and structural fidelity assessment. a Hierarchical screening pipeline applied to crystal structures generated by DiffCrysGen for discovering RE-free magnetic materials with high saturation magnetization. The filtering process selects valid, unique, and novel (V.U.N.) compounds without RE elements ($Z_{max}\le54$), followed by screening based on formation energy ($h_{form}$) and saturation magnetization ($M_s$) as predicted by machine-learning surrogate models. The shortlisted candidates are refined through two complementary workflows: DFT (workflow-1) and combined MLFF-DFT (workflow-2) for structural optimization. The final set of materials is then evaluated with DFT to confirm their thermodynamic, dynamical, and magnetic properties. b Distribution of root-mean-square deviation (RMSD) between structures generated by DiffCrysGen and those optimized with DFT. c Distribution of RMSD between DiffCrysGen-generated and MLFF-optimized structures. d Distribution of RMSD between MLFF-optimized and DFT-optimized structures.
• Figure 4: Electronic and magnetic properties of $\text{Fe}_2\text{Zn}\text{O}_3$.a Side and top views of the crystal structure. b Phonon band structure. c Total density of states (DOS) with projections onto Fe-$d$, O-$p$, and Zn-$d$ orbitals. d Projected DOS of the five Fe-$d$ orbitals. e Fe-$d$ orbital-resolved spin–orbit coupling (SOC) matrix element contributions to the magnetocrystalline anisotropy energy (MAE).
• Figure 5: Electronic and magnetic properties of $\text{Mn}_2\text{Rh}_3\text{Ti}$.a Side and top views of the crystal structure. b Phonon band structure. c Total density of states (DOS) with projections onto Mn-$3d$, Rh-$4d$, and Ti-$3d$ orbitals.