High-throughput discovery of high Curie point two-dimensional ferromagnetic materials

Two-dimensional (2D) ferromagnetic (FM) materials have immense potential for revolutionizing spintronics, valleytronics, and memory technologies. While many 2D FM materials have been computationally predicted, a crucial parameter for practical applications—the Curie temperature (Tc)—has been largely missing from existing databases. This is due to the complexity of Tc calculation, which typically involves manually intensive processes like ground-state and low-energy spin configuration searches, magnetic exchange identification, and Monte Carlo simulations. The choice of Hamiltonian model (Ising vs. Heisenberg) also affects accuracy. This research addresses this gap by developing an automated, high-throughput computational framework for accurate Tc prediction. The framework combines first-principles calculations with Heisenberg model-based Monte Carlo simulations. A high-throughput screening of a database containing 786 materials classified as FM yielded 157 materials with successfully computed Tc values, of which 26 exhibited Tc values above 400 K. A machine learning (ML) pipeline was developed using these results to accelerate the discovery of additional high-Tc materials.

Recent experimental discoveries of ferromagnetism in 2D materials like CrI₃ and Cr₂Ge₂Te₃ at low temperatures, and subsequently room-temperature ferromagnetism in monolayer VSe₂ and MnSe₂, have spurred significant interest. Several computational studies have predicted numerous 2D FM materials, but these predictions often lacked crucial information like Tc. Existing databases contain hundreds to thousands of 2D materials, but they typically lack Tc data due to the complexity of its calculation. The computational determination of Tc involves manual heuristics-based searches for ground-state and low-energy spin configurations, identification of magnetic exchange interactions, and Monte Carlo simulations. The choice of Hamiltonian (Ising or Heisenberg) influences the accuracy of the predicted Tc. Previous algorithms existed for bulk materials but weren't optimized for the complexities of 2D materials.

The developed code performs a series of automated steps: (1) It begins with a material's unit cell, utilizing the pymatgen library to generate FM and AFM spin configurations. (2) Collinear density functional theory with Hubbard correction (DFT+U) is used to relax these configurations and calculate their energies. AFM materials are discarded. Magnetic moments are calculated. (3) Non-collinear DFT with spin-orbit coupling (SOC) is used to compute the magnetocrystalline anisotropy energy (MAE) and determine the easy magnetization axis (EMA). (4) DFT energies are fitted to a Heisenberg Hamiltonian, incorporating interactions from nearest neighbors (N1) to fourth nearest neighbors (N4). (5) A GPU-accelerated Monte Carlo simulation solves the Heisenberg Hamiltonian to estimate Tc. For XY magnets, Tc is calculated using a formula derived from Monte Carlo simulations of the XY model. (6) The code employs just-in-time (JIT) compilation with Numba to significantly speed up the computationally intensive Monte Carlo simulations. (7) The study utilized the C2DB database, containing 786 materials initially classified as FM. (8) The study also employed an automated machine learning pipeline, using the library automatminer, to create a model that predicts Tc from chemical features derived from the crystal structures. The pipeline used TPOT for model and hyperparameter space search, generating over 60,000 pipelines. (9) The ML model was tested on materials from other databases, both for Tc prediction and FM/AFM classification. (10) Ab initio molecular dynamics (AIMD) simulations assessed high-temperature structural stability of selected materials.

The high-throughput screening of 786 materials revealed that 368 were actually antiferromagnetic (AFM), highlighting the importance of rigorous computational methods. Tc values were successfully computed for 157 FM materials, with 26 materials exhibiting Tc values exceeding 400 K. The accuracy of the Tc calculations was validated by close agreement with experimental Tc values for CrI₃, Cr₂Ge₂Te₆, and MnSe₂. The study showed that including higher-order neighbor interactions in the Hamiltonian is crucial for accurate Tc prediction in certain materials, particularly those with multiple metal layers or square/rectangular lattices. The ML model showed high accuracy on the training dataset (MSE = 94.57 K²), but less accuracy on the testing dataset (MSE = 30335.46 K²), highlighting the limitations of training with a small dataset and unseen crystal structures. However, it still successfully identified several high-Tc materials, including CrO₂_P4/mmm and ZnNi₂O₅. Several violations of the Goodenough-Kanamori rules were observed, suggesting the limitations of applying these rules directly to 2D materials. High-temperature AIMD simulations revealed that some of the high-Tc materials are structurally stable at 400 K, while others are not. Specifically, CrIN_Pmmm, RhCl₂_C2/m, and ZnNi₂O₅ maintained their structure, while Mn₂H₂CO₂_P-3m1 decomposed.

This work successfully addressed the challenge of accurately predicting Tc in 2D FM materials by developing a robust, automated, and high-throughput computational framework. The findings substantially expand the catalog of potential 2D FM materials suitable for high-temperature applications. The discovery of numerous high-Tc materials containing metals (Mo, W, Ti) previously ignored in heuristic searches underscores the power of the automated approach. While the ML model's performance was affected by the limited size of the training dataset, its success in identifying new high-Tc materials demonstrates its potential for accelerating future discoveries. The violations of the Goodenough-Kanamori rules observed highlight the need for more sophisticated theoretical models for 2D materials. The high-temperature stability analysis provides crucial insights for practical device applications.

This study presents a significant advancement in the discovery and characterization of 2D FM materials with high Tc. The development of an automated, high-throughput computational workflow, coupled with machine learning, allows for efficient and accurate identification of promising candidate materials. The discovery of 26 materials with Tc > 400 K opens exciting avenues for technological advancements in spintronics and related fields. Future research should focus on expanding the training dataset for the ML model to improve its predictive power, and exploring the synthesis and experimental characterization of the identified high-Tc materials.

The main limitation of this study is the relatively small size of the training dataset for the machine learning model, which affected its generalization capability. The accuracy of the DFT+U calculations depends on the choice of the Hubbard U parameter; using material-specific U values improves accuracy but increases computational cost. Some high-Tc materials identified might have low thermodynamic or dynamic stability, potentially limiting their practical applications. The study primarily focuses on collinear and non-collinear magnetic order, and other types of magnetic ordering were not considered.