Active Learning Guided Computational Discovery of 2D Materials with Large Spin Hall Conductivity

TL;DR

Several features such as orbital symmetry near the Fermi energy, types of atomic species, material composition, covalent radii, and electronegativity of constituent atoms were found to play critical role in shaping the spin Hall response in 2D systems.

Abstract

Two-dimensional (2D) materials are promising candidates for next-generation spintronic devices due to their tunable properties and potential for efficient spin-charge interconversion. However, discovering materials with intrinsically high spin Hall conductivity (SHC) is hindered by the vast chemical space and expensive nature of conventional experimental and first-principles methods. In this work, we employ an active learning framework to accelerate the discovery of high-SHC 2D materials. Machine learning (ML) models were trained on SHC values computed from density functional theory calculations, incorporating the Kubo formalism via tight-binding Hamiltonians constructed from maximally localized Wannier functions, with explicit treatment of spin-orbit coupling. Starting from random but chemically diverse 24 2D systems, the dataset was expanded to 41 cases (from an overall pool of around 2000 materials) over three active learning loops using an expected improvement acquisition strategy. The ML technique successfully identified several high SHC candidates with the best candidate exhibiting a SHC of 271.52 (hbar/e) Ohm^-1, nearly 23 times higher than the top performer in the initial round. Beyond candidate discovery, several features such as orbital symmetry near the Fermi energy, types of atomic species, material composition, covalent radii, and electronegativity of constituent atoms were found to play critical role in shaping the spin Hall response in 2D systems. The data generated is made publicly available to facilitate further advances in 2D spintronics.

Figures (5)

• Figure 1: Active machine learning framework to identify 2D materials with high SHC. The workflow primarily consists of DFT (for EBS computation), MLWF (for minimal basis set formation), TB modeling (for computation of Berry curvature and thereby SHC) and ML techniques (for SHC prediction and material selection). First, 2D structures are obtained from MC2D database for which EBS is determined. This is followed by MLWF construction using projection matrices generated from EBS using Wannier90 codemostofi_updated_2014. The best-fit TB model Hamiltonian is then set up using MLWF basis to obtain Berry curvature and SHC. These values are used to create training dataset which also comprises of 26 hand-crafted symmetry and electronic features as well as 132 matminer library-based elemental features. The ML models are then trained using 5-fold cross validation (CV), recursive feature elimination and symmetric log scaling of the target property. The model with lowest CV error is used to screen 5-7 best candidates using expected improvement acquisition strategy for the next round of DFT--SOC+TB computations. The freshly computed SHC data is are added to the training dataset and next active learning loop is initiated. The final ML model is later subjected to SHAP feature analysis to extract important chemical insights.
• Figure 2: Performance of active learning rounds: (a) 2D systems selected across different rounds for SHC (or THC) computations using active learning approach. While diverse candidates were manually selected in Round 1, EI was used for selection in Rounds 2.1, 2.2 and 3. The number in parenthesis next to the system name indicates its rank when ordered based on absolute SHC value. (b) Variation in joint kernel density and multi-class scatter plot of THC and SHC with different active learning rounds in absolute symmetric log space. (c) The box-and-whisker plot of modulus of SHC in symmetric log space with horizontal lines in the box showing median, first and third quartiles whereas whiskers (range of the data) are 1.5 times inter-quartile range. The data points beyond the whiskers are outliers marked as circles.
• Figure 3: Predictive capability of ML Models. Parity plot comparing the ML predictions against true (computed) SHC values in modulus symmetric log space. Results are shown for candidates screened in Round 2.2 (yellow squares) and Round 3 (blue triangles). The error bars indicate uncertainty ($\pm$1$\sigma$) in model predictions. The diagonal and vertical dashed line denote the parity line and the SHC value for best candidate (AuSe) from Round 1, respectively. A general trend of discovery of 2D systems with increasing SHC magnitude with each active learning loop can be observed.
• Figure 4: Chemical insights from ML model (a) SHAP summary plot highlighting the most influential features for the final ML model trained on 41 SHC computations (in symlog space). (b) The Pearson correlation coefficients between features retained after RFE for the final model and Symlog(SHC). The variation in saturation of color (green and orange) indicates variation in intensity of correlation (positive and negative) respectively.
• Figure 5: Variation of Hall conductivity with energy. The plot shows energy-dependent variation of orbital (OHC) and spin (SHC) Hall conductivity for best candidate systems from each round computed using TB model $\mathcal{H}_{\text{TB}}$ and Kubo formalism. The abscissa of point on curves at which zero energy (E-EF) horizontal dashed line intersects are taken as OHC and SHC values.