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SpinMultiNet: Neural Network Potential Incorporating Spin Degrees of Freedom with Multi-Task Learning

Koki Ueno, Satoru Ohuchi, Kazuhide Ichikawa, Kei Amii, Kensuke Wakasugi

TL;DR

The model successfully reproduces the energy ordering of stable spin configurations originating from superexchange interactions and accurately captures the rhombohedral distortion of the rocksalt structure, paving the way for new possibilities in materials simulations that consider spin degrees of freedom.

Abstract

Neural Network Potentials (NNPs) have attracted significant attention as a method for accelerating density functional theory (DFT) calculations. However, conventional NNP models typically do not incorporate spin degrees of freedom, limiting their applicability to systems where spin states critically influence material properties, such as transition metal oxides. This study introduces SpinMultiNet, a novel NNP model that integrates spin degrees of freedom through multi-task learning. SpinMultiNet achieves accurate predictions without relying on correct spin values obtained from DFT calculations. Instead, it utilizes initial spin estimates as input and leverages multi-task learning to optimize the spin latent representation while maintaining both $E(3)$ and time-reversal equivariance. Validation on a dataset of transition metal oxides demonstrates the high predictive accuracy of SpinMultiNet. The model successfully reproduces the energy ordering of stable spin configurations originating from superexchange interactions and accurately captures the rhombohedral distortion of the rocksalt structure. These results pave the way for new possibilities in materials simulations that consider spin degrees of freedom, promising future applications in large-scale simulations of various material systems, including magnetic materials.

SpinMultiNet: Neural Network Potential Incorporating Spin Degrees of Freedom with Multi-Task Learning

TL;DR

The model successfully reproduces the energy ordering of stable spin configurations originating from superexchange interactions and accurately captures the rhombohedral distortion of the rocksalt structure, paving the way for new possibilities in materials simulations that consider spin degrees of freedom.

Abstract

Neural Network Potentials (NNPs) have attracted significant attention as a method for accelerating density functional theory (DFT) calculations. However, conventional NNP models typically do not incorporate spin degrees of freedom, limiting their applicability to systems where spin states critically influence material properties, such as transition metal oxides. This study introduces SpinMultiNet, a novel NNP model that integrates spin degrees of freedom through multi-task learning. SpinMultiNet achieves accurate predictions without relying on correct spin values obtained from DFT calculations. Instead, it utilizes initial spin estimates as input and leverages multi-task learning to optimize the spin latent representation while maintaining both and time-reversal equivariance. Validation on a dataset of transition metal oxides demonstrates the high predictive accuracy of SpinMultiNet. The model successfully reproduces the energy ordering of stable spin configurations originating from superexchange interactions and accurately captures the rhombohedral distortion of the rocksalt structure. These results pave the way for new possibilities in materials simulations that consider spin degrees of freedom, promising future applications in large-scale simulations of various material systems, including magnetic materials.
Paper Structure (19 sections, 10 equations, 4 figures, 4 tables)

This paper contains 19 sections, 10 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Equivariance
  5. $E(3)$ Equivariance
  6. Time-Reversal Equivariance
  7. Model Architecture
  8. Embedding Layer
  9. Interaction Layer
  10. Output Layer
  11. Dataset
  12. Results
  13. Model Performance
  14. Identification of Stable Spin Configurations
  15. Ablation Study
  16. ...and 4 more sections

Figures (4)

  • Figure 1: Overall model architecture. (a) Input and output of the model. The atomic number $Z$, the initial magnetic moment estimate $\vec{m}$, and interatomic vectors $\vec{r}_{ij}$ are input and processed through the Embedding Layer, $N$ Interaction Layers, and the Output Layer to output the energy $U_{\text{pred}}$ and magnetic moments $\vec{m}_{i, \text{pred}}$. (b) Embedding Layer (edge). Edge features are created using the magnetic moments of two atoms and the interatomic vector. ToUnit represents the operation of converting a vector to a unit vector, and $||$ represents the concatenation of tensors. (c) Embedding Layer (node). Element embedding vectors and initial node features are created using the atomic number and the magnetic moment. (d) Convolution. Messages are created and aggregated using node and edge features. (e) Output Layer. Steerable features for energy and magnetic moment predictions are extracted from the latent features. (f) Interaction Layer. Node features are updated. $Y$ represents the expansion using spherical harmonics, and $\otimes$ represents the tensor product.
  • Figure 2: Scatter plots of predicted values versus DFT calculated values for each property in the Mn-Co-Ni dataset. (a) Energy, (b) Forces, (c) Magnetic moments.
  • Figure 3: (a) Two types of antiferromagnetic structures. In AFM type-I, spins are aligned parallel within the (001) plane, while in AFM type-II, spins are aligned parallel within the (111) plane. (b) Energy comparison after structural optimization. The energy difference relative to the FM configuration is plotted.
  • Figure A.1: Visualization of the latent features of the Ni atom in a Ni-O two-atom system. The upper part represents the case where Ni has an up-spin, and the lower part represents the down-spin case. The vertical axis indicates the changes in features when the input structure is rotated.