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

First-principles calculations based on Density Functional Theory (DFT) have been widely utilized as a powerful tool for understanding electronic structures and material properties [1-3]. Although DFT calculations can accurately predict energies and forces acting on atoms, they are often hindered by high computational costs. This limitation can become a significant bottleneck, particularly for large-scale systems or long-time simulations. To address this issue, Neural Network Potentials (NNPs) have emerged as a promising alternative to accelerate DFT calculations [4-10]. NNPs learn the relationship between atomic configurations and energies from data obtained through DFT calculations, enabling significant reduction in computational cost while maintaining accuracy comparable to DFT calculations. In particular, NNPs based on the Graph Neural Network (GNN) are well-suited for constructing accurate potential models, as they can effectively capture the local atomic environments [6, 11-13]. However, most conventional NNPs do not account for spin degrees of freedom, limiting their application to material systems where spin states play a critical role in determining properties, such as transition metal oxides (TMOs). TMOs are known to exhibit diverse magnetic properties due to the presence of transition metal ions with partially filled d-orbitals, and incorporating spin degrees of freedom is crucial for understanding their properties [14].