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Spin Neural Network Potential for Magnetic Phase Transitions in Uranium Dioxide

Keita Kobayashi, Hiroki Nakamura, Mitsuhiro Itakura

Abstract

Uranium dioxide (UO2) is a prototypical nuclear fuel material, yet predicting its thermophysical properties across a wide temperature range remains challenging. One factor contributing to this difficulty is the complex magnetic ordering at low temperatures, where spin-orbit coupling produces strong coupling between spin and lattice degrees of freedom. Direct DFT simulations of magnetic phase transitions at finite temperatures are computationally prohibitive. Here, we develop a spin neural network potential (SpinNNP) that explicitly incorporates spin degrees of freedom together with spin-orbit coupling to describe the magnetic states of UO2.Reference datasets were generated using magnetic constrained DFT+U calculations with spin-orbit coupling, covering a wide range of non-collinear spin configurations. The SpinNNP accurately reproduces DFT energies, atomic forces, spin forces, and lattice constants. Machine learning molecular dynamics simulations with spin dynamics successfully capture the antiferromagnetic-paramagnetic transition. Although the predicted magnetic ground state differs from experiment due to known limitations of the underlying DFT description, the transition temperature obtained is of the correct order of magnitude compared with experiment. These results demonstrate that machine-learning potentials can enable large-scale spin-lattice simulations of actinide oxides and provide a practical route toward predictive modeling of complex magnetic materials.

Spin Neural Network Potential for Magnetic Phase Transitions in Uranium Dioxide

Abstract

Uranium dioxide (UO2) is a prototypical nuclear fuel material, yet predicting its thermophysical properties across a wide temperature range remains challenging. One factor contributing to this difficulty is the complex magnetic ordering at low temperatures, where spin-orbit coupling produces strong coupling between spin and lattice degrees of freedom. Direct DFT simulations of magnetic phase transitions at finite temperatures are computationally prohibitive. Here, we develop a spin neural network potential (SpinNNP) that explicitly incorporates spin degrees of freedom together with spin-orbit coupling to describe the magnetic states of UO2.Reference datasets were generated using magnetic constrained DFT+U calculations with spin-orbit coupling, covering a wide range of non-collinear spin configurations. The SpinNNP accurately reproduces DFT energies, atomic forces, spin forces, and lattice constants. Machine learning molecular dynamics simulations with spin dynamics successfully capture the antiferromagnetic-paramagnetic transition. Although the predicted magnetic ground state differs from experiment due to known limitations of the underlying DFT description, the transition temperature obtained is of the correct order of magnitude compared with experiment. These results demonstrate that machine-learning potentials can enable large-scale spin-lattice simulations of actinide oxides and provide a practical route toward predictive modeling of complex magnetic materials.
Paper Structure (6 sections, 21 equations, 2 figures, 2 tables)

This paper contains 6 sections, 21 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Computational Framework
  3. Spin Symmetry Functions
  4. Reference Dataset Preparation and Model Fitting
  5. Results and Discussion
  6. Conclusion

Figures (2)

  • Figure 1: Energies for various magnetically ordered states computed by DFT and SpinNNP. L1k, L2k, and L3k denote longitudinal 1--3k antiferromagnetic ordered states, respectively. T1k, T2k, and T3k denote transverse 1--3k antiferromagnetic ordered states, respectively. FM$_{lmk}$ denotes ferromagnetic ordered states with spin orientation along the $[lmk]$ direction.
  • Figure 2: (a) Temperature dependence of the lattice constants of UO$_2$ obtained from MLMD simulations. (b) Order parameter $\max|S_{\mathbf{k}}|$ characterizing the magnetic ordering as a function of temperature. (c) Calculated specific heat $C_p$ as a function of temperature, obtained from numerical differentiation of the enthalpy. Solid lines denote heating simulations from 1 K to 40 K, whereas dashed lines correspond to cooling simulations from 40 K to 1 K. The hysteresis between heating and cooling runs reflects the first-order nature of the magnetic transition.