Time-reversal equivariant neural network potential and Hamiltonian for magnetic materials

Abstract

This work presents Time-reversal Equivariant Neural Network (TENN) framework. With TENN, the time-reversal symmetry is considered in the equivariant neural network (ENN), which generalizes the ENN to consider physical quantities related to time-reversal symmetry such as spin and velocity of atoms. TENN-e3, as the time-reversal-extension of E(3) equivariant neural network, is developed to keep the Time-reversal E(3) equivariant with consideration of whether to include the spin-orbit effect for both collinear and non-collinear magnetic moments situations for magnetic material. TENN-e3 can construct spin neural network potential and the Hamiltonian of magnetic material from ab-initio calculations. Time-reversal-E(3)-equivariant convolutions for interactions of spinor and geometric tensors are employed in TENN-e3. Compared to the popular ENN, TENN-e3 can describe the complex spin-lattice coupling with high accuracy and keep time-reversal symmetry which is not preserved in the existing E(3)-equivariant model. Also, the Hamiltonian of magnetic material with time-reversal symmetry can be built with TENN-e3. TENN paves a new way to spin-lattice dynamics simulations over long-time scales and electronic structure calculations of large-scale magnetic materials.

De novo inverse materials design by combining optimization algorithm, universal potential and universal property model

“…For BO, a new structure with targeted property was recommended and the recommendation model was re-trained based on all previous pairs of (Crys, ECrys, PCrys) in a manner of active learning. We employ TPE-based BO as implemented in Hyperopt 25 and Optuna 26 , and choose observation quantile γ as 0.25 27 . In elemental pool, we considered materials containing elements within the first five periods in the periodic table because DFT results based on local density approximation or grand gradient approximation in the training set may not effectively deal with elements with f electrons in the sixth and seventh periods.…”

Interatomic Interaction Models for Magnetic Materials: Recent Advances

“…The calculated DW energies were found to be 65 J/m 2 , 170 J/m 2 , and 185 J/m 2 , respectively, consistent with previous studies. Later, SpinGNN++ was developed [74]. In addition to non-collinear magnetism, SpinGNN++ method incorporates spin-orbit coupling in explicit Heisenberg, Dzyaloshinskii-Moriya, Kitaev, biquadratic, and implicit high-order spin-lattice interactions.…”

“…Many of the developed magnetic MLIPs incorporate non-collinear magnetism. One more crucial aspect of magnetic MLIPs is the consideration of spin-orbit coupling [30], which has been accounted for in SpinGNN++ [74]. However, a notable drawback of magnetic MLIPs is the substantial amount of DFT data required -sometimes exceeding 10000 configurations -to accurately fit the potentials and predict the desired properties.…”

Representations of Materials for Machine Learning

“…Gong et al (63) found that if the pooled representation after convolutions was concatenated with human-tuned descriptors, errors could be reduced by 90% for related predictions, including phonon internal energy and heat capacity. Algorithms have attempted to more explicitly account for long-range interactions by modulating convolutions with a mask defined by a local basis of Gaussians and a periodic basis of plane waves (65), employing a unique global pooling scheme that could include additional context such as stoichiometry (66), or constructing additional features from the reciprocal representation of the crystal (67). Other strategies have leveraged assumptions about the relationships among predicted variables, such as representing phonon spectra by using a Gaussian mixture model (68).…”