Spin-Aware Neural Network Interatomic Potential for Atomistic Simulation

Abstract

Computational modeling is key in materials science for developing mechanistic insight that enables new applications. ab initio methods capture exceptional phenomenological richness to high numerical accuracy, but at high cost and limited scale. Empirical potentials are faster and scale better, but cannot compare to ab initio in numerical and physical accuracy. Machine learning (ML) interatomic potentials (IPs) of recent years offer a balance: excellent phenomenology and accuracy, while scaling well and at moderate cost. Interatomic potentials are generally formulated as functions of atomic coordinates only—i.e. spin-agnostic. For materials whose structures or energetics are influenced by spin, this is insufficient. Iron’s strong magnetism is coupled to its mechanical properties. This confounds spin-agnostic IPs because they implicitly use an expectation value across spin states for a given geometry.

Thus, this work offers a novel ML engine employing: (1) novel basis functions that translate spin information into neural network (NN) inputs, (2) and novel NN architectures that improve their ability to learn and express relationships between geometry, spin, and energy.

When applied to a broad dataset with high variance in both geometry and spin, the new bases achieve a 4x reduction in energy prediction error compared to the spin-agnostic Behler- Parrinello (BP) framework, and 5x using both the new bases and new NN architecture. When applied to a high spin-variance dataset, the new bases reduce energy prediction error by over 10x. Even when applied to a dataset with low spin-variance, the new bases reduce energy prediction error by 45%. These predictive improvements come at an increased computational cost of about 5% compared to spin-agnostic BP using only the new bases, but roughly 3x using both the new bases and NN.

This work presents two physical predictions to further elucidate the capabilities and value of the Spin-Aware NN IP (SANNIP). First, Monte Carlo (MC) spin relaxations using SANNIP exhibit behavior consistent with hysteresis in that the relaxed spin state is dependent on its initial alignment. Second, MC spin relaxations resolve the temperature beyond which ferromagnetically initialized systems lose their magnetization to between 1100 and 1150K, which is roughly consistent with experimental measurement of the Curie Temperature (TC) of 1043K.

The evaluation of numerical accuracy and physical predictions demonstrate the utility of the novel bases and NN architectures. Future work can generate a broader dataset and deploy SANNIP potentials in molecular dynamics (MD) seeking insight into the role of spin in mechanical properties, defect interactions, etc. Additional bases and can explicitly treat externally applied electric and magnetic fields. Further NN architecture innovations can incorporate transfer learning into treatment of multi-component systems. This work is foun- dational to and enabling of many new avenues of investigation in computational materials science with the aim of improving materials design, fabrication, remediation, recycling, and disposal.