Exploring Noncollinear Magnetic Energy Landscapes with Bayesian Optimization

TL;DR

This paper demonstrates that Bayesian Optimization can efficiently explore complex noncollinear magnetic energy landscapes using fewer DFT calculations, significantly improving the process of finding ground states in magnetic materials.

Contribution

The study introduces the application of Bayesian Optimization to magnetic energy landscape exploration, reducing computational costs compared to traditional methods.

Findings

Bayesian Optimization effectively models magnetic energy as a function of spin angles.

The approach requires fewer DFT calculations than conventional methods.

Significant efficiency improvements are observed in analyzing complex magnetic materials.

Abstract

The investigation of magnetic energy landscapes and the search for ground states of magnetic materials using ab initio methods like density functional theory (DFT) is a challenging task. Complex interactions, such as superexchange and spin-orbit coupling, make these calculations computationally expensive and often lead to non-trivial energy landscapes. Consequently, a comprehensive and systematic investigation of large magnetic configuration spaces is often impractical. We approach this problem by utilizing Bayesian Optimization, an active machine learning scheme that has proven to be efficient in modeling unknown functions and finding global minima. Using this approach we can obtain the magnetic contribution to the energy as a function of one or more spin canting angles with relatively small numbers of DFT calculations. To assess the capabilities and the efficiency of the approach we investigate the noncollinear magnetic energy landscapes of selected materials containing 3d, 5d and 5f magnetic ions: Ba$_3$MnNb$_2$O$_9$, LaMn$_2$Si$_2$, $\beta$-MnO$_2$, Sr$_2$IrO$_4$, UO$_2$ and Ba$_2$NaOsO$_6$. By comparing our results to previous ab initio studies that followed more conventional approaches, we observe significant improvements in efficiency.