Ab initio calculation of magnetic field induction of nanowires

Abstract The narrower a conductor is, the more significant is its induced magnetic field, the Ørsted magnetic field. The calculation of the Ørsted magnetic field in current-carrying wires is a standard textbook exercise that generally assumes that the wire has a circular cross-section, and applies a simplified form of the Biot-Savart equation. For non-circular cross-sections, such as infinitely thin or rectangular slabs, there are also simplified forms of the equation, but are less known. While such formalism can be suitable for macroscopic wire structures, it will not be ideal for nano-sized wire structures because of the presence of structural features that are likely to have significant consequences on the structure of the Ørsted magnetic field. This work introduces a novel approach for the prediction of the Ørsted magnetic field in a nanowire that combines the current magnetization hypothesis [Eur. Phys. J. Plus 137, 378 (2022)] with a molecular dynamics simulation approach using the electron force field. This formalism is applied in the present work for the prediction of the induced magnetic field in a lithium nanowire, and is shown to exhibit agreement with the Biot-Savart results. The formalism can be utilized for predicting the Ørsted magnetic field of more complex nano-conductors, as well as high-precision magnetic sensing for molecules.