# The generalized spin-orbit interaction: a microscopic origin of the {\O}rsted magnetic field

## TL;DR

This paper introduces a generalized spin-orbit interaction (GSOI) that describes magnetic fields from moving charged particles at all points in space and in both reference frames, challenging traditional microscopic magnetic field theories.

## Contribution

It presents a new GSOI framework that extends classical spin-orbit interaction theory to a more comprehensive, microscopic description of magnetic fields generated by moving charges.

## Key findings

- GSOI reproduces the macroscopic  magnetic field.
- GSOI conflicts with the Biot-Savart law at the microscopic level.
- Implications for 2D materials like graphene are discussed.

## Abstract

This work introduces a generalization of the form of the spin-orbit interaction, the generalized spin-orbit interaction (GSOI). It expresses the magnetic field induced by two charged particles moving with a non-zero relative velocity as a field defined at all points in space, and exists in the reference frames of both particles. This is in contrast to spin-orbit interaction theory, in which the generated magnetic field is defined at only one point in space, and exists in the reference frame of one of the two particles. At the macroscopic scale, it is shown that the GSOI theory implies the same form of the \O{}rsted magnetic field produced by a current-carrying wire. However, the theory is incompatible with the microscopic form of the Biot-Savart equation that implies that a charged particle induces a magnetic field by having a non-zero velocity. The implications of the GSOI theory on properties of the \O{}rsted magnetic field in current-carrying atomically thin two-dimensional materials, such as graphene, are discussed. The framework established in this paper aims at re-imagining classical physical concepts in light of an advanced microscopic understanding.