Magnetic fields from microscopic sources: a new quantum-based discrete interaction approach

Abstract

At nanometer scales, the Ørsted magnetic field generated by electrical current no longer strictly follows continuum magnetostatics. A nitrogen–vacancy magnetometry experiment reported suppressed and spatially reshaped magnetic fields in metallic nanowires, and these deviations are not captured by the Biot–Savart law. We introduce a microscopic current–magnetisation (CMH) framework that reconstructs magnetic induction directly from electron–ion correlations within atomically resolved conductors. Each carrier generates a locally screened axial source determined by its motion relative to nearby ions, yielding an exactly divergence-free magnetic field through a compact vector-potential formulation. The Biot–Savart kernel emerges only as a long-distance coarse-grained limit. When device dimensions approach the screening length, CMH predicts intrinsic field suppression and spatial smoothing. Crucially, the framework enables direct prediction of molecular orbital ring-current fields, revealing near-field structures that differ qualitatively from continuum loop models while preserving correct long-range behavior. CMH reframes current-induced magnetism at the atomic scale, where classical approaches fail, and opens a new and predictive pathway for engineering magnetic responses to enable design of next-generation nanomagnetic devices with improved performance.