Negative permeability in magnetostatics and its experimental demonstration

TL;DR

This paper introduces the concept of negative static permeability in magnetostatics, extending Maxwell's equations, and demonstrates an experimental spherical shell that emulates negative permeability to manipulate magnetic fields.

Contribution

It presents the first theoretical and experimental realization of negative-permeability materials in magnetostatics, a new paradigm for magnetic field control.

Findings

Extended Maxwell equations to include negative permeability

Designed a current-based negative-permeability shell

Experimentally demonstrated magnetic field manipulation

Abstract

The control of magnetic fields, essential for our science and technology, is currently achieved by magnetic materials with positive permeability, including ferromagnetic, paramagnetic, and diamagnetic types. Here we introduce materials with negative static permeability as a new paradigm for manipulating magnetic fields. As a first step, we extend the solutions of Maxwell magnetostatic equations to include negative-permeability values. The understanding of these new solutions allow us to devise a negative-permeability material as a suitably tailored set of currents arranged in space, overcoming the fact that passive materials with negative permeability do no exist in magnetostatics. We confirm the theory by experimentally creating a spherical shell that emulates a negative-permeability material in a uniform magnetic field. Our results open new possibilities for creating and manipulating magnetic fields, which can be useful for practical applications.