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The control of magnetic fields underpins a wide variety of cutting-edge technologies, ranging from the guiding of micro-robots for medical applications to the trapping of atoms for quantum experiments. Relying on different arrangements of coils, these technologies demand advances in the manipulation of magnetic fields at a distance from the sources that generate them. Here, we present a strategy for remotely shaping magnetic fields based on active magnetic metamaterials with negative permeability and we theoretically and experimentally demonstrate the possibility of emulating and cancelling magnetic sources at distance. Our strategy provides magnetic field focusing deep into physically inaccessible volumes where neither sources of magnetic field nor magnetic materials can be placed., Comment: main text: 5 pages, 4 figures; supplementary material: 18 pages, 13 figures, 1 table

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.

Controlling electromagnetic energy is essential for an efficient and sustainable society. A key requirement is concentrating magnetic energy in a desired volume of space in order to either extract the energy to produce work or store it. Metamaterials have opened new possibilities for controlling electromagnetic energy. Recently, a superconductor-ferromagnetic metamaterial that allows unprecedented concentration and amplification of magnetic energy, and also its transmission at distance through free space, has been devised theoretically. Here we design and build an actual version of the superconductor-ferromagnetic metamaterial and experimentally confirm these properties. We show that also a ferromagnetic metamaterial, without superconducting parts, can achieve concentration and transmission of energy with only a slight decrease in the performance. Transmission of magnetic energy at a distance by magnetic metamaterials may provide new ways of enhancing wireless power transmission, where efficiency depends critically on the magnetic coupling strength between source and receiver., Comment: 5 pages, 4 figures

We show how the static magnetic field of a finite source can be transferred and routed to arbitrary long distances. This is achieved by using transformation optics, which results in a device made of a material with a highly anisotropic magnetic permeability. We show that a simplified version of the device, made by a superconducting-ferromagnet hybrid, also leads to an excellent transfer of the magnetic field. The latter is demonstrated with a proof-of-principle experiment where a ferromagnet tube coated with a superconductor improves the transfer of static magnetic fields with respect to conventional methods by a 400\% factor over distances of 14cm., Comment: 5 pages, 5 figures, and Supplementary Material; revised version

Magnetic energy is one the main agents powering our society: generating energy in power plants, keeping information in magnetic memories, moving our devices with motors. All of these applications require a certain spatial distribution of magnetic energy, for example concentrating it in a transformer core or in a magnetic sensor. We introduce in this work a way to collect magnetic energy and distribute it in space with unprecedented efficiency and flexibility, allowing very large concentration of magnetic energy in a free space region, an enhanced magnetic coupling between two magnetic sources, and the transfer of magnetic energy from a source to a given distant point separated by empty space. All these features are achieved with a single device, a magnetic shell designed by transformation optics., Comment: 15 pages, 5 figures

The experimental realization of cloaks for electromagnetic fields has been possible only in reduced schemes because of extreme material conditions required in exact cloaks. Here we analytically demonstrate that a simple arrangement of two concentric homogeneous and isotropic layers with different permeabilities can keep a uniform externally applied magnetic field unperturbed. If the inner layer is superconducting, the device prevents exterior fields from entering an enclosed region, which represents a case for an exact cloaking of uniform fields. When the applied field is inhomogeneous the cloaking property is reduced but may be optimized by changing the thickness of the layers., Comment: 3 figures