Manipulating magnetic fields in inaccessible regions by negative magnetic permeability

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.