Magnetic levitation of metamaterial bodies enhanced with magnetostatic surface resonances

We propose that macroscopic objects built from negative-permeability metamaterials may experience resonantly enhanced magnetic force in low-frequency magnetic fields. Resonant enhancement of the time-averaged force originates from magnetostatic surface resonances (MSRs), which are analogous to the electrostatic resonances of negative-permittivity particles, well known as surface plasmon resonances in optics. We generalize the classical problem of the MSR of a homogeneous object to include anisotropic metamaterials and consider the most extreme case of anisotropy, where the permeability is negative in one direction but positive in the others. It is shown that deeply subwavelength objects made of such indefinite (hyperbolic) media exhibit a pronounced magnetic dipole resonance that couples strongly to uniform or weakly inhomogeneous magnetic field and provides strong enhancement of the magnetic force, enabling applications such as enhanced magnetic levitation.