  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 (MSR) 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
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.
