  A permanent magnet can be levitated simply by placing it in the vicinity of
another permanent magnet that rotates in the order of 200 Hz. This surprising
effect can be easily reproduced in the lab with off-the-shelf components. Here
we investigate this novel type of magnetic levitation experimentally and
clarify the underlying physics. Using a 19 mm diameter spherical NdFeB magnet
as rotor magnet, we capture the detailed motion of levitating, spherical NdFeB
magnets, denoted floater magnets. We find that as levitation occurs, the
floater magnet frequency-locks with the rotor magnet, and, noticeably, that the
magnetization of the floater is oriented close to the axis of rotation and
towards the like pole of the rotor magnet. This is in contrast to what might be
expected by the laws of magnetostatics as the floater is observed to align its
magnetization essentially perpendicular to the magnetic field of the rotor.
Moreover, we find that the size of the floater has a clear influence on the
levitation: the smaller the floater, the higher the rotor speed necessary to
achieve levitation, and the further away the levitation point shifts. We verify
that magnetostatic interactions between the rotating magnets are responsible
for creating the equilibrium position of the floater. Hence, this type of
magnetic levitation does not rely on gravity as a balancing force to achieve an
equilibrium position. Based on theoretical arguments and a numerical model, we
show that a constant, vertical field and eddy-current enhanced damping is
sufficient to produce levitation from rest. This enables a gyroscopically
stabilised counter-intuitive steady-state moment orientation, and the resulting
magnetostatically stable, mid-air equilibrium point. The numerical model
display the same trends with respect to rotation speed and the floater magnet
size as seen in the experiments.
