The application of a magnetic field perpendicular to the surface of a graphene cantilever generates a bending force owing to the strong anisotropy of the magnetic susceptibility. We calculate the mechanically stable equilibrium shape of a graphene cantilever in the presence of a magnetic field by minimizing the magnetic and bending energies, which are calculated using the tight-binding model and the Tersoff–Brenner potential, respectively. Furthermore, the introduction of a continuous model enables the size-dependence of the displacement by bending to be considered.

A graphene disk can be levitated above a magnet by a repulsive force arising from their diamagnetic interaction if the product of the magnetic field and its gradient is sufficiently large. The diamagnetic force also causes the rotation of the graphene disk because of the strong anisotropy of the magnetic permeability of graphene; thus a motion of centroid and rotation are considered by solving simultaneous Langevin equations. Furthermore, the dependence of a fluctuations of the position and angle of the levitated graphene disk on the size and temperature is also explained.