  Optical Faraday rotation is one of the most direct and practically important
manifestations of magnetically broken time-reversal symmetry. The rotation
angle is proportional to the distance traveled by the light, and up to now
sizeable effects were observed only in macroscopically thick samples and in
two-dimensional electron gases with effective thicknesses of several
nanometers. Here we demonstrate that a single atomic layer of carbon - graphene
- turns the polarization by several degrees in modest magnetic fields. The
rotation is found to be strongly enhanced by resonances originating from the
cyclotron effect in the classical regime and the inter-Landau-level transitions
in the quantum regime. Combined with the possibility of ambipolar doping, this
opens pathways to use graphene in fast tunable ultrathin infrared
magneto-optical devices.
