  We investigate the phase diagram of TmB4, an Ising magnet on a frustrated
Shastry-Sutherland lattice by neutron diffraction and magnetization
experiments. At low temperature we find Neel order at low field, ferrimagnetic
order at high field and an intermediate phase with magnetization plateaus at
fractional values M/Msat = 1/7, 1/8, 1/9 ... and spatial stripe structures.
Using an effective S = 1/2 model and its equivalent two-dimensional (2D)
fermion gas we suggest that the magnetic properties of TmB4 are related to the
fractional quantum Hall effect of a 2D electron gas.
