Magnetization of an incompressible two-dimensional electron gas

We have measured the magnetization of several single layer, high mobility 2D electron gases, using an ultra-sensitive torque magnetometer. Sharp diamagnetic jumps in the magnetization are observed when an integer number of Landau levels is filled. We relate these jumps to incompressibility gaps in the energy spectrum on the order of the cyclotron energy, in which a small fraction of the total number of states is present. We show that a simple hypothesis for the density of states with almost no Landau level overlap accounts for the observed shape of the magnetization oscillations. The spin-splitting of the Landau levels is observed as well, in particular at v = 1, and gives a measure of the enhancement of the g-factor.