MAGNETIZATION AND INCOMPRESSIBILITY OF A HIGH MOBILITY 2D ELECTRON GAS IN THE IQHE

We have measured the magnetization of a single layer, high mobility 2D electron gas in the quantum limit. 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 of the order of the cyclotron energy, in which a small fraction of the total number of states is present. The spin-splitting of the Landau levels is observed as well, in particular at ν=1, and gives a measure of the enhancement of the g-factor.