Magnetization of an incompressible two-dimensional electron gas

We have measured the magnetization of several single layer, high mobility 2 D electron gases, using an ultra-sensitive torque magnetometer. Sharp diama gnetic jumps in the magnetization are observed when an integer number of La ndau levels is filled. We relate these jumps to incompressibility gaps in t he energy spectrum on the order of the cyclotron energy, in which a small f raction of the total number of states is present. We show that a simple hyp othesis for the density of states with almost no Landau level overlap accou nts for the observed shape of the magnetization oscillations, The spin-spli tting of the Landau levels is observed as well, in particular at v = 1, and gives a measure of the enhancement of the g-factor. (C) 1998 Elsevier Scie nce B.V. All rights reserved.