Magnetization and Energy Gaps of a High-Mobility 2D Electron Gas in the Quantum Limit

We have measured the magnetization of several single-layer, high-mobility 2D electron gas AlGaAs-GaAs heterostructures in the quantum limit. Abrupt jumps in the magnetization are observed when an integer number of Landau levels is filled. The width and the magnitude of the jumps identify 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. Sizable magnetization steps associated with the spin splitting are observed at odd filling factors (including $\nu =1\mathrm{}$) and give a measure of the exchange enhancement of the spin splitting.