Magnetization of Interacting Electrons in Low-Dimensional Systems

In this article, we review selected experiments on the magnetization of low-dimensional electron systems in GaAs-based semiconductor heterostructures. The magnetization monitors the ground state energy of the electron system and is thus of fundamental interest. We discuss the experimental advances in highly sensitive magnetometry that made these experiments possible. Following a short introduction to magnetic quantum oscillations, i.e., the de Haas–van Alphen effect in two-dimensional electron systems, we review key experimental results with particular emphasis on the effects of electron–electron interaction in the regime of the integer and fractional quantum Hall effects. Magnetization experiments on quantum wires and quantum dots created by a top-down approach from two-dimensional systems highlight the effects of external confining potentials and the electron–electron interaction on the ground state energy.