Torque magnetometry at low temperature and in high magnetic fields B is performed on MgZnO/ZnO heterostructures incorporating high-mobility two-dimensional electron systems. We find a sawtoothlike quantum oscillatory magnetization M(B), i.e., the de Haas-van Alphen (dHvA) effect. At the same time, nonequilibrium currents and unexpected spikelike overshoots in M are observed which allow us to identify the microscopic nature and density of the residual disorder. The acceptorlike scatterers give rise to a magnetic thaw down effect which enhances the dHvA amplitude beyond the electron-electron interaction effects being present in the MgZnO/ZnO heterostructures.