The quantum Hall ferromagnet at high filling factors: A magnetic field induced Stoner transition

Spin splitting in the integer quantum Hall effect is investigated for a series of ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}∕\mathrm{GaAs}$ heterojunctions and quantum wells. Magnetoresistance measurements are performed at mK temperature to characterize the electronic density of states and estimate the strength of many body interactions. A simple model with no free parameters correctly predicts the magnetic field required to observe spin splitting, confirming that the appearance of spin splitting, is a result of a competition between the disorder induced energy cost of flipping spins and the exchange energy gain associated with the polarized state. In this model, the single particle Zeeman energy plays no role, so that the appearance of this quantum Hall ferromagnet in the highest occupied Landau level can also be thought of as a magnetic field induced Stoner transition.