Quantum Hall ferromagnetism in the presence of tunable disorder

In this Letter, we report our recent experimental results on the energy gap of the ν=1 quantum Hall state (Δ(ν=1)) in a quantum antidot array sample, where the effective disorder potential can be tuned continuously. Δ(ν=1) is nearly constant at small effective disorders, and collapses at a critical disorder. Moreover, in the weak disorder regime, Δ(ν=1) shows a B(total)(1/2) dependence in tilted magnetic field measurements, while in the strong disorder regime, Δ(ν=1) is linear in B(total), where B(total) is the total magnetic field at ν=1. We discuss our results within several models involving the quantum Hall ferromagnetic ground state and its interplay with sample disorder.