Quantum Hall Ferromagnets, Co-Operative Transport Anisotropy, and the Random Field Ising Model

Abstract

We discuss the behaviour of a quantum Hall system when two Landau levels with opposite spin and combined filling factor near unity are brought into energetic coincidence using an in-plane component of magnetic field. At coincidence, the system is an Ising pseudospin ferromagnet, since exchange energy is lowest when one or other Landau level is maximally occupied. At low temperature it has a transition between positive and negative pseudospin orientation which is driven by tilting the sample relative to the magnetic field. We focus on the interpretation of recent experiments under these conditions [Zeitler et al, Phys. Rev. Lett. 86, 866 (2001); Pan et al, Phys. Rev. B 64, 121305 (2001)], in which a large resistance anisotropy develops at the critical tilt angle, at low temperatures. We point out that sample surface roughness will generate a random field that couples to pseudospins. This random field has spatial correlations which are intrinsically anisotropic, even if surface roughness is isotropic, because the in-plane magnetic field component selects a direction. We suggest that transport anisotropy reflects domain formation induced by the random field, and use a model calculation to account by this mechanism for the observed magnitude of resistance anisotropy.Keywordsquantum Hall ferromagnettransport anisotropyLandau level coincidencerandom field Ising modelsurface roughness