First-Order Phase Transition in a Quantum Hall Ferromagnet

The single-particle energy spectrum of a two-dimensional electron gas in a perpendicular magnetic field consists of equally-spaced spin-split Landau levels, whose degeneracy is proportional to the magnetic field strength. At integer and particular fractional ratios between the number of electrons and the degeneracy of a Landau level (filling factors n) quantum Hall effects occur, characterised by a vanishingly small longitudinal resistance and quantised Hall voltage. The quantum Hall regime offers unique possibilities for the study of cooperative phenomena in many-particle systems under well-controlled conditions. Among the fields that benefit from quantum-Hall studies is magnetism, which remains poorly understood in conventional material. Both isotropic and anisotropic ferromagnetic ground states have been predicted and few of them have been experimentally studied in quantum Hall samples with different geometries and filling factors. Here we present evidence of first-order phase transitions in n = 2 and 4 quantum Hall states confined to a wide gallium arsenide quantum well. The observed hysteretic behaviour and anomalous temperature dependence in the longitudinal resistivity indicate the occurrence of a transition between the two distinct ground states of an Ising quantum-Hall ferromagnet. Detailed many-body calculations allowed the identification of the microscopic origin of the anisotropy field.