First-order phase transitions 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 energy states, know n as Landau levels. Each level is split owing to spin interactions, and its degeneracy is proportional to the magnetic field strength. When the ratio, v (or 'filling factor'), of the number of electrons and the degeneracy of a Landau level takes an integer or particular fractional values, quantum Ha ll effects(1) occur, characterized by a vanishingly small longitudinal resi stance and a quantized (transverse) Hall voltage(2). The quantum Hall regim e may be used for the controlled study of many-particle cooperative phenome na, such as order-disorder phase transitions (analogous to those observed i n conventional magnets). Both isotropic and anisotropic ferromagnetic groun d states have been predicted(3-8) to occur in the quantum Hall regime, some of which have been investigated experimentally(9-13) in samples with diffe rent geometries and filling factors. Here we report evidence for first-orde r phase transitions in quantum Hall states (v = 2, 4) confined to a wide ga llium arsenide quantum well. We observe hysteresis and an anomalous tempera ture dependence in the longitudinal resistivity, indicative of a transition between two distinct ground states of an Ising quantum Hall ferromagnet. T he microscopic origin of the anisotropy field is identified using detailed many-body calculations.