  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.
