Evidence for Ising Ferromagnetism and First-Order Phase Transitions in the Two-Dimensional Electron Gas

Abstract

The two-dimensional (2D) electron gas in the quantum Hall regime offers unique possibilities to study the impact of many-body correlations under well-controlled conditions. One of the fields to which quantum Hall effect studies are bringing new microscopic insight is ferromagnetism. At filling factor í = 1, for instance, the exchange interaction leads to an isotropic ferromagnetic ground state even in the limit of vanishing Zeeman energy[1]. Systems with two nearby 2D electron layers can develop at í = 1 ground states with spontaneous inter-layer coherence[2]. In these systems a pseudospin index can be associated to the layer and phase transitions between states with different pseudospin polarizations can be driven changing the level alignment of the two layers, e. g. by applying a bias potential or an in-plane magnetic field. This configuration led to the observation of soft collective excitations associated to a continuous (second order) quantum phase transition by resonant inelastic light scattering[3].

While continuous quantum phase transitions were recently observed and extensively studied[1], [4], till now no clear evidence of first-order transitions between Ising-ferromagnetic and paramagnetic ground states was reported. We shall present experimental evidence of such kind of phase transition in the two-dimensional electron gas formed in a wide GaAs/AlGaAs quantum well in the quantum-Hall regime at v = 2 and 4. Theoretical calculations based on local-density and Hartree- Fock approximations will also be presented providing quantitative agreement with experimental results.

Experimental evidence of a first-order phase transition was found in the longitudinal resistivity as a function of external magnetic and electric fields. Striking features associated to an anomalous evolution of integer quantum Hall minima developed at temperatures below 1 K when two Landau levels with opposite pseudospin (that originate from two different subbands) were brought close to resonance. Remarkably, at even values of n and low temperatures we observed a complete suppression of the quantum-Hall-state excitation gap correlating with the emergence of hysteretical behavior of the diagonal resistivity in up and down sweeps of the magnetic field. At these particular values of n, the two Landau levels with opposite pseudospin have also different spins. These observations demonstrate that crossing of these levels lead to the formation of easy-axis ferromagnetic states associated to a first-order phase transition. Detailed many-body calculations provide an unambiguous identification of the nature of the transition and allowed the determination of the exact properties of the electron ground states involved in the transition. We also investigated the temperature dependence of the observed hysteresis. These measurements displayed evidence of an additional finite-temperature transition at critical temperatures close to TC = 900 mK. These additional results suggest that large domains of particular pseudospin orientation lead to the hysteretic behavior and indicate that the finite-temperature properties of the spin-polarized 2D electron gas are similar to those of a classical Ising ferromagnet.