First-order phase transitions in a quantum Hall ferromagnet

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Abstract

The single-particle energy spectrum of a two-dimensional electron gas in a perpendicular magnetic field consists of equally spaced energy states, known as Landau levels. Each level is split owing to spin interactions, and its degeneracy is proportional to the magnetic field strength. When the ratio, ν (or ‘filling factor’), of the number of electrons and the degeneracy of a Landau level takes an integer or particular fractional values, quantum Hall effects1 occur, characterized by a vanishingly small longitudinal resistance and a quantized (transverse) Hall voltage2. The quantum Hall regime may be used for the controlled study of many-particle cooperative phenomena, such as order–disorder phase transitions (analogous to those observed in conventional magnets). Both isotropic and anisotropic ferromagnetic ground states have been predicted3,4,5,6,7,8 to occur in the quantum Hall regime, some of which have been investigated experimentally9,10,11,12,13 in samples with different geometries and filling factors. Here we report evidence for first-order phase transitions in quantum Hall states (ν = 2,4) confined to a wide gallium arsenide quantum well. We observe hysteresis and an anomalous temperature dependence in the longitudinal resistivity, indicative of a transition between two distinct ground states of an Ising quantum Hall ferromagnet. The microscopic origin of the anisotropy field is identified using detailed many-body calculations.

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Figure 1: Longitudinal resistivity as a function of the magnetic field and gate voltage.
Figure 2: Energy spectra and resistivity behaviour for ν = 2,4.
Figure 3: Resistivity traces.

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Acknowledgements

We thank M. Bichler for technical support during sample growth, and G. F. Giuliani for discussions. The work at Scuola Normale Superiore was funded in part by MURST. The work at Indiana University was supported by the NSF, and at Institute of Physics ASCR by the Ministry of Education of the Czech Republic and the Grant Agency of the Czech Republic.

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Correspondence to Vincenzo Piazza.

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Piazza, V., Pellegrini, V., Beltram, F. et al. First-order phase transitions in a quantum Hall ferromagnet. Nature 402, 638–641 (1999) doi:10.1038/45189

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