Magnetism of quantum Hall states

The most spectacular properties of the quantum Hall states are associated with charge transport and their longitudinal and transverse conductivities. However these correlated electron systems also display interesting magnetic properties which are coming under increasing experimental scrutiny. The spin properties of the simplest single layer quantum Hall states are dominated the ferromagnetic exchange interaction between the electrons. There is an interesting interplay between quantum and thermal fluctuations in these two-dimensional ferromagnets: the theory is discussed in paper 1 and compared with NMR experiments of S. E. Barrett et al., Physical Review Letters 74, 5112 (1995). Double layer quantum Hall states have an additional anti-ferromagnetic interaction between the two layers: the competing ferro- and antiferromangetic interactions lead to an interesting phase diagram as a function of layer separation, electron density, and applied magnetic field. These issues are discussed in papers 3, 4, 5, and the experimental observations are in V. Pellegrini et al., Science 281, 799 (1998).


  1. Continuum quantum ferromagnets at finite temperature and the quantum Hall effect, N. Read and S. Sachdev, Physical Review Letters 75, 3509 (1995); cond-mat/9507103.
  2. Zero temperature phase transitions in quantum Heisenberg ferromagnets, S. Sachdev and T. Senthil, Annals of Physics 251, 76 (1996); cond-mat/9602028.
  3. Double-layer quantum Hall antiferromagnetism at filling fractions 2/(odd integer), S. Das Sarma, S. Sachdev, and L. Zheng, Physical Review Letters 79, 917 (1997); cond-mat/9701142.
  4. Canted antiferromagnetic and spin singlet quantum Hall states in double-layer systems, S. Das Sarma, S. Sachdev, and L. Zheng, Physical Review B 58, 4672 (1998); cond-mat/9709315.
  5. Universal critical temperature for Kosterlitz-Thouless transitions in bilayer quantum magnets, M. Troyer and S. Sachdev, Physical Review Letters 81, 5418 (1998); cond-mat/9807393.
  6. Quantum Hall to insulator transition in the bilayer quantum hall ferromagnet, G. Murthy and S. Sachdev, Physical Review Letters 101, 226801 (2008); arXiv:0808.3702.