Quantum Hall ferromagnet at high filling factors: A magnetic-field-induced Stoner transition

Piot, B. A.; Maude, D. K.; Henini, M.; Wasilewski, Z. R.; Friedland, K.‐J.; Hey, R.; Ploog, K.; Toropov, A. I.; Airey, R.; Hill, G.

doi:10.1103/physrevb.72.245325

Cited by 40 publications

(45 citation statements)

References 31 publications

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“…Quantum Hall ferromagnetism was thus entirely absent in these experiments. This is almost certainly due to a collapse of the exchange gap responsible for quantum Hall ferromagnetism by strong disorder, a phenomenon that has been established both theoretically 15,32,33 and experimentally 34,35 . As discussed in the introduction, more recent experiments utilizing higher magnetic fields observed additional quantized Hall plateaus at ν = 0, ±1, and ±4.…”

Section: Experimental Relevance?mentioning

confidence: 89%

Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

2006

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Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field. Initially, we consider a clean graphene system within this effective theory and explore integer quantum Hall ferromagnetism stabilized by exchange from the long-range Coulomb repulsion. We study in detail the ground state and excitations at ν = 0 and ν = ±1, taking into account small symmetry-breaking terms that arise from the lattice-scale interactions, and also explore the ground states selected at ν = ±3, ±4, and ±5. We argue that the ferromagnetic regime may not yet be realized in current experimental samples, which at the above filling factors perhaps remain paramagnetic due to strong disorder. In an attempt to access the latter regime where the role of exchange is strongly suppressed by disorder, we apply Hartree theory to study the effects of interactions. Here, we find that Zeeman splitting together with symmetry-breaking interactions can in principle produce integer quantum Hall states in a paramagnetic system at ν = 0, ±1 and ±4, but not at ν = ±3 or ±5, consistent with recent experiments in high magnetic fields. We make predictions for the activation energies in these quantum Hall states which will be useful for determining their true origin.

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Section: Experimental Relevance?mentioning

confidence: 89%

Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

2006

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“…31 By contrast many of the measurements on systems such as GaAs are made under conditions where the single-particle splittings are considerably smaller than the broadening. 7,22,34,41 As a result the observation of spin split peaks is found to be critically dependent on the broadening and is less dependent on the magnitude of the single-particle splittings. 34,41 We speculate therefore that the large initial single-particle splittings and even larger total values including enhancement, may lead to significantly increased interaction effects due to the relatively smaller importance of disorder effects.…”

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confidence: 94%

“…7,22,34,41 As a result the observation of spin split peaks is found to be critically dependent on the broadening and is less dependent on the magnitude of the single-particle splittings. 34,41 We speculate therefore that the large initial single-particle splittings and even larger total values including enhancement, may lead to significantly increased interaction effects due to the relatively smaller importance of disorder effects. A further possibility which arises due to the narrow gap band structure is that the Rashba coupling may be interacting with the exchange effects to enhance one or other of the two terms.…”

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confidence: 94%

Giant enhanced g-factors in an InSb two-dimensional gas

et al. 2009

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We report measurements of the electron g-factor in InSb quantum wells using the coincidence technique, polarization transition, and temperature-dependent resistivity. All three methods show that there is a giant enhancement of the spin slitting which is proportional to the spin polarization. Electron Zeeman energies as high as 51 meV are measured leading to the conclusion that the additional contribution to the spin splitting is of order 30 meV, more than ten times larger than expected from conventional theories.

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“…The values used for Γ and X used in the calculation have been independently determined for this sample as explained in Ref. [8].…”

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confidence: 99%

Influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors

et al. 2007

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In a recent paper [Phys.Rev.B.72,245325(2005)], we have shown that the lifting of the electron spin degeneracy in the integer quantum Hall effect at high filling factors should be interpreted as a magnetic-field-induced Stoner transition. In this work we extend the analysis to investigate the influence of the single particle Zeeman energy on the quantum Hall ferromagnet at high filling factors. The single particle Zeeman energy is tuned through the application of an additional in-plane magnetic field. Both the evolution of the spin polarization of the system and the critical magnetic field for spin splitting are well-described as a function of the tilt angle of the sample in the magnetic field. The integer quantum Hall effect has historically been described within the framework of a single electron picture. Electron-electron interactions are then introduced as a correction, leading to enhanced spin gaps at odd filling factors. Clearly, from a perturbation theory point of view, this approach is wrong, at least for the most widely investigated GaAs system, for which the energy scale of the electron-electron interactions (e 2 /4πǫℓ B ) is more than an order of magnitude larger than the single particle Zeeman energy (g * µ B B). At high magnetic field (low filling factors), this has wide ranging consequences, with the observation of the itinerant quantum Hall ferromagnet, 1 with spin wave 2 or spin texture excitations 3 at filling factor ν = 1.The collapse of spin splitting at low magnetic fields (high filling factors) has been investigated experimentally 4,5,6 and theoretically. 7 Leadley and coworkers 6 showed that the critical filling factor for the collapse of spin splitting is found to increase with increasing tilt angle. The Zeeman energy, greatly enhanced at high tilt angles, favors the transition to a polarized state. This latter point is theoretically supported by the pioneering work of Fogler and Shklovskii, 7 who proposed an order parameter, δν, to quantitatively characterize the collapse of spin splitting. This order parameter corresponds to the filling factor difference between two consecutive resistance maxima in R xx (B), related to spin up and down sub-levels associated with a given Landau level. In the Fogler and Shklovskii model, the spin splitting (δν) collapses, when the disorder broadening of the Landau levels is comparable to the exchange enhanced spin gap.In an equivalent, but intuitively different approach, we have recently shown 8 that the appearance of spin splitting results from a competition between the disorder induced energy cost of flipping spins and the exchange energy gain associated with the polarized state. In this case the Zeeman energy plays no role, and the only effect of the magnetic field is to modify the density of states at the Fermi energy, essentially through the Landau level degeneracy eB/h. Here, we use the experimental behavior of the order parameter δν to probe the appearance of spin splitting in Al x Ga 1−x As/GaAs heterojunction (HJ) and quantum well (QW) structures....

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Quantum Hall ferromagnet at high filling factors: A magnetic-field-induced Stoner transition

Cited by 40 publications

References 31 publications

Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

Giant enhanced g-factors in an InSb two-dimensional gas

Influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors

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