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

Abstract

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....

Quantum electron transport in magnetically entangled subbands

“…The g-factor obtained from the angular evolution of MISO (see next section) is g MISO =0.15-0.25. The obtained g-factors are close to the bare g-factor in GaAs quantum wells 39,40 and significantly smaller the one obtained from QPMR 28 and SdH oscillations [41][42][43] in GaAs quantum well with a single populated subband. Figure 5(c) shows the angular dependence of the quantum scattering times τ (i)…”

Quantum Hall Ferromagnetism in the Presence of Tunable Disorder

“…[13] and experimentally examined in Ref. [26]. It is not known whether the same mechanism is also responsible for our observation at ¼ 1 in high magnetic fields, since only high Landau level fillings ( !…”

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

“…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.…”

“…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.…”