Evidence for a spin transition in the nu =2/3 fractional quantum Hall effect

Excitons in the fractional quantum Hall effect

Excitons, Coulomb-driven bound states of electrons and holes, are typically composed of integer charges1,2. However, in bilayer systems influenced by charge fractionalization3,4, a more interesting form of interlayer exciton can emerge, in which pairing occurs between constituents that carry fractional charges. Despite numerous theoretical predictions for these fractional excitons5-16, their experimental observation has remained unexplored. Here we report transport signatures of excitonic pairing in fractional quantum Hall effect states. By probing the composition of these excitons and their impact on the underlying wavefunction, we discover two new types of quantum phases of matter. One of these can be viewed as the fractional counterpart of the exciton condensate at a total filling of 1, whereas the other involves a more unusual type of exciton that obeys non-bosonic quantum statistics, challenging the standard model of bosonic excitons.

Unusual Quasiparticles and Tunneling Conductance in Quantum Point Contacts in ν=2/3 Fractional Quantum Hall Systems

Understanding topological matter in the fractional quantum Hall (FQH) effect requires identifying the nature of edge state quasiparticles. FQH edge state at the filling factor ν=2/3 in the spin-polarized and unpolarized phases is represented by the two modes of composite fermions (CF) with the parallel or opposite spins described by the chiral Luttinger liquids. Tunneling through a quantum point contact (QPC) between different or similar spin phases is solved exactly. With the increase of the applied voltage, the QPC conductance grows from zero and saturates at e^{2}/2h while a weak electron tunneling between the edge modes with the same spin transforms into a backscattering carried by the charge q=e/2 quasiparticles. These unusual quasiparticles and conductance plateau emerge when one or two CF spin-polarized modes in the QPC tunnel into a single mode. We propose experiments on the applied voltage and temperature dependence of the QPC conductance and noise that can shed light on the nature of edge states and FQH transport.

Half-Integer Conductance Plateau at the ν=2/3 Fractional Quantum Hall State in a Quantum Point Contact

The ν=2/3 fractional quantum Hall state is the hole-conjugate state to the primary Laughlin ν=1/3 state. We investigate transmission of edge states through quantum point contacts fabricated on a GaAs/AlGaAs heterostructure designed to have a sharp confining potential. When a small but finite bias is applied, we observe an intermediate conductance plateau with G=0.5(e^{2}/h). This plateau is observed in multiple QPCs, and persists over a significant range of magnetic field, gate voltage, and source-drain bias, making it a robust feature. Using a simple model that considers scattering and equilibration between counterflowing charged edge modes, we find this half-integer quantized plateau to be consistent with full reflection of an inner counterpropagating -1/3 edge mode while the outer integer mode is fully transmitted. In a QPC fabricated on a different heterostructure which has a softer confining potential, we instead observe an intermediate conductance plateau at G=(1/3)(e^{2}/h). These results provide support for a model at ν=2/3 in which the edge transitions from a structure having an inner upstream -1/3 charge mode and outer downstream integer mode to a structure with two downstream 1/3 charge modes when the confining potential is tuned from sharp to soft and disorder prevails.

Size dependence- and induced transformations- of fractional quantum Hall effects under tilted magnetic fields

Two-dimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electron-spin, is removed by a small Zeeman spin splitting, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g \mu _B B$$\end{document}gμBB, comparable to the correlation energy. Then, a change of the Zeeman splitting relative to the correlation energy can lead to a re-ordering between spin polarized, partially polarized, and unpolarized many body ground states at a constant filling factor. We show here that tuning the spin energy can produce fractionally quantized Hall effect transitions that include both a change in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu$$\end{document}ν for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{xx}$$\end{document}Rxx minimum, e.g., from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu = 11/7$$\end{document}ν=11/7 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu = 8/5$$\end{document}ν=8/5, and a corresponding change in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{xy}$$\end{document}Rxy, e.g., from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{xy}/R_{K} = (11/7)^{-1}$$\end{document}Rxy/RK=(11/7)-1 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{xy}/R_{K} = (8/5)^{-1}$$\end{document}Rxy/RK=(8/5)-1, with increasing tilt angle. Further, we exhibit a striking size dependence in the tilt angle interval for the vanishing of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu = 4/3$$\end{document}ν=4/3 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu = 7/5$$\end{document}ν=7/5 resistance minima, including “avoided crossing” type lineshape characteristics, and observable shifts of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{xy}$$\end{document}Rxy at the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{xx}$$\end{document}Rxx minima- the latter occurring for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu = 4/3, 7/5$$\end{document}ν=4/3,7/5 and the 10/7. The results demonstrate both size dependence and the possibility, not just of competition between different spin polarized states at the same \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu$$\end{document}ν and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{xy}$$\end{document}Rxy, but also the tilt- or Zeeman-energy-dependent- crossover between distinct FQHE associated with different Hall resistances.

Marginal metallic state at a fractional filling of '8/5' and '4/3' of Landau levels in the GaAs/AlGaAs 2D electron system

A metallic state with a vanishing activation gap, at a filling factor [Formula: see text] in the untilted specimen with [Formula: see text], and at [Formula: see text] at [Formula: see text] under a [Formula: see text] tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest, remarkably, that at the possible degeneracy point of states with different spin polarization, where the 8/5 or 4/3 FQHE vanish, there occurs a peculiar marginal metallic state that differs qualitatively from a quantum Hall insulating state and the usual quantum Hall metallic state. Such a marginal metallic state occurs most prominently at [Formula: see text], and at [Formula: see text] under tilt as mentioned above, over the interval [Formula: see text], that also includes the [Formula: see text] state, which appears perceptibly gapped in the first instance.

Piezo-driven sample rotation system with ultra-low electron temperature

Piezo-driven rotator is convenient for tilted magnetic field experiments due to its precise angle control. However, the rotator itself and the sample mounted on it are difficult to be cooled down because of extra heat leaks and presumably bad thermal contacts from the piezo. Here, we report a piezo-driven sample rotation system designed for ultra-low temperature environment. The sample, as well as the rotating sample holder, can be cooled to as low as 25 mK by customized thermal links and thermal contacts. More importantly, the electron temperature in the electrical transport measurements can also be cooled down to 25 mK with the help of home-made filters. To demonstrate the application of our rotation system at ultra-low electron temperature, a measurement revealing tilt-induced localization and delocalization in the second Landau level of two-dimensional electron gas is provided.

Counter-propagating charge transport in the quantum Hall effect regime

The quantum Hall effect, observed in a two-dimensional (2D) electron gas subjected to a perpendicular magnetic field, imposes a 1D-like chiral, downstream, transport of charge carriers along the sample edges. Although this picture remains valid for electrons and Laughlin's fractional quasiparticles, it no longer holds for quasiparticles in the so-called hole-conjugate states. These states are expected, when disorder and interactions are weak, to harbor upstream charge modes. However, so far, charge currents were observed to flow exclusively downstream in the quantum Hall regime. Studying the canonical spin-polarized and spin-unpolarized v = 2/3 hole-like states in GaAs-AlGaAs heterostructures, we observed a significant upstream charge current at short propagation distances in the spin unpolarized state.

Polaron Polaritons in the Integer and Fractional Quantum Hall Regimes

Elementary quasiparticles in a two-dimensional electron system can be described as exciton polarons since electron-exciton interactions ensures dressing of excitons by Fermi-sea electron-hole pair excitations. A relevant open question is the modification of this description when the electrons occupy flat bands and electron-electron interactions become prominent. Here, we perform cavity spectroscopy of a two-dimensional electron system in the strong coupling regime, where polariton resonances carry signatures of strongly correlated quantum Hall phases. By measuring the evolution of the polariton splitting under an external magnetic field, we demonstrate the modification of polaron dressing that we associate with filling factor dependent electron-exciton interactions.

Light-Induced Fractional Quantum Hall Phases in Graphene

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

Mesoscopic Transport in Electrostatically Defined Spin-Full Channels in Quantum Hall Ferromagnets

In this work, we use electrostatic control of quantum Hall ferromagnetic transitions in CdMnTe quantum wells to study electron transport through individual domain walls (DWs) induced at a specific location. These DWs are formed due to the hybridization of two counterpropagating edge states with opposite spin polarization. Conduction through DWs is found to be symmetric under magnetic field direction reversal, consistent with the helical nature of these DWs. We observe that long domain walls are in the insulating regime with a localization length of 4-6  μm. In shorter DWs, the resistance saturates to a nonzero value at low temperatures. Mesoscopic resistance fluctuations in a magnetic field are investigated. The theoretical model of transport through impurity states within the gap induced by spin-orbit interactions agrees well with the experimental data. Helical DWs have the required symmetry for the formation of synthetic p-wave superconductors. The achieved electrostatic control of a single helical domain wall is a milestone on the path to their reconfigurable network and ultimately to a demonstration of the braiding of non-Abelian excitations.

Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect

The spin transitions in the fractional quantum Hall effect provide a direct measure of the tiny energy differences between differently spin-polarized states and thereby serve as an extremely sensitive test of the quantitative accuracy of the theory of the fractional quantum Hall effect, and, in particular, of the role of Landau-level mixing in lifting the particle-hole symmetry. We report on an accurate quantitative study of this physics, evaluating the effect of Landau-level mixing in a nonperturbative manner using a fixed-phase diffusion Monte Carlo method. We find excellent agreement between our calculated critical Zeeman energies and the experimentally measured values. In particular, we find, as also do experiments, that the critical Zeeman energies for fractional quantum Hall states at filling factors ν=2-n/(2n±1) are significantly higher than those for ν=n/(2n±1), a quantitative signature of the lifting of particle-hole symmetry due to Landau-level mixing.

Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet

In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back locally, modifying the local electronic Zeeman energy. Here we report a nonlocal effect arising from the interplay between nuclear polarization and the spatial structure of electronic domains in a ν=2/3 fractional quantum Hall state. In our experiments, we use a quantum point contact to locally control and probe the domain structure of different spin configurations emerging at the spin phase transition. Feedback between nuclear and electronic degrees of freedom gives rise to memristive behavior, where electronic transport through the quantum point contact depends on the history of current flow. We propose a model for this effect which suggests a novel route to studying edge states in fractional quantum Hall systems and may account for so-far unexplained oscillatory electronic-transport features observed in previous studies.

Cavity quantum electrodynamics with many-body states of a two-dimensional electron gas

Light-matter interaction has played a central role in understanding as well as engineering new states of matter. Reversible coupling of excitons and photons enabled groundbreaking results in condensation and superfluidity of nonequilibrium quasiparticles with a photonic component. We investigated such cavity-polaritons in the presence of a high-mobility two-dimensional electron gas, exhibiting strongly correlated phases. When the cavity was on resonance with the Fermi level, we observed previously unknown many-body physics associated with a dynamical hole-scattering potential. In finite magnetic fields, polaritons show distinct signatures of integer and fractional quantum Hall ground states. Our results lay the groundwork for probing nonequilibrium dynamics of quantum Hall states and exploiting the electron density dependence of polariton splitting so as to obtain ultrastrong optical nonlinearities.

Fractional quantum Hall phase transitions and four-flux states in graphene

Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=-1/2 and -1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches -1/2, suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.

Spin transition in the ν=8/3 fractional quantum Hall effect

We present here the results from a density dependent study of the activation energy gaps of the fractional quantum Hall effect states at Landau level fillings ν=8/3 and 7/3 in a series of high quality quantum wells. In the density range from 0.5×10(11) to 3×10(11) cm(-2), the 7/3 energy gap increases monotonically with increasing density, supporting its ground state being spin polarized. For the 8/3 state, however, its energy gap first decreases with increasing density, almost vanishes at n~0.8×10(11) cm(-2), and then turns around and increases with increasing density, clearly demonstrating a spin transition.

Observation of nonconventional spin waves in composite-fermion ferromagnets

We find unexpected low energy excitations of fully spin-polarized composite-fermion ferromagnets in the fractional quantum Hall liquid, resulting from a complex interplay between a topological order manifesting through new energy levels and a magnetic order due to spin polarization. The lowest energy modes, which involve spin reversal, are remarkable in displaying unconventional negative dispersion at small momenta followed by a deep roton minimum at larger momenta. This behavior results from a nontrivial mixing of spin-wave and spin-flip modes creating a spin-flip excitonic state of composite-fermion particle-hole pairs. The striking properties of spin-flip excitons imply highly tunable mode couplings that enable fine control of topological states of itinerant two-dimensional ferromagnets.

Piezoelectric rotator for studying quantum effects in semiconductor nanostructures at high magnetic fields and low temperatures

We report the design and development of a piezoelectric sample rotation system, and its integration into an Oxford Instruments Kelvinox 100 dilution refrigerator, for orientation-dependent studies of quantum transport in semiconductor nanodevices at millikelvin temperatures in magnetic fields up to 10 T. Our apparatus allows for continuous in situ rotation of a device through >100° in two possible configurations. The first enables rotation of the field within the plane of the device, and the second allows the field to be rotated from in-plane to perpendicular to the device plane. An integrated angle sensor coupled with a closed-loop feedback system allows the device orientation to be known to within ±0.03° while maintaining the sample temperature below 100 mK.

Dynamic nuclear polarization in the fractional quantum Hall regime

We investigate dynamic nuclear polarization in quantum point contacts (QPCs) in the integer and fractional quantum Hall regimes. Following the application of a dc bias, fractional plateaus in the QPC shift symmetrically about half filling of the lowest Landau level, ν=1/2, suggesting an interpretation in terms of composite fermions. Polarizing and detecting at different filling factors indicates that Zeeman energy is reduced by the induced nuclear polarization. Mapping effects from integer to fractional regimes extends the composite fermion picture to include hyperfine coupling.

Direct measurements of fractional quantum Hall effect gaps

We measure the chemical potential jump across the fractional gap in the low-temperature limit in the two-dimensional electron system of GaAs/AlGaAs single heterojunctions. In the fully spin-polarized regime, the gap for filling factor nu=1/3 increases linearly with the magnetic field and is coincident with that for nu=2/3, reflecting the electron-hole symmetry in the spin-split Landau level. In low magnetic fields, at the ground-state spin transition for nu=2/3, a correlated behavior of the nu=1/3 and nu=2/3 gaps is observed.

Tilt-induced localization and delocalization in the second Landau level

We have investigated the behavior of electronic phases of the second Landau level under tilted magnetic fields. The fractional quantum Hall liquids at nu=2+1/5 and 2+4/5 and the solid phases at nu=2.30, 2.44, 2.57, and 2.70 are quickly destroyed with tilt. This behavior can be interpreted as a tilt driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and a delocalization through the melting of solid phases in the top Landau level, respectively. The evolution towards the classical Hall gas of the solid phases is suggestive of antiferromagnetic ordering.

Cooper-pair tunneling in junctions of singlet quantum Hall States and superconductors

We propose tunnel junctions of a Hall bar and a superconducting lead for observing Cooper-pair tunneling into singlet fractional quantum Hall edge states. These tunnel junctions provide a natural means of extracting precise information of the spin polarization and the filling factor of the state. The low energy regime of one of the setups is governed by a novel quantum entangled fixed point.

Direct measurement of the g factor of composite fermions

The activation gap Delta of the fractional quantum Hall states at constant fillings nu=2/3 and 2/5 has been measured as a function of the perpendicular magnetic field B. A linear dependence of Delta on B is observed while approaching the spin-polarization transition. This feature allows a direct measurement of the g factor of composite fermions which appears to be heavily renormalized by interactions and strongly sensitive to the electronic filling factor.

Anomalous-filling-factor-dependent nuclear-spin polarization in a 2D electron system

Spin-related electronic phase transitions in the fractional quantum Hall regime are accompanied by a large change in resistance. Combined with their sensitivity to spin orientation of nuclei residing in the same plane as the 2D electrons, they offer a convenient electrical probe to carry out nuclear magnetometry. Despite conditions which should allow both electronic and nuclear-spin subsystems to approach thermodynamic equilibrium, we uncover for the nuclei a remarkable and strongly electronic filling-factor-dependent deviation from the anticipated thermal nuclear-spin polarization.

Phase diagram of interacting composite fermions in the bilayer nu=2/3 quantum hall effect

We study the phase diagram of composite fermions (CFs) in the presence of spin and pseudospin degrees of freedom in the bilayer nu=2/3 quantum Hall (QH) state. Activation studies elucidate the existence of three different QH states with two different types of hysteresis in the magnetotransport. While a noninteracting CF model provides a qualitative account of the phase diagram, the observed renormalization of tunneling gap and a non-QH state at high densities are not explained in the noninteracting CF model, and are suggested to be manifestations of interactions between CFs.

New phase transition between partially and fully polarized quantum Hall states with charge and spin gaps at nu = 2/3

The average electron spin polarization Rho of a two-dimensional electron gas confined in GaAs/GaAlAs multiple quantum wells was measured by NMR near the fractional quantum Hall state with filling factor nu = 2/3. Above this filling factor (2/3< or = nu < 0.85), a strong depolarization is observed corresponding to two spin flips per additional flux quantum. The most remarkable behavior of the polarization is observed at nu = 2/3, where a quantum phase transition from a partially polarized (Rho approximately 3/4) to a fully polarized (Rho = 1) state can be driven by increasing the ratio between the Zeeman and the Coulomb energy above a critical value eta(c) = Delta(Z)/Delta(C) = 0.0185.

Ising ferromagnetism and domain morphology in the fractional quantum Hall regime

The density driven quantum phase transition between the unpolarized and fully spin polarized nu = 2/3 fractional quantum Hall state is accompanied by hysteresis in accord with 2D Ising ferromagnetism and domain formation. The temporal behavior is reminiscent of the Barkhausen and time-logarithmic magnetic after-effects ubiquitous in familiar ferromagnets. It too suggests domain morphology and, in conjunction with NMR, intricate domain dynamics, which is partly mediated by the contact hyperfine interaction with nuclear spins of the host semiconductor.

Quantum hall ferromagnetism in a two-dimensional electron system

Experiments on a nearly spin degenerate two-dimensional electron system reveals unusual hysteretic and relaxational transport in the fractional quantum Hall effect regime. The transition between the spin-polarized (with fill fraction nu = 1/3) and spin-unpolarized (nu = 2/5) states is accompanied by a complicated series of hysteresis loops reminiscent of a classical ferromagnet. In correlation with the hysteresis, magnetoresistance can either grow or decay logarithmically in time with remarkable persistence and does not saturate. In contrast to the established models of relaxation, the relaxation rate exhibits an anomalous divergence as temperature is reduced. These results indicate the presence of novel two-dimensional ferromagnetism with a complicated magnetic domain dynamic.

NMR determination of 2D electron spin polarization at nu = 1/2

Using a "standard" NMR spin-echo technique we determined the spin polarization P of two-dimensional electrons, confined to GaAs quantum wells, from the hyperfine shift of Ga nuclei located in the wells. Concentrating on the temperature ( 0.05 less, similarT less, similar10 K) and magnetic field ( 7 less, similarB less, similar17 T) dependencies of P at Landau level filling factor nu = 1/2, we find that the results are described well by a simple model of noninteracting composite fermions, although some inconsistencies remain when the two-dimensional electron system is tilted in the magnetic field.