Spin Excitations of a Two-Dimensional Electron Gas in the Limit of Vanishing Landé g Factor

Robust Quantum Hall Ferromagnetism near a Gate-Tuned ν=1 Landau Level Crossing

In a low-disorder two-dimensional electron system, when two Landau levels of opposite spin or pseudospin cross at the Fermi level, the dominance of the exchange energy can lead to a ferromagnetic, quantum Hall ground state whose gap is determined by the exchange energy and has skyrmions as its excitations. This is normally achieved via applying either hydrostatic pressure or uniaxial strain. We study here a very high-quality, low-density, two-dimensional hole system, confined to a 30-nm-wide (001) GaAs quantum well, in which the two lowest-energy Landau levels can be gate tuned to cross at and near filling factor ν=1. As we tune the field position of the crossing from one side of ν=1 to the other by changing the hole density, the energy gap for the quantum Hall state at ν=1 remains exceptionally large, and only shows a small dip near the crossing. The gap overall follows a sqrt[B] dependence, expected for the exchange energy. Our data are consistent with a robust quantum Hall ferromagnet as the ground state.

Spontaneous Valley Polarization of Itinerant Electrons

Memory or transistor devices based on an electron's spin rather than its charge degree of freedom offer certain distinct advantages and comprise a cornerstone of spintronics. Recent years have witnessed the emergence of a new field, valleytronics, which seeks to exploit an electron's valley index rather than its spin. An important component in this quest would be the ability to control the valley index in a convenient fashion. Here we show that the valley polarization can be switched from zero to 1 by a small reduction in density, simply tuned by a gate bias, in a two-dimensional electron system. This phenomenon, which is akin to Bloch spin ferromagnetism, arises fundamentally as a result of electron-electron interaction in an itinerant, dilute electron system. Essentially, the kinetic energy favors an equal distribution of electrons over the available valleys, whereas the interaction between electrons prefers single-valley occupancy below a critical density. The gate-bias-tuned transition we observe is accompanied by a sudden, twofold change in sample resistance, making the phenomenon of interest for potential valleytronic transistor device applications. Our observation constitutes a quintessential demonstration of valleytronics in a very simple experiment.

Enhanced stability of quantum Hall skyrmions under radio-frequency radiations

We present in this paper the results from a recent study on the stability of the quantum Hall skyrmions state at a Landau level filling factor (ν) close to ν = 1 in a narrow GaAs quantum well. Consistent with previous work, a resonant behavior is observed in the resistively detected NMR measurements. In the subsequent current-voltage (I-V) measurements to examine its breakdown behavior under radio frequency radiations, we observe that the critical current assumes the largest value right at the ⁷⁵As nuclear resonant frequency. We discuss possible origin for this unexpectedly enhanced stability.

Spin-rotation mode in a quantum Hall ferromagnet

A spin-rotation mode emerging in a quantum Hall ferromagnet due to laser pulse excitation is studied. This state, macroscopically representing a rotation of the entire electron spin-system to a certain angle, is not microscopically equivalent to a coherent turn of all spins as a single-whole and is presented in the form of a combination of eigen quantum states corresponding to all possible S _z spin numbers. The motion of the macroscopic quantum state is studied microscopically by solving a non-stationary Schrödinger equation and by means of a kinetic approach where damping of the spin-rotation mode is related to an elementary process, namely, transformation of a 'Goldstone spin exciton' to a 'spin-wave exciton'. The system exhibits a spin stochastization mechanism (determined by spatial fluctuations of the Landé factor) ensuring damping, transverse spin relaxation, but irrelevant to decay of spin-wave excitons and thus not involving longitudinal relaxation, i.e. recovery of the S _z number to its equilibrium value.

Disorder-Induced Stabilization of the Quantum Hall Ferromagnet

We report on an absolute measurement of the electronic spin polarization of the ν=1 integer quantum Hall state. The spin polarization is extracted in the vicinity of ν=1 (including at exactly ν=1) via resistive NMR experiments performed at different magnetic fields (electron densities) and Zeeman energy configurations. At the lowest magnetic fields, the polarization is found to be complete in a narrow region around ν=1. Increasing the magnetic field (electron density) induces a significant depolarization of the system, which we attribute to a transition between the quantum Hall ferromagnet and the Skyrmion glass phase theoretically expected as the ratio between Coulomb interactions and disorder is increased. These observations account for the fragility of the polarization previously observed in high mobility 2D electron gas and experimentally demonstrate the existence of an optimal amount of disorder to stabilize the ferromagnetic state.

Skyrmions in a doped antiferromagnet

Magnetization and magnetoresistance have been measured in insulating antiferromagnetic La2Cu0.97Li0.03O4 over a wide range of temperatures, magnetic fields, and field orientations. The magnetoresistance step associated with a weak ferromagnetic transition exhibits a striking nonmonotonic temperature dependence, consistent with the presence of Skyrmions.

Quantum Hall ferromagnetism in the presence of tunable disorder

In this Letter, we report our recent experimental results on the energy gap of the ν=1 quantum Hall state (Δ(ν=1)) in a quantum antidot array sample, where the effective disorder potential can be tuned continuously. Δ(ν=1) is nearly constant at small effective disorders, and collapses at a critical disorder. Moreover, in the weak disorder regime, Δ(ν=1) shows a B(total)(1/2) dependence in tilted magnetic field measurements, while in the strong disorder regime, Δ(ν=1) is linear in B(total), where B(total) is the total magnetic field at ν=1. We discuss our results within several models involving the quantum Hall ferromagnetic ground state and its interplay with sample disorder.

Pinning-mode resonance of a Skyrme crystal near Landau-level filling factor ν=1

Microwave pinning-mode resonances found around integer quantum Hall effects, are a signature of crystallized quasiparticles or holes. Application of in-plane magnetic field to these crystals, increasing the Zeeman energy, has negligible effect on the resonances just below Landau-level filling ν=2, but increases the pinning frequencies near ν=1, particularly for smaller quasiparticle or hole densities. The charge dynamics near ν=1, characteristic of a crystal order, are affected by spin, in a manner consistent with a Skyrme crystal.

Ferromagnetic fractional quantum Hall states in a valley-degenerate two-dimensional electron system

We study a two-dimensional electron system where the electrons occupy two conduction band valleys with anisotropic Fermi contours and strain-tunable occupation. We observe persistent quantum Hall states at filling factors nu=1/3 and 5/3 even at zero strain when the two valleys are degenerate. This is reminiscent of the quantum Hall ferromagnet formed at nu=1 in the same system at zero strain. In the absence of a theory for a system with anisotropic valleys, we compare the energy gaps measured at nu=1/3 and 5/3 to the available theory developed for single-valley, two-spin systems, and find that the gaps and their rates of rise with strain are much smaller than predicted.

Hamiltonian theory of disorder at nu = 1/3

The Hamiltonian theory of the fractional quantum Hall regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this Letter we include disorder in our treatment and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures.

Optical absorption to probe the quantum Hall ferromagnet at filling factor nu=1

Optical absorption measurements are used to probe the spin polarization in the integer and fractional quantum Hall effect regimes. The system is fully spin polarized only at filling factor nu=1 and at very low temperatures ( approximately 40 mK). A small change in filling factor (deltanu approximately +/-0.01) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at nu=1 is surprisingly fragile against increasing temperature, or against small changes in filling factor.

Quantum Hall ferromagnetic states and spin-orbit interactions in the fractional regime

The competition between the Zeeman energy and the Rashba and Dresselhaus spin-orbit couplings is studied for fractional quantum Hall states by including correlation effects. A transition of the direction of the spin polarization is predicted at specific values of the Zeeman energy. We show that these values can be expressed in terms of the pair-correlation function, and thus provide information about the microscopic ground state. We examine the particular examples of the Laughlin wave functions and the 5/2-Pfaffian state. We also include effects of the nuclear bath.

Bosonization, coherent states and semiclassical quantum Hall skyrmions

We bosonize (2+1)-dimensional fermionic theory using coherent states. The gauge-invariant subspace of boson-Chern-Simons Hilbert space is mapped to fermionic Hilbert space. This subspace is then equipped with a coherent state basis. These coherent states are labelled by a dynamic spinor field. The label manifold could be assigned a physical meaning in terms of density and spin density. A path-integral representation of the evolution operator in terms of these physical variables is given. The corresponding classical theory when restricted to LLL is described by spin fluctuations alone and is found to be the NLSM with Hopf term. The formalism developed here is suitable to study quantum Hall skyrmions semiclassically and/or beyond the hydrodynamic limit. The effects of Landau level mixing or the presence of slowly varying external fields can also be easily incorporated.

Soft spin wave near nu=1: evidence for a magnetic instability in Skyrmion systems

The ground state of the two-dimensional electron gas near nu=1 is investigated by inelastic light scattering measurements carried down to very low temperatures. Away from nu=1, the ferromagnetic spin wave collapses and a new low-energy spin wave emerges below the Zeeman gap. The emergent spin wave shows soft behavior as its energy increases with temperature and reaches the Zeeman energy for temperatures above 2 K. The observed softening indicates an instability of the two-dimensional electron gas towards a magnetic order that breaks spin rotational symmetry. We discuss our findings in light of the possible existence of a Skyrme crystal.

Low-Frequency Spin Dynamics in a Canted Antiferromagnet

Resistively detected nuclear spin relaxation measurements in closely separated two-dimensional electron systems reveal strong low-frequency electron-spin fluctuations in the quantum Hall regime. As the temperature is decreased, the spin fluctuations, manifested by a sharp enhancement of the nuclear spin-lattice relaxation rate 1/T1, continue to grow down to the lowest temperature of 66 millikelvin. The observed divergent behavior of 1/T1 signals a gapless spin excitation mode and is a hallmark of canted antiferromagnetic order. Our data demonstrate the realization of a two-dimensional system with planar broken symmetry, in which fluctuations do not freeze out when approaching the zero temperature limit.

Observation of quantum Hall "valley Skyrmions"

We report measurements of the interaction-induced quantum Hall effect in a spin-polarized AlAs two-dimensional electron system where the electrons occupy two in-plane conduction band valleys. Via the application of in-plane strain, we tune the energies of these valleys and measure the energy gap of the quantum Hall state at filling factor nu = 1. The gap has a finite value even at zero strain and, with strain, rises much faster than expected from a single-particle picture, suggesting that the lowest energy charged excitations at nu = 1 are "valley Skyrmions."

Charge excitations in easy-axis and easy-plane quantum Hall ferromagnets

We study charge excitations in quantum Hall ferromagnets realized in a symmetric quantum well. Landau levels (LLs) with different subband and orbital indices crossing at the Fermi level act as up and down pseudospin levels. The activation energy measured as a function of the pseudospin Zeeman energy, Delta(Z), reveals easy-plane and easy-axis ferromagnetism for LL filling of nu = 3 and 4, respectively, for which the crossing levels have parallel and antiparallel spin. For nu = 4, we observe a sharp reduction in the gap for Delta(Z)-->0, which we discuss in terms of a topological excitation in domain walls akin to Skyrmions.

Spectroscopic evidence for the localization of Skyrmions near nu = 1 as T --> 0

Optically pumped nuclear magnetic resonance measurements of 71Ga spectra were carried out in an n-doped GaAs/Al(0.1)Ga0.9As multiple quantum well sample near the integer quantum Hall ground state nu = 1. As the temperature is lowered (down to T approximately 0.3 K), a "tilted plateau" emerges in the Knight shift data, which is a novel experimental signature of quasiparticle localization. The dependence of the spectra on both T and nu suggests that the localization is a collective process. The frozen limit spectra appear to rule out a 2D lattice of conventional Skyrmions.

Spin-orbit coupling effect on quantum hall ferromagnets with vanishing zeeman energy

We present the phase diagram of a ferromagnetic nu = 2N+1 quantum Hall liquid in a narrow quantum well with vanishing single-particle Zeeman splitting, varepsilon(Z), and a pronounced spin-orbit coupling. Upon decreasing varepsilon(Z) the spin-polarization field of a liquid takes, first, the easy-axis configuration, followed by the formation of a helical state which affects the transport and NMR properties of a liquid and the form of topological defects in it.