Resistively detected nuclear magnetic resonance in the quantum hall regime: possible evidence for a Skyrme crystal

Wigner solids of domain wall skyrmions

Detection and characterization of a different type of topological excitations, namely the domain wall (DW) skyrmion, has received increasing attention because the DW is ubiquitous from condensed matter to particle physics and cosmology. Here we present experimental evidence for the DW skyrmion as the ground state stabilized by long-range Coulomb interactions in a quantum Hall ferromagnet. We develop an alternative approach using nonlocal resistance measurements together with a local NMR probe to measure the effect of low current-induced dynamic nuclear polarization and thus to characterize the DW under equilibrium conditions. The dependence of nuclear spin relaxation in the DW on temperature, filling factor, quasiparticle localization, and effective magnetic fields allows us to interpret this ground state and its possible phase transitions in terms of Wigner solids of the DW skyrmion. These results demonstrate the importance of studying the intrinsic properties of quantum states that has been largely overlooked.

Skyrmions, a topological spin texture, have been found in a variety of magnetic systems, including quantum hall ferromagnets. Here, Yang et al demonstrate the existence of skyrmions in domain walls in a quantum Hall ferromagnet, and suggest that these skyrmions form a 1D Wigner crystal.

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.

Role of chiral quantum Hall edge states in nuclear spin polarization

Resistively detected NMR (RDNMR) based on dynamic nuclear polarization (DNP) in a quantum Hall ferromagnet (QHF) is a highly sensitive method for the discovery of fascinating quantum Hall phases; however, the mechanism of this DNP and, in particular, the role of quantum Hall edge states in it are unclear. Here we demonstrate the important but previously unrecognized effect of chiral edge modes on the nuclear spin polarization. A side-by-side comparison of the RDNMR signals from Hall bar and Corbino disk configurations allows us to distinguish the contributions of bulk and edge states to DNP in QHF. The unidirectional current flow along chiral edge states makes the polarization robust to thermal fluctuations at high temperatures and makes it possible to observe a reciprocity principle of the RDNMR response. These findings help us better understand complex NMR responses in QHF, which has important implications for the development of RDNMR techniques.

Quantum Hall phases in two-dimensional systems have chiral edges, along which electrons propagate in one direction without backscattering. Here, the authors use nuclear magnetic resonance to demonstrate how chiral modes establish dynamical nuclear polarization in a quantum Hall ferromagnet.

Manipulation of a Nuclear Spin by a Magnetic Domain Wall in a Quantum Hall Ferromagnet

The manipulation of a nuclear spin by an electron spin requires the energy to flip the electron spin to be vanishingly small. This can be realized in a many electron system with degenerate ground states of opposite spin polarization in different Landau levels. We present here a microscopic theory of a domain wall between spin unpolarized and spin polarized quantum Hall ferromagnet states at filling factor two with the Zeeman energy comparable to the cyclotron energy. We determine the energies and many-body wave functions of the electronic quantum Hall droplet with up to N = 80 electrons as a function of the total spin, angular momentum, cyclotron and Zeeman energies from the spin singlet ν = 2 phase, through an intermediate polarization state exhibiting a domain wall to the fully spin-polarized phase involving the lowest and the second Landau levels. We demonstrate that the energy needed to flip one electron spin in a domain wall becomes comparable to the energy needed to flip the nuclear spin. The orthogonality of orbital electronic states is overcome by the many-electron character of the domain - the movement of the domain wall relative to the position of the nuclear spin enables the manipulation of the nuclear spin by electrical means.

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.

Electronic Magnetization of a Quantum Point Contact Measured by Nuclear Magnetic Resonance

We report an electronic magnetization measurement of a quantum point contact (QPC) based on nuclear magnetic resonance (NMR) spectroscopy. We find that NMR signals can be detected by measuring the QPC conductance under in-plane magnetic fields. This makes it possible to measure, from Knight shifts of the NMR spectra, the electronic magnetization of a QPC containing only a few electron spins. The magnetization changes smoothly with the QPC potential barrier height and peaks at the conductance plateau of 0.5×2e^{2}/h. The observed features are well captured by a model calculation assuming a smooth potential barrier, supporting a no bound state origin of the 0.7 structure.

W line shape in the resistively detected nuclear magnetic resonance

The resistively detected nuclear magnetic resonance (RDNMR) performed on a two-dimensional electron gas is known to exhibit a peculiar 'dispersive' line shape at some filling factors, especially around ν = 1. Here, we study in detail the inversion of the dispersive line shape as a function of the filling factor from ν = 1 to 2/3. The RDNMR spectra show a new characteristic W line shape in the longitudinal resistance, whereas dispersive lines detected in the Hall resistance remain unchanged. This W resonance, like the dispersive line, can be fitted correctly by a model of two independent response functions, which are the signatures of polarized and unpolarized electronic sub-systems.

Electron spin polarization by isospin ordering in correlated two-layer quantum Hall systems

Enhancement of the electron spin polarization in a correlated two-layer, two-dimensional electron system at a total Landau level filling factor of 1 is reported. Using resistively detected nuclear magnetic resonance, we demonstrate that the electron spin polarization of two closely spaced two-dimensional electron systems becomes maximized when interlayer Coulomb correlations establish spontaneous isospin ferromagnetic order. This correlation-driven polarization dominates over the spin polarizations of competing single-layer fractional quantum Hall states under electron density imbalances.

Probing the microscopic structure of the stripe phase at filling factor 5/2

A prominent manifestation of the competition between repulsive and attractive interactions acting on different length scales is the self-organized ordering of electrons in a stripelike fashion in material systems such as high-T_{c} superconductors. Such stripe phases are also believed to occur in two-dimensional electron systems exposed to a perpendicular magnetic field, where they cause a strong anisotropy in transport. The addition of an in-plane field even enables us to expel fractional quantum Hall states, to the benefit of such anisotropic phases. An important example represents the disappearance of the 5/2 fractional state. Here, we report the use of nuclear magnetic resonance spectroscopy to probe the electron density distribution of this emergent anisotropic phase. A surprisingly strong spatial density modulation was found. The observed behavior suggests a stripe pattern with a period of 2.6±0.6 magnetic lengths and an amplitude as large as 20% relative to the total density.

The quantum Hall effect at 5/2 filling factor

Experimental discovery of a quantized Hall state at 5/2 filling factor presented an enigmatic finding in an established field of study that has remained an open issue for more than twenty years. In this review we first examine the experimental requirements for observing this state and outline the initial theoretical implications and predictions. We will then follow the chronology of experimental studies over the years and present the theoretical developments as they pertain to experiments, directed at sets of issues. These topics will include theoretical and experimental examination of the spin properties at 5/2; is the state spin polarized? What properties of the higher Landau levels promote development of the 5/2 state, what other correlation effects are observed there, and what are their interactions with the 5/2 state? The 5/2 state is not a robust example of the fractional quantum Hall effect: what experimental and material developments have allowed enhancement of the effect? Theoretical developments from initial pictures have promoted the possibility that 5/2 excitations are exceptional; do they obey non-abelian statistics? The proposed experiments to determine this and their executions in various forms will be presented: this is the heart of this review. Experimental examination of the 5/2 excitations through interference measurements will be reviewed in some detail, focusing on recent results that demonstrate consistency with the picture of non-abelian charges. The implications of this in the more general physics picture is that the 5/2 excitations, shown to be non-abelian, should exhibit the properties of Majorana operators. This will be the topic of the last review section.

NMR probing of the spin polarization of the ν=5/2 quantum Hall state

Resistively detected nuclear magnetic resonance is used to measure the Knight shift of the 75As nuclei and determine the electron spin polarization of the fractional quantum Hall states of the second Landau level. We show that the 5/2 state is fully polarized within experimental error, thus confirming a fundamental assumption of the Moore-Read theory. We measure the electron heating under radio frequency excitation and show that we are able to detect NMR at electron temperatures down to 30 mK.

Low-frequency spin fluctuations in Skyrmions confined by wires: measurements of local nuclear spin relaxation

We investigate low-frequency electron spin dynamics in a quantum Hall system with wire confinement by nuclear spin relaxation measurements. We developed a technique to measure the local nuclear spin relaxation rate T(1)(-1). T(1)(-1) is enhanced on both sides of the local filling factor ν(wire)=1, reflecting low-frequency fluctuations of electron spins associated with Skyrmions inside the wire. As the wire width is decreased, the fast nuclear spin relaxation is suppressed in a certain range of Skyrmion density. This suggests that the multi-Skyrmion state is modified and the low-frequency spin fluctuations are suppressed by the wire confinement.

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.

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.

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.

NMR probing of spin excitations in the ring structure of a two-subband system

Resistively detected nuclear magnetic resonance (NMR) is observed inside the ringlike structure, with a quantized Hall conductance of 6e(2)/h, in the phase diagram of a two-subband electron system. The NMR signal persists up to 470 mK and is absent in other states with the same quantized Hall conductance. The nuclear spin-lattice relaxation time T1, is found to decrease rapidly towards the ring center. A strong dynamic nuclear polarization by the biasing current has also been observed only inside the ring. These observations are consistent with the assertion of the ringlike region being a ferromagnetic state that is accompanied by collective spin excitations.

Spin transition in the half-filled Landau level

The transition from partial to complete spin polarization of two-dimensional electrons at half filling of the lowest Landau level has been studied using resistively detected nuclear magnetic resonance (RDNMR). The nuclear spin-lattice relaxation time is observed to be density independent in the partially polarized phase but to increase sharply at the transition to full polarization. At low temperatures the RDNMR signal exhibits a strong maximum near the critical density.

Dynamic nuclear polarization and nuclear magnetic resonance in the vicinity of edge states of a 2DES in GaAs quantum wells

Nuclear magnetic resonance is detected via the in-plane conductivity of a two-dimensional electron system at unity Landau level filling factor in the regime of the quantum Hall effect in narrow and wide quantum wells. The NMR is spatially selective to nuclei with a coupling to electrons in the current carrying edge states at the perimeter of the 2DES. Interpretation of the electron-nuclear double resonance signals is facilitated by numerical simulations. A new RF swept method for conductivity-detected NMR is introduced which offers more efficient signal averaging. The method is applied to the study of electric quadrupole interactions, weakly allowed overtone transitions, and evaluation of the extent of electron wave function delocalization in the wide quantum well.

Electrical readout of the local nuclear polarization in the quantum Hall effect: a hyperfine battery

It is demonstrated that the now well-established "flip-flop" mechanism of spin exchange between electrons and nuclei in the quantum Hall effect can be reversed. We use a sample geometry which utilizes separately contacted edge states to establish a local nuclear spin polarization--close to the maximum value achievable--by driving a current between electron states of different spin orientation. When the externally applied current is switched off, the sample exhibits an output voltage of up to a few tenths of a mV, which decays with a time constant typical for the nuclear spin relaxation. The surprising fact that a sample with a local nuclear spin polarization can act as a source of energy and that this energy is well above the nuclear Zeeman splitting is explained by a simple model which takes into account the effect of a local Overhauser shift on the edge state reconstruction.

Evidence for skyrmion crystallization from NMR relaxation experiments

A resistively detected NMR technique was used to probe the two-dimensional electron gas in a GaAs/AlGaAs quantum well. The spin-lattice relaxation rate (1/T(1)) was extracted at near complete filling of the first Landau level by electrons. The nuclear spin of (75)As is found to relax much more efficiently with T --> 0 and when a well developed quantum Hall state with R(xx) approximately 0 occurs. The data show a remarkable correlation between the nuclear spin relaxation and localization. This suggests that the magnetic ground state near complete filling of the first Landau level may contain a lattice of topological spin texture, i.e., a Skyrmion crystal.

Gate control of dynamic nuclear polarization in GaAs quantum wells

Gate control of dynamic nuclear polarization under optical orientation is demonstrated in a Schottky-gated n-GaAs/AlGaAs (110) quantum well by time-resolved Kerr rotation measurements. Spin relaxation of electrons due to mechanisms other than the hyperfine interaction is effectively suppressed as the donor induced background electron density is reduced from metallic to insulating regimes. Subsequent accumulation of photoexcited electron spins dramatically enhances dynamic nuclear polarization at low magnetic field, allowing us to tune nuclear spin polarization by external gate voltages.

Spin transition in strongly correlated bilayer two-dimensional electron systems

Using a combination of heat pulse and nuclear magnetic resonance techniques, we demonstrate that the phase boundary separating the interlayer phase coherent quantum Hall effect at nu(T) = 1 in bilayer electron gases from the weakly coupled compressible phase depends upon the spin polarization of the nuclei in the host semiconductor crystal. Our results strongly suggest that, contrary to the usual assumption, the transition is attended by a change in the electronic spin polarization.

Local manipulation of nuclear spin in a semiconductor quantum well

The shaping of nuclear spin polarization profiles and the induction of nuclear resonances are demonstrated within a parabolic quantum well using an externally applied gate voltage. Voltage control of the electron and hole wave functions results in nanometer-scale sheets of polarized nuclei positioned along the growth direction of the well. Applying rf voltages across the gates induces resonant spin transitions of selected isotopes. This depolarizing effect depends strongly on the separation of electrons and holes, suggesting that a highly localized mechanism accounts for the observed behavior.

Microwave resonance of the 2D Wigner crystal around integer Landau fillings

We have observed a resonance in the real part of the finite frequency diagonal conductivity using microwave absorption measurements in high quality 2D electron systems near integer fillings. The resonance exists in some neighborhood of filling factor around corresponding integers and is qualitatively similar to previously observed resonance of weakly pinned Wigner crystal in high B and very small filling factor regime. Data measured around both nu=1 and nu=2 are presented. We interpret the resonance as the signature of the Wigner crystal state around integer Landau levels.