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Melinte, Sorin; Freytag, Nicolas; Horvatić, M.; Berthier, Y.; Lévy, Laurent-Patrick; Bayot, Vincent; Shayegan, M.

doi:10.1103/physrevlett.84.354

Cited by 90 publications

(99 citation statements)

References 22 publications

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“…Other experiments using various experimental probes confirmed such findings and expanded on them [17,18,19]. Measurements of the heat capacity in multiple quantum wells showed a sharp heat capacity peak at T ∼ 40 mk near ν ∼ 1 which was interpreted as a possible transition between a liquid and lattice state of skyrmions [5,6].…”

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confidence: 54%

Evidence for Skyrmion Crystallization from NMR Relaxation Experiments

et al. 2005

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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/T1) 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 Rxx ≃ 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.PACS numbers: 73.43.Fj,75.30.Ds In his seminal work on nuclear matter more than forty years ago Skyrme showed that baryons emerge mathematically as a static solution of a meson field described by the so-called Skyrme Lagrangian [1]. His work provided the foundation for the quantum theory of solitons, and more recently found an interesting and a priori surprising connection to the physics of electrons confined to a twodimensional plane. In the presence of a strong perpendicular magnetic field, the orbital motion of these electrons is quantized into discrete Landau levels. When only the lowest of such level is almost completely occupied, the elementary excitations of the system become large topologically stable spin texture known as Skyrmions [2]. It was further proposed that at T=0 Skyrmions would localize on a square lattice [3]. This ground state represents a new type of magnetic ordering which possesses long-range orientation and positional order. This is the solid-state analogue of the Skyrmion crystal state which is used to describe dense nuclear matter using Skyrme's topological excitation model [4]. In this work, we present an extensive study of nuclear magnetic resonance (NMR) spin-lattice relaxation rate in the first Landau level of an extremely high-quality GaAs/AlGaAs sample. We find strong and enhanced relaxation in the limit of T → 0 and R xx → 0 where localization of electronic states occurs. This is consistent with previous measurements of the heat capacity in multiple quantum wells at very low temperatures [5,6], and with the predictions of a magnetic ground state containing a Skyrme crystal [7].Several theoretical publications [2,3,7,8,9,10,11,12] have pointed toward the existence of Skyrmions in a twodimensional electron gas (2DEG). At filling factor ν = 1, where ν is defined by the ratio of the electronic density n to the magnetic flux density, ν = n B/Φ = nh eB , the quantized Hall state is ferromagnetic. For sufficiently small Zeeman-to-Coulomb energy ratio η = E z /E c = g ⋆ µB B e 2 /ǫlB , where g ⋆ is the electronic g-factor and l B = /eB is the magnetic length, Sondhi et al. showed that the low-lying excitations are not single spin-flips, but rather a smooth distortion of the spin field in which several spins (4-30) participate [2]. These Skyrmions are topologically stable, charged ±e, and gapped excitations which are the result of an energy tradeoff whe...

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confidence: 54%

Evidence for Skyrmion Crystallization from NMR Relaxation Experiments

et al. 2005

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“…This assumption seems reasonable for the QH state, and is indeed verified by numerical calculation [6]. We note, however, that because of the small g-factor in GaAs, a monolayer two-dimensional electron system (2DES) at ν = 1/2 is not fully spin polarized in the relevant magnetic field region, B 10 T [11,12,13]. Hence, if the bilayer ν = 1 compressible state consists of two indepen- * Present address: Institute of Applied Physics, Hamburg University, Jungiusstrasse 11, D-20355 Hamburg, Germany.…”

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confidence: 96%

“…The nuclear spin relaxation rate 1/T 1 thus probes the spectral density at zero energy of the electron spin system. While nuclear spins have often been used as a useful probe of the electron spin state, a small number of nuclei in contact with the 2DES and the overwhelming background due to the thick substrate have limited their applicability mostly to multilayer samples with fixed electron densities [13]. We here employed a current-pump and resistive-detection technique [14], which enables us to measure 1/T 1 in a single pair of fully-density-tunable 2DESs over a wide range of magnetic field.…”

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confidence: 99%

Spin Degree of Freedom in theν=1Bilayer Electron System Investigated by Nuclear Spin Relaxation

Kumada

Muraki

Hashimoto³

et al. 2005

Phys. Rev. Lett.

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The nuclear-spin-relaxation rate 1/T1 has been measured in a bilayer electron system at and around total Landau level filling factor ν = 1. The measured 1/T1, which probes electron spin fluctuations, is found to increase gradually from the quantum Hall (QH) state at low fields through a phase transition to the compressible state at high fields. Furthermore, 1/T1 in the QH state shows a small but noticeable increase away from ν = 1. These results demonstrate that, as opposed to common assumption, the electron spin degree of freedom is completely frozen neither in the QH nor compressible states.The bilayer electron system at total Landau level filling factor ν = 1 (1/2 in each layer) have been continuously drawing intensive research interest because of its unique phase diagram [1,2]. Two parameters play crucial role: the ratio of the intralayer to interlayer Coulomb interactions, given by the ratio between the interlayer distance d and the magnetic length l B = /eB (and hence controlled by the magnetic field B), and the tunneling gap ∆ SAS . For d/l B below a certain critical value, strong interlayer interactions lead to a many-body quantum Hall (QH) state even in the limit of zero tunneling gap, supported by spontaneous interlayer coherence [3]. When intralayer interactions dominate at larger d/l B , in contrast, the QH state collapses into a compressible state having lower intralayer correlation energy even for finite ∆ SAS [4]. Recent interests have focused on the nature of the phase transition between these limits. Interlayer tunneling [3] and Coulomb drag [5] experiments carried out on samples with vanishingly small ∆ SAS have revealed that below a critical d/l B the interlayer coherence develops somewhat continuously, in contrast to the result of a numerical study [6] that the transition is likely to be first order at any value of ∆ SAS . In spite of various theoretical models [7,8,9, 10] motivated by these findings, a comprehensive understanding is not yet achieved.In all these theories, it is routinely assumed that the spin degree of freedom is frozen by the Zeeman coupling to the magnetic field, and physics is governed solely by the pseudospin representing the layer degree of freedom. This assumption seems reasonable for the QH state, and is indeed verified by numerical calculation [6]. We note, however, that because of the small g-factor in GaAs, a monolayer two-dimensional electron system (2DES) at ν = 1/2 is not fully spin polarized in the relevant magnetic field region, B 10 T [11,12,13]. Hence, if the bilayer ν = 1 compressible state consists of two indepen- * Present address: Institute of Applied Physics, Hamburg University, Jungiusstrasse 11, D-20355 Hamburg, Germany. dent monolayers of 1/2 fillings, the phase transition must be accompanied by changes not only in the pseudospin but also in the spin configurations. While spin states in monolayer systems have been studied by various optical means [11], little is known about the spin states in bilayer systems, presumably because of the difficulty in i...

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“…In contrast to other quantitative measurements of P which use optical techniques [9], standard NMR is a quasiequilibrium probe of the 2DEG polarization and does not affect the electron system. At high T , where K S is small, we take advantage of the much shorter nuclear spin-lattice relaxation times T 1 of Ga nuclei in the QWs compared to those in the barriers in order to distinguish their contributions to the signal [5]. An NMR pulse-sequence first destroys the nuclear magnetization M 0 in the whole sample.…”

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confidence: 99%

“…At higher temperatures (1.5 K ≤ T ≤ 10 K), the NMR experiment was performed in a variable temperature insert as a function of T , B, and θ. At lower temperatures (40 mK ≤ T ≤ 1.5 K), the RF-coils were mounted at fixed θ into the mixing chamber of a dilution refrigerator.NMR is a very sensitive direct measurement of the spin polarization of 2D-electrons in the QWs, since the Fermi contact interaction H = 8π 3 |γ e |γ nh 2 ij S i · I j δ( r i − R j ) (γ is the gyromagnetic ratio) between itinerant electron spins S i at position r i and nuclear spins I j at R j shifts the resonance frequency of 71 Ga nuclei in the QWs by a magnetic hyperfine shift K S proportional to P [5,6,7]. The NMR signal from barriers (without electrons) remains unshifted and is used as a reference.…”

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New Phase Transition between Partially and Fully Polarized Quantum Hall States with Charge and Spin Gaps atν=23

et al. 2001

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The average electron spin-polarization P of two-dimensional electron gas confined in GaAs/GaAlAs multiple quantum-wells was measured by nuclear magnetic resonance (NMR) near the fractional quantum Hall state with filling factor ν = 2 3 . Above this filling factor ( 2 3 ≤ ν < 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 ν = 2 3 , where a quantum phase transition from a partially polarized (P ≈ 3 4 ) to a fully polarized (P = 1) state can be driven by increasing the ratio between the Zeeman and the Coulomb energy above a critical value ηc = ∆ Z ∆ C = 0.0185.The integer quantum Hall effect (QHE) occurs when the Landau level (LL) filling factor ν is an integer p and the lowest p LL's are filled [1]. However, if the Zeeman splitting ∆ Z = |g|µ B B is increased with respect to the LL spacinghω c (g = 0.44 is the electronic Landé factor in GaAs, µ B the Bohr magneton, B the magnetic field and ω c the cyclotron frequency), crossings of LL's with different spin states occur when k ·hω c = ∆ Z . If the level crossing occurs for LL's at the Fermi energy, the spin configuration of the electrons changes [2]. The fractional QHE (FQHE) occurs when ν = p 2mp±1 , where m = 1, 2 and can be visualized with the composite fermion (CF) model [3]. In this picture FQHE corresponds to integer QHE of CF's, where the CF-LL spacing is now determined by the Coulomb energy ∆ C = 1 4πǫ0ǫr e ℓB ∝ √ B ⊥ (ǫ 0 ǫ r is the permittivity GaAs, ℓ B = h/eB ⊥ is the magnetic length, the average distance of two electrons). Hence similar spin transitions do also occur in the FQHE. Since the relevant energy scales for CF's are the Zeeman and the Coulomb energies, the spin configuration of a 2DEG is mainly driven by the exchange part of the Coulomb energy (∝ √ B ⊥ ) at low B, whereas at large fields, the Zeeman energy (∝ B) favors spin-polarized states. For example, ν = 2 3 corresponds to two filled CF-LL's: only two states are possible, P = 0 at low B and P = 1 in the opposite limit. The transition between these states are controlled by the ratio η = ∆Z ∆C at a given ν. This ratio can be changed by varying the electron density (n) or by rotating the angle (θ) between the normal to the 2DEG and the applied magnetic field, keeping the perpendicular field B ⊥ constant (tilted field technique).In this Letter, we report an NMR observation of a phase transition between a new, partially polarized QH phase and the fully polarized high field phase at ν = 2 3 . The partially polarized phase has charge and spin gaps and is completely unexpected by theory. Furthermore, this is the first observation of a phase transition between QH states without the gap going through a minimum at the transition point.In this study, two GaAs/GaAlAs multiple (100) quantum well (QW) samples M280 (M242) with electron densities n = 8.5 · 10 10 (1.4 · 10 11 ) cm −2 and mobilities µ 0 = 7 · 10 5 (3 · 10 5 ) cm 2Vs have been used [4]. The w = 30 (25) nm wide GaAs QWs are ...

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NMR Determination of 2D Electron Spin Polarization atν=1/2

Cited by 90 publications

References 22 publications

Evidence for Skyrmion Crystallization from NMR Relaxation Experiments

Evidence for Skyrmion Crystallization from NMR Relaxation Experiments

Spin Degree of Freedom in theν=1Bilayer Electron System Investigated by Nuclear Spin Relaxation

New Phase Transition between Partially and Fully Polarized Quantum Hall States with Charge and Spin Gaps atν=23

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