Evidence for Skyrmion Crystallization from NMR Relaxation Experiments

Abstract

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...

Landauer-Büttiker approach for hyperfine mediated electronic transport in the integer quantum Hall regime

“…The matrix Γ N M R (ξ) takes into account the net rate of transition between consecutive nuclear spin levels depending on the energy of the RF frequency photons ( ω) and is given by (details given in Appendix D): 26) with τ N M R being of the order of 100µs [4,5]. It can be shown that when η → 0, in the absence of RF field perturbation, (16) becomes identical to (8).…”

“…Using this approach, we show that the hysteresis noted in both the conductance and the RDNMR traces [3,11,18,19,[21][22][23][24][25][26] results from a lack of steady state between electronic transport and nuclear polarization evolution and can be explained by taking into account the finite rate of electron-nuclear spin flip-flops in a source limited channel in addition to a finite nuclear spin-lattice relaxation time. The self-consistent simulation framework between the nuclear spin dynamics and the edge state electronic transport developed here offers crucial insights into the dynamic nuclear polarization effects on electronic transport and in turn the electron-spin polarization effects on the nuclear spin dynamics.…”

“…Despite several advancements in the transport experiments involving such set ups, theoretical models for hyperfine interaction mediated edge transport through the QPC in the Hall geometry are clearly missing in the current literature. The object of this work is hence to develop transport models that couple the dynamics of the host nuclei with edge channel electronic transport as an attempt to fill this gap and theoretically interpret various experiments with specific focus on the conductance-voltage traces [3] and the RDNMR lineshapes [11,18,19,[21][22][23][24][25][26] . * bm@ee.iitb.ac.in…”

Spin and Charge Ordering in the Quantum Hall Regime

“…A similar behavior was observed by Tracy et al [194]. In contrast, Gervais et al found in the same temperature range an increased relaxation when cooling the system [195]. For small deviations from = 1, Fig.…”

Comparison of nuclear electric resonance and nuclear magnetic resonance in integer and fractional quantum Hall states

“…This interaction opened up opportunities to study quantum Hall states (QHSs) via nuclear magnetic resonance (NMR) spectra. For instance, the NMR combined with the resistance detection technique was used to investigate the dynamic nuclear spin polarization [1][2][3][4][5][6] and Skyrmion physics [7][8][9] in the quantum Hall effect (QHE) regime. NMR also allowed sensitive probing of the electron spin polarization of the QHE phases using the Knight shift of the resonance lines [10][11][12][13] and more recently probing of the local electron density in quantum solids.…”