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TWO-DIMENSIONAL ELECTRON GAS 2009Dispersive line shape of the resistively detected NMR on either side of fillingfactor ν = 1The resistively detected nuclear magnetic resonance (RD-NMR) technique is a tool which allows the detection of theresonant excitation of nuclear spins using electrical measurement.This technique is especially well suited to probeNMR in high mobility two-dimensional electron gases inthe quantum Hall regime, over a wide range of filling factors.The underlying effect is the hyperfine interactionwhich couples the nuclear and electronic spins. At the resonantradio-frequency (RF) field, the nuclear spin magnetizationis reduced which, through the hyperfine interaction,leads to a change in the apparent magnetic field seen bythe electron spins. The resulting variation of the electronicZeeman energy leads to a change in the sample resistance.Early measurements performed on GaAs/AlGaAs heterostructuresrevealed anomalous RDNMR lines characterizedby a dispersive-like shape which occur on each sideof filling factor ν = 1 [Desrat et al. Phys. Rev. Lett. 88,256807 (2002)]. Such a line shape, composed of a negativeand a positive response of the resistance cannot be explainedby a simple uniform Zeeman energy change only.The origin of the anomalous line shape remains the subjectof debate. Two main ideas have arisen linking the line shapeto, (i)the contribution of domains with different electronicpolarizations or (ii) the role of thermal effects (heating).The latter was supported by the inversion of the RDNMRdispersive lineshape observed between ν = 1 and ν = 2/3which coincided with the change in sign of dR xx /dT .temperature increase leads to a negative (positive) ∆R xy onthe low (high) field side of ν = 1. For R xx a sign changeoccurs on each side of ν = 1. The magnetic fields forwhich ∆R xx has extrema are the fields previously introduced(B = 5.3, 5.525, 7.7 and 8 T) and labelled a, b, c and d,respectively. The comparison between the dispersive RD-NMR shapes and the sign of dR/dT shows that the minmax(max-min) shapes always correspond to positive (negative)dR/dT . This is verified for both the longitudinal andthe Hall resistance.This result strongly suggests that thermal effects play a rolein the anomalous RDNMR lineshape and that the Zeemanenergy change is not the unique contribution at the resonantRF field.Here we report similar measurements but extended to bothsides of filling factor ν = 1 and to both longitudinal and Hallresistances. The eight bottom graphs in figure34 representRDNMR lines measured either in R xx or in R xy at four differentincreasing magnetic fields, B = 5.3, 5.525, 7.7 and8 T, labeled a, b, c and d, respectively. Cases a and b areon the low field side of ν = 1 (i.e. between ν = 4/3 and1), while cases c and d are on the high field side, towardsν = 2/3. All spectra show dispersive-like shapes but someconsist of a resistance minimum followed by a maximumwith increasing RF, or inversely a maximum followed bya minimum with increasing RF. The min-max shape is observedin R xx for cases b and c and in R xy for cases c andd.Now we turn to the temperature dependence of the R xx (B)and R xy (B) curves traced in the top graph of figure34. Onesees that a slight increase of the temperature, from T = 60mK to T = 70 mK, leads to a narrower plateau in R xy anda narrower dissipationless region in R xx . The resulting resistancechanges ∆R xx and ∆R xy are plotted in the middlegraph by dashed and solid lines respectively. We see that aFigure 34: (Top) R xx and R xy as a function of B for two differenttemperatures T = 60 mK (solid) and T = 70 mK (dash). (Middle)Resistance change ∆R = R 70 mK − R 60 mK vs B for the longitudinal(dash) and Hall resistances (solid). (Bottom) RDNMR spectrameasured in R xx and R xy at the magnetic fields indicated above,respectively). All spectra are plotted over a range of 100 kHz.B.A. Piot, D.K. MaudeW. Desrat (GES-UM2, Montpellier), Z. R. Wasilewski (Institute of Microstructural Sciences, NRC, Ottawa)28