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We determined the nuclear-spin-lattice relaxation rate in the vicinity of the two-dimensional electrons in GaAs heterostructures at liquid-helium temperatures in the magnetic-field range 4 < B < 8.5 T. The occurring magnetoquantum oscillations are, by a model calculation, proved to be due to interaction between nuclear and 2D-electronic spins (Korringa relaxation), and give new information on the electronic density of states. PACS numbers: 72.20.My, 72.80.Ey, 76.30.Pk, 76.60.EsThe investigation of the nuclear-spin-relaxation in solids provides important information at low temperatures, especially about their electronic properties. 1,2 In this Letter, we demonstrate for the case of GaAs-Al x Gaix As heterostructures that this is also true for solids containing a two-dimensional electron gas (2DEG). 3 The experimental problem here is that there are only extremely few nuclei interacting with the 2DEG, whereas the overwhelming majority of nuclei in the bulk of the samples cannot interact with the electrons. Conventional methods for the investigation of nuclei interacting with a 2DEG are, therefore, not applicable. We solve these problems of sensitivity and selectivity by determining the nuclear-spin-lattice relaxation rate \/T\ (of the lattice nuclei 69 Ga, 71 Ga, 75 As) indirectly via ESR of 2D electrons. In the quantum Hall regime, this can be measured with an extreme sensitivity by studying the microwave-induced change of the magnetoresistivity p xx . 4 ESR yields information on the nuclear spins, since the actual ESR position B TCS depends on the nuclear-spin polarization (/>: The ESR line is shifted by the "Overhauser shift" B N =A{I)/gp B <*(l) (Ref. 1) [^ is the hyperfine structure constant, and gp B ^ -OApB (Ref. 4) is the effective magnetic moment of the electronic spin]. A nonequilibrium (/), thus, results in a nonequilibrium ESR position, which relaxes towards the equilibrium B TQS with the nuclear \/T\, and so allows us to determine l/T\ systematically as a function of the magnetic field B.Not only the Overhauser shift but also, as will be proven, the nuclear-spin-lattice relaxation is mediated, in our case, by the hyperfine interaction 1,2 AVS between the nuclear (I) and electronic (S) spins. The resulting Korringa relaxation rate \/T\ due to conduction electrons turns out to be proportional to the electronic spinspin correlation function. 5 Therefore, \/T\ undergoes magnetoquantum oscillations which have been analyzed for bulk conduction electrons in the case of InSb. 6 A similar Korringa relaxation for a strongly anisotropic 3D electronic system has been analyzed by Vagner and coworkers. 7 In the following, we will discuss nuclear-spin-

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The microwave-induced change of the magnetoresistivity of Gao.47In0. 53As-InP heterostructures reveals resonant structure which is attributed to electron-spin resonance of the two-dimensional conduction electrons. With microwave frequencies up to 480 GHz and in magnetic fields up to 12 T, we studied the spin splitting of the two lowest Landau levels in different samples. The spin splitting of these Landau levels is a quadratic function of the magnetic field and its extrapolation to zero magnetic field leads to vanishing spin splitting. The g factors depend on the magnetic field 8 and the Landau level N as follows: g(B,iV) gse(N+ -, ' )8, where gQ and c are sample-dependent parameters, which are of the order of go=4. 1 and c=0.08 T ', in the studied heterostructures.Electron-spin resonance (ESR), detected in the resonant change of the magnetoresist'ivity p"", turned out to be a worthwhile method for the investigation of g factors of the two-dimensional electron systems in GaAs-Al"-Gal "As heterostructures' and also in GaAs-Gal "In"P heterostructures.Together with the effective mass m the g factor determines the energy spectrum of a twodimensional electron gas (2D EG) in a perpendicular magnetic field B:Here, Ei is the subband energy, e is the elementary charge, 5 is Planck's constant, and pe is Bohr's magneton. N 0, 1,2, . . . is the Landau-level index and m, is the magnetic spin quantum number that takes the values m, + -, ' ("spin up") and m, --, ' ("spin down").Both m and g are not constants, but depend on the magnetic field and the Landau quantum number. For the g factor in GaAs-Al"Gal -"As heterostructures, it is well known that this is mainly due to the nonparabolicity of the GaAs conduction band and only to a negligible extent due to spin-orbit coupling in the electric field at the interface. Furthermore, the g factor is mainly determined by the GaAs properties, and not by those of the barrier material, as the electronic wave function enters only slightly into the barrier. In the material combination used in this Rapid Communication, the electrons are on the GaQ47Ino 53As side of the interface and the InP acts as the barrier. Therefore, the spin splitting of the 2D EG is expected to depend mainly on the properties of the GaQ471no 53As and especially on its g factor. There is, however, no certainty about this value up to now. The g factor for Gal "In"As has been experimentally determined only for 0~x~0.1 (Ref. 5) and x l. s For x 0.53, a simple linear interpolation between g -0.44 for GaAs and g -14.7 for InAs yields a g factor of g -8.0. The interpretation of electrorefiectance data in terms of a three-band k p theory gave g -3.38, and the interpretation of interband magnetoabsorption data resulted in g -4.5 (Ref.8) for Gao.471nQ. 53As. These different calculations are completed by an optically detected magnetic resonance study on a 15-nm-thick Gao47InQ 53As quantum well, layered between InP barriers, 9 where the g factor turned out to be i g i 5.6+0.3 (at B=0.1 T) for the optically excited two-dimensional ...