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TWO-DIMENSIONAL ELECTRON GAS 2009Spin polarisation of a disordered GaAs 2D electron gas in a strong in-planemagnetic fieldAn in-plane magnetic field couples to the spins of a 2Dsystem, and can thus be used to probe the impact of manybody effects on the ground state of the 2D electron gas (2-DEG). For example, the longitudinale resistance under parallelmagnetic field generally exhibits a saturation or a kinkfor a magnetic field B = B p signaling the complete spin polarizationof the 2D system [T. Okamoto et al., Phys. Rev.Lett. 82, 3875 (1999)].present in disordered systems and should under no circumstancesbe interpreted as evidence for a ferromagnetic instability.Using high magnetic fields up to 32 T, we report on the particularlyrich parallel field physics occurring in 2D electrongas in GaAs, revealing an interplay between these spin effects,disorder, and orbital effects. The magneto resistancekink usually associated with the 2-DEG complete spin polarizationis observed up to B p ∼ 30 T, and shifts down continuouslyon more than 20 T as the electron density (andconsequently mobility) is lowered in the sample (see figure37(a). This reduction of B p with decreasing electrondensity is consistent with the predicted electron-electron interactionenhancement of the spin susceptibility at low density,favoring the 2-DEG polarization. However, the absolutevalue of B p remains 2-3 times smaller than the one calculatedat T = 0K for a disorder-free system, and extrapolatesto B p = 0 at a relatively “high” electron density, whereno ferromagnetic states have ever been observed. We arguethis behaviour is due to the localization of electrons whichare subsequently subtracted from the total free carrier density[B.A. Piot et al. Phys. Rev. B 80, 115337 (2009)]. Inthis situation the Fermi sea appears effectively smaller andless magnetic field is required to fully polarize the system.This approach is motivated by the strong mobility dropmeasured as the electron density is decreased in this veryregion. The temperature dependence of B p , which dependson the effective size of the Fermi sea, corresponds to thepolarization of a smaller Fermi sea, and indicates that thefraction of localized states increases as the electron densityis reduced. From this temperature behavior, a density of delocalizedelectron can be estimated, and used to re-plot theexperimental B p of figure 37(b) (triangles), giving a betterquantitative agreement with theory.In summary, the magnetic field at which complete spin polarizationoccurs is dramatically reduced both by electronlocalization and electron-electron interaction enhanced atlow carrier density. The large value of the extrapolatedcarrier density for full spin polarization at zero magneticfield simply reflects the large number of localized electronsFigure 37: (a) Magneto resistance for different electron densities.(b) Field associated with the complete spin polarization B pas a function of the electron density (circles and squares), and asa function of the “corrected” electron density (triangles). TheoreticalT = 0 K calculations of the magnetic field for full spin polarizationincluding many-body effects: Random Phase Approximation(RPA) [Y. Zhang and S. D. Sarma, Phys. Rev. Lett. 96,196602 (2006)], and Quantum Monte Carlo Calculation (QMC)[A. L. Subasi and B. Tanatar, Phys. Rev. B 78, 155304 (2008)].B.A. Piot, D. K. MaudeU. Gennser, A. Cavanna, D. Mailly (Laboratoire de Photonique et de Nanostructures, Marcoussis, France)30