Interplay among spin, orbital effects, and localization in a GaAs two-dimensional electron gas in a strong in-plane magnetic field

The magnetoresistance of a low carrier density disordered GaAs based two-dimensional (2D) electron gas has been measured in parallel magnetic fields up to 32 T. The feature in the resistance associated with the complete spin polarization of the carriers shifts down by more than 20 T as the electron density is reduced, consistent with recent theories taking into account the enhancement of the electron-electron interactions at low densities. Nevertheless, the magnetic field for complete polarization, $B_p$, remains 2–3 times smaller than predicted for a disorder-free system. We show, in particular, by studying the temperature dependence of $B_p$ to probe the effective size of the Fermi sea that localization plays an important role in determining the spin polarization of a 2D electron gas.

Figure 1

(Color online) Longitudinal resistivity $\rho$ as a function of the parallel magnetic field for different electron densities $n_s$ in ${10}^{10}{\text{cm}}^{-2}$. $T=1.17\text{K}$. Inset: temperature dependence of $\rho \left(B_{\parallel }\right)$ at $n_s=4.94\times {10}^{10}{\text{cm}}^{-2}$.

Figure 2

(Color online) (a) Complete polarization field $B_p$ as a function of the electron density. Data at $T=1.17\text{K}$ and $T=4.2\text{K}$ from this work (open circles and open squares, respectively), and at $T=25\text{mK}$ from Refs. 3, 8 (solid left and right triangles, respectively.) Data at $T=1.17\text{K}$ plotted as a function of the “corrected” electron density (diamonds) (see text). Theoretical $T=0\text{K}$ calculations of the magnetic field for full spin polarization in a single-particle picture (solid line) and including many-body effects: RPA (Ref. 4) (thick solid line) and QMC (Ref. 9) (dotted line) (see text). (b) Temperature dependence of $B_p$ normalized with respect to the value at 1.17 K, measured for different densities given in ${10}^{10}{\text{cm}}^{-2}$ (symbols). Calculation in a single-particle picture for $n_s=0.5$, 2.1, and $5\times {10}^{10}{\text{cm}}^{-2}$ (dotted line) (see text).

Figure 3

(Color online) Resistivity $\rho$ in the high parallel field regime at $T=1.17\text{K}$, for different densities $n_s$ in $\times {10}^{10}{\text{cm}}^{-2}$ (symbols). $\text{ln}\left(\rho \right)\propto B^2$ (dashed lines) and qualitative trend combining spin and orbital effects (solid lines) (see text).