Spin Susceptibility of Two-Dimensional Electrons in Narrow AlAs Quantum Wells

We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a $45\AA$ wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to two-dimensional electrons in Si-MOSFETs but with only one valley occupied. We observe an enhancement of the spin susceptibility over the band value that increases as the density is decreased, following closely the prediction of quantum Monte Carlo calculations and continuing at finite values through the metal-insulator transition.

Figure 1

Longitudinal resistivity (${\rho }_{xx}$) for sample A1 at $n=5.55\times {10}^{11}{\mathrm{cm}}^{-2}$. Inset: temperature dependence of the amplitude ($\Delta {\rho }_{xx}$) of SdH oscillations, normalized to the zero-field resistivity (${\rho }_0$), at $\nu =7$ for samples A1 ($n=1.82\times {10}^{11}{\mathrm{cm}}^{-2}$, $\mu =4.7{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$) and A3 ($n=1.89\times {10}^{11}{\mathrm{cm}}^{-2}$, $\mu =3.3{\mathrm{m}}^2/\mathrm{V}\mathrm{s}$). The Dingle fits give effective masses of 0.45 and 0.30, respectively.

Figure 2

Parallel-field magnetoresistance at a fixed density for different temperatures. A field-induced transition from metallic to insulating behavior occurs at 7.7 T, and the 2DES becomes fully spin polarized at $B_P=10.1\mathrm{T}$ (vertical arrow). Inset: measured spin polarization fields ($B_P$) vs density for samples A1 (up triangles), A3 (down triangles), and B1 (circles). The solid curve represents the QMC prediction for $B_P$, and the dotted line represents the zero-field metal-insulator transition (MIT) observed in our samples.

Figure 3

Strength of SdH minima as a function of tilt angle for several different filling factors. LL crossings are indicated by dashed lines, with the even fillings experiencing a crossing at ${\theta }_c=57.7°$ and the odd at $74.7°$. Inset: dependence of the LL crossing angle, ${\theta }_c$, on crossing index, $i$.

Figure 4

Shown as a function of density are (a) spin susceptibility, (b) effective mass, and (c) mobility. In all plots, up triangles correspond to sample A1, squares to A2, down triangles to A3, and circles to B1. The QMC prediction of $g^{*}{m}^{*}$ at zero (dotted line) and full (solid line) polarization is included in (a). The vertical dashed line indicates the density corresponding to the zero-field MIT.