Pauli Spin Susceptibility of a Strongly Correlated Two-Dimensional Electron Liquid

Thermodynamic measurements reveal that the Pauli spin susceptibility of strongly correlated two-dimensional electrons in silicon grows critically at low electron densities—behavior that is characteristic of the existence of a phase transition.

Figure 1

Imaginary current component in the magnetization experiment as a function of the electron density in a magnetic field of 5 T and $T=0.4\mathrm{K}$. Grey area depicts the insulating phase. Magnetization vs $n_s$ is displayed in the inset. Note that the maximum $M$ is coincident within the experimental uncertainty with ${\mu }_B{n}_s$.

Figure 2

(a) The experimental $d\mu /dB$ as a function of electron density in different magnetic fields and $T=0.4\mathrm{K}$. The curves are vertically shifted for clarity. Grey area depicts the insulating phase. Note that the onset of full spin polarization in our experiment always takes place in the metallic regime. (b) Scaling of the $d\mu /dB$ curves, normalized by magnetic field magnitude, at high electron densities. The dashed line represents the “master curve.” Spin susceptibility obtained by integrating the master curve (dashed line) and raw data at $B=1.5$, 3, and 6 T is displayed in the inset.

Figure 3

(a) Magnetocapacitance vs electron density for different magnetic fields. (b) Deviation of the $C(n_s)$ dependences for different magnetic fields from the $B=0$ reference curve. The traces are vertically shifted for clarity. The onset of full spin polarization is indicated by arrows.

Figure 4

Dependence of the Pauli spin susceptibility on electron density obtained by all three methods described in text: integral of the master curve (dashed line), $d\mu /dB=0$ (circles), and magnetocapacitance (squares). The dotted line is a guide to the eye. Also shown by a solid line is the transport data of Ref. 7. Inset: polarization field as a function of the electron density determined from the magnetization (circles) and magnetocapacitance (squares) data. The symbol size for the magnetization data reflects the experimental uncertainty, and the error bars for the magnetocapacitance data extend to the middle of the jump in $C$. The data for $B_c$ are described by a linear fit which extrapolates to a density $n_{\chi }$ close to the critical density $n_c$ for the $B=0$ MIT.