Magnetization of a Strongly Interacting Two-Dimensional Electron System in Perpendicular Magnetic Fields

We measure the thermodynamic magnetization of a low-disordered, strongly correlated two-dimensional electron system in silicon in perpendicular magnetic fields. A new, parameter-free method is used to directly determine the spectrum characteristics (Landé $g$ factor and the cyclotron mass) when the Fermi level lies outside the spectral gaps and the interlevel interactions between quasiparticles are avoided. Intralevel interactions are found to strongly modify the magnetization, without affecting the determined $g^{*}$ and $m^{*}$.

Figure 1

Out-of-phase (solid line) and in-phase (dotted line) current components as a function of the electron density in a perpendicular magnetic field of 5 T and $T=0.8\mathrm{K}$. $B_{\mathrm{mod}}=0.022\mathrm{T}$ and $f=0.45\mathrm{Hz}$. The value $d\mu /dB$ is indicated in units of the Bohr magneton ${\mu }_B$. In the right-hand inset, we demonstrate proportionality of $\mathrm{Im}i$ to frequency: the solid and dashed lines (vertically shifted for clarity) correspond to 0.45 and 0.1 Hz, respectively; the $y$ component of the latter is multiplied by 4.5. The left-hand inset illustrates magnetization per electron.

Figure 2

(a) Capacitance in $B=8\mathrm{T}$ and in $B=0$ as indicated. The (noise-averaged) geometric capacitance is depicted by a dashed line. (b) $\mathrm{Im}i\propto d\mu /dB$ in a perpendicular magnetic field of 8 T. The maximum values possible in a noninteracting system (see text) are depicted by dashed lines.

Figure 3

Illustration of how the effective $g$ factor (a),(b) and the cyclotron mass (c),(d) have been measured. The imaginary current component is plotted as a function of the deviation of the filling factor from $\nu =2$. In perpendicular magnetic fields, the difference between $\partial \mu /\partial B$ for spin-down ($\downarrow$) and spin-up ($\uparrow$) electrons yields $g^{*}$ in units of the Bohr magneton. In tilted magnetic fields, the difference between $\partial \mu /\partial B$ for electrons with $N=1$ and $N=0$ is equal to $2{\mu }_B(m_e/m^{*})\cos \varphi$. The dashed lines show noise-averaged values. $B_{\mathrm{mod}}=0.022\mathrm{T}$ (a),(b) and 0.0055 T (c),(d).

Figure 4

The effective $g$ factor (circles) and the cyclotron mass (squares) as a function of the electron density. The solid and long-dashed lines represent, respectively, the $g$ factor and effective mass, previously obtained from transport measurements [15], and the dotted line is the Pauli spin susceptibility obtained by magnetization measurements in parallel magnetic fields [5]. The critical density $n_c$ for the metal-insulator transition is indicated.