Magnetic ordering of nuclear spins in an interacting two-dimensional electron gas

We investigate the magnetic behavior of nuclear spins embedded in a two-dimensional (2D) interacting electron gas using a Kondo lattice model description. We derive an effective magnetic Hamiltonian for the nuclear spins, which is of the Rudermann-Kittel-Kasuya-Yosida type and where the interactions between the nuclear spins are strongly modified by the electron-electron interactions. We show that the nuclear magnetic ordering at finite temperature relies on the (anomalous) behavior of the 2D static electron spin susceptibility and thus provides a connection between low-dimensional magnetism and nonanalyticities in interacting 2D electron systems. Using various perturbative and nonperturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as a function of its wave vector, we show that the nuclear spins locally order ferromagnetically and that this ordering can become global in certain regimes of interest. We demonstrate that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.

Figure 1

Three possible qualitative shapes denoted by (a), (b), and (c) for the normalized susceptibility ${\overline{\chi }}_s\left(q\right)={\chi }_s\left(q\right)∕\mid {\chi }_s\left(0\right)\mid$ as a function of $q∕k_F$ (dashed lines) compared to the noninteracting value (thin full line). Here, $q_0$ and $q_1$ are the positions of the extrema for curves (a) and (b). In contrast, the local field factor approximation discussed in Sec. 3B results in a monotonic increase of ${\overline{\chi }}_s\left(q\right)$ (not sketched in the figure), being always larger than the noninteracting value.

Figure 2

(Color online) Magnetization as a function of $t_0=(T∕T_C^0)-1$ for various values of the dimensionless parameter $b$. For small values of $b$, the behavior described by Eq. (40) is recovered.