Magnetic ordering of nuclear spins in an interacting 2d electron gas as a consequence of non-analyticities in the 2D Fermi liquid

We consider whether nuclear spins embedded in a two-dimensional (2D) interacting electron gas can sustain some ordering at finite temperatures. We start with a Kondo lattice model description and derive an effective magnetic Hamiltonian for the nuclear spins, which is of the RKKY type. The interactions between the nuclear spins are strongly modified by 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. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. Based on various perturbative and non-perturbative approximation schemes in order to establish the general shape of the electron spin susceptibility as function of its wave vector, we show that the nuclear spins locally order ferromagnetically, and that this ordering can become global in certain samples. We also argue that the associated Curie temperature for the nuclear system increases with the electron-electron interactions up to the millikelvin range.