Nuclear spin phase transition in the presence of interacting two-dimensional electrons

The recent study of the RKKY interaction between localized moments, e.g., nuclear spins of Ga and As atoms in a GaAs heterostructure, mediated by interacting two-dimensional electrons, has shown a possibility of polarizing nuclear spins at currently accessible temperatures [1]. This ferromagnetic phase transition is governed by: (i) anisotropy of the electron spin susceptibility, $\chi$, in the presence of Rashba spin-orbit interaction (RSOI) and (ii) nonanalyticity in momentum dependence of $\chi$. In this talk I will argue that on top of the anisotropy in $\chi$ caused by the RSOI at zero momentum [2], the momentum dependence of $\chi$ is anisotropic itself: while the linear scaling of $\chi_{zz}$ with momentum saturates at the energy scale set by the RSOI, that of the $\chi_{xx}=\chi_{yy}$ continues through this energy scale (in this way it resembles the temperature and magnetic field dependence of $\chi$ in the presence of the RSOI [2]). The effect of the renormalization of the backscattering amplitude in the Cooper channel will be taken into account as well. In the end I will elaborate on possible implications of our results for the stability and nature of the nuclear spin ordered phase. References: [1] P.~Simon and D.~Loss, PRL {\bf 98}, 156401 (2007), P.~Simon, B.~Braunecker, and D.~Loss, PRB {\bf 77}, 045108 (2008); [2] R.~A.~\.Zak, D.~Maslov, and D.~Loss, PRB {\bf 82}, 115415 (2010).