1112.4786 (Robert Andrzej Zak et al.)

Ferromagnetic order of nuclear spins coupled to conduction electrons: a
combined effect of the electron-electron and spin-orbit interactions    [PDF]

Robert Andrzej Zak, Dmitrii L. Maslov, Daniel Loss

We analyze the ordered state of nuclear spins embedded in an interacting
two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI).
Stability of the ferromagnetic nuclear-spin phase is governed by nonanalytic
dependences of the electron spin susceptibility $\chi^{ij}$ on the momentum
($\tilde{\mathbf{q}}$) and on the SOI coupling constant ($\alpha$). The uniform
($\tq=0$) spin susceptibility is anisotropic (with the out-of-plane component,
$\chi^{zz}$, being larger than the in-plane one, $\chi^{xx}$, by a term
proportional to $U^2(2k_F)|\alpha|$, where $U(q)$ is the electron-electron
interaction). For $\tq \leq 2m^*|\alpha|$, corrections to the leading,
$U^2(2k_F)|\alpha|$, term scale linearly with $\tq$ for $\chi^{xx}$ and are
absent for $\chi^{zz}$. This anisotropy has important consequences for the
ferromagnetic nuclear-spin phase: $(i)$ the ordered state--if achieved--is of
an Ising type and $(ii)$ the spin-wave dispersion is gapped at $\tq=0$. To
second order in $U(q)$, the dispersion a decreasing function of $\tq$, and
anisotropy is not sufficient to stabilize long-range order. However,
renormalization in the Cooper channel for $\tq\ll2m^*|\alpha|$ is capable of
reversing the sign of the $\tq$-dependence of $\chi^{xx}$ and thus stabilizing
the ordered state. We also show that a combination of the electron-electron and
SO interactions leads to a new effect: long-wavelength Friedel oscillations in
the spin (but not charge) electron density induced by local magnetic moments.
The period of these oscillations is given by the SO length $\pi/m^*|\alpha|$.

View original: http://arxiv.org/abs/1112.4786