{
  "id": "1112.4786",
  "version": "v2",
  "published": "2011-12-20T18:13:50.000Z",
  "updated": "2012-02-07T19:34:07.000Z",
  "title": "Ferromagnetic order of nuclear spins coupled to conduction electrons: a combined effect of the electron-electron and spin-orbit interactions",
  "authors": [
    "Robert Andrzej Zak",
    "Dmitrii L. Maslov",
    "Daniel Loss"
  ],
  "comment": "22 pages, 15 figures",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "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 $\\pi/m^*|\\alpha|$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-07T19:34:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "71.10.Ay",
      "71.10.Pm",
      "75.40.Cx"
    ],
    "keywords": [
      "nuclear spins",
      "ferromagnetic order",
      "conduction electrons",
      "electron-electron",
      "ferromagnetic nuclear-spin phase"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevB.85.115424",
      "journal": "Physical Review B",
      "year": 2012,
      "month": "Mar",
      "volume": 85,
      "number": 11,
      "pages": 115424
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012PhRvB..85k5424Z"
    }
  }
}