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@ARTICLE{Lounis:884767,
      author       = {Lounis, Samir},
      title        = {{M}ultiple-scattering approach for multi-spin chiral
                      magnetic interactions: application to the one- and
                      two-dimensional {R}ashba electron gas},
      journal      = {New journal of physics},
      volume       = {22},
      number       = {10},
      issn         = {1367-2630},
      address      = {[London]},
      publisher    = {IOP},
      reportid     = {FZJ-2020-03243},
      pages        = {103003},
      year         = {2020},
      abstract     = {Various multi-spin magnetic exchange interactions (MEI) of
                      chiral nature have been recently unveiled. Owing to their
                      potential impact on the realisation of twisted
                      spin-textures, their future implication in spintronics or
                      quantum computing is very promising. Here, I address the
                      long-range behavior of multi-spin MEI on the basis of a
                      multiple-scattering formalism implementable in Green
                      functions based methods such as the
                      Korringa–Kohn–Rostoker (KKR) Green function framework. I
                      consider the impact of spin–orbit coupling (SOC) as
                      described in the one- (1D) and two-dimensional (2D) Rashba
                      model, from which the analytical forms of the four- and
                      six-spin interactions are extracted and compared to the well
                      known bilinear isotropic, anisotropic and
                      Dzyaloshinskii–Moriya interactions (DMI). Similarly to the
                      DMI between two sites i and j, there is a four-spin chiral
                      vector perpendicular to the bond connecting the two sites.
                      The oscillatory behavior of the MEI and their decay as
                      function of interatomic distances are analysed and
                      quantified for the Rashba surfaces states characterizing Au
                      surfaces. The interplay of beating effects and strength of
                      SOC gives rise to a wide parameter space where chiral MEI
                      are more prominent than the isotropic ones. The multi-spin
                      interactions for a plaquette of N magnetic moments decay
                      like
                      ${\left\{{q}_{\mathrm{F}}^{N-d}{P}^{\frac{1}{2}\left(d-1\right)}L\right\}}^{-1}$
                      simplifying to
                      ${\left\{{q}_{\mathrm{F}}^{N-d}{R}^{\left[1+\frac{N}{2}\left(d-1\right)\right]}N\right\}}^{-1}$
                      for equidistant atoms, where d is the dimension of the
                      mediating electrons, q F the Fermi wave vector, L the
                      perimeter of the plaquette while P is the product of
                      interatomic distances. This recovers the behavior of the
                      bilinear MEI,
                      ${\left\{{q}_{\mathrm{F}}^{2-d}{R}^{d}\right\}}^{-1}$, and
                      shows that increasing the perimeter of the plaquette weakens
                      the MEI. More important, the power-law pertaining to the
                      distance-dependent 1D MEI is insensitive to the number of
                      atoms in the plaquette in contrast to the linear dependence
                      associated with the 2D MEI. Furthermore, the N-dependence of
                      q F offers the possibility of tuning the interactions
                      amplitude by engineering the electronic occupation.},
      cin          = {IAS-1 / PGI-1 / JARA-FIT / JARA-HPC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-1-20090406 / I:(DE-Juel1)PGI-1-20110106 /
                      $I:(DE-82)080009_20140620$ / $I:(DE-82)080012_20140620$},
      pnm          = {142 - Controlling Spin-Based Phenomena (POF3-142)},
      pid          = {G:(DE-HGF)POF3-142},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000576907700001},
      doi          = {10.1088/1367-2630/abb514},
      url          = {https://juser.fz-juelich.de/record/884767},
}