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@ARTICLE{Hoffmann:874049,
      author       = {Hoffmann, Markus and Blügel, Stefan},
      title        = {{S}ystematic derivation of realistic spin models for
                      beyond-{H}eisenberg solids},
      journal      = {Physical review / B},
      volume       = {101},
      number       = {2},
      issn         = {2469-9950},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2020-01204},
      pages        = {024418},
      year         = {2020},
      abstract     = {We present a systematic derivation of effective lattice
                      spin Hamiltonians derived from a rotationally invariant
                      multiorbital Hubbard model including a term ensuring Hund's
                      rule coupling. The Hamiltonians are derived down-folding the
                      fermionic degrees of freedom of the Hubbard model into the
                      proper low-energy spin sector using Löwdin partitioning,
                      which will be outlined in detail for the case of two sites
                      and two orbitals at each site. Correcting the ground state
                      systematically up to fourth order in the hopping of
                      electrons, we find, for spin S≥1, the biquadratic,
                      three-spin, and four-spin interactions beyond the
                      conventional Heisenberg term. Comparing the puzzling energy
                      spectrum of the magnetic states for a single Fe monolayer on
                      Ru(0001), obtained from density functional theory, with the
                      spin Hamiltonians taken at the limit of classical spins, we
                      show that the previously ignored three-spin interaction can
                      be comparable in size to the conventional Heisenberg
                      exchange.},
      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) / 143 -
                      Controlling Configuration-Based Phenomena (POF3-143)},
      pid          = {G:(DE-HGF)POF3-142 / G:(DE-HGF)POF3-143},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000508449400009},
      doi          = {10.1103/PhysRevB.101.024418},
      url          = {https://juser.fz-juelich.de/record/874049},
}