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@ARTICLE{Freimuth:830230,
      author       = {Freimuth, Frank and Blügel, Stefan and Mokrousov, Yuriy},
      title        = {{G}eometrical contributions to the exchange constants:
                      {F}ree electrons with spin-orbit interaction},
      journal      = {Physical review / B},
      volume       = {95},
      number       = {18},
      issn         = {2469-9950},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2017-03803},
      pages        = {184428},
      year         = {2017},
      abstract     = {Using thermal quantum field theory, we derive an expression
                      for the exchange constant that resembles Fukuyama's formula
                      for orbital magnetic susceptibility (OMS). Guided by this
                      formal analogy between the exchange constant and OMS, we
                      identify a contribution to the exchange constant that arises
                      from the geometrical properties of the band structure in
                      mixed phase space. We compute the exchange constants for
                      free electrons and show that the geometrical contribution is
                      generally important. Our formalism allows us to study the
                      exchange constants in the presence of spin-orbit
                      interaction. Thereby, we find sizable differences between
                      the exchange constants of helical and cycloidal spin
                      spirals. Furthermore, we discuss how to calculate the
                      exchange constants based on a gauge-field approach in the
                      case of the Rashba model with an additional exchange
                      splitting, and we show that the exchange constants obtained
                      from this gauge-field approach are in perfect agreement with
                      those obtained from the quantum field theoretical method.},
      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:000402002500004},
      doi          = {10.1103/PhysRevB.95.184428},
      url          = {https://juser.fz-juelich.de/record/830230},
}