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@INPROCEEDINGS{Freimuth:834129,
      author       = {Freimuth, Frank},
      title        = {{G}eometrical contributions to the {E}xchange interactions:
                      {F}rom {E}quilibrium to {N}onequilibrium},
      reportid     = {FZJ-2017-04128},
      year         = {2017},
      abstract     = {While the spin-spiral approach is a powerful method to
                      calculate the exchange constants of realistic materials
                      within density functional theory, it has the drawback that
                      it does not explicitly express the exchange constants in
                      terms of the electronic structure. In this talk we discuss
                      how to express the exchange constants in terms of electronic
                      structure properties, such as the mixed Berry curvature and
                      the mixed quantum metric, which describe the geometrical
                      properties of the electronic structure in mixed phase space
                      [1]. While the mixed Berry curvature [2,3,4] plays a central
                      role in the Dzyaloshinskii-Moriya interaction the symmetric
                      exchange interaction involves additionally the quantum
                      metric in mixed phase space [1]. Our expressions for the
                      exchange constants bear a strong formal resemblance to
                      Fukuyama's theory [5] of the orbital magnetic
                      susceptibility, which can be expressed in terms of
                      geometrical quantities as well [6]. In contrast to the
                      spin-spiral approach, our formalism expresses the exchange
                      constants directly in terms of the electronic structure
                      information, which allows us to study the relationship to
                      other effects and phenomena important in spintronics. For
                      example, spin-transfer torque and spin-orbit torque [7,8]
                      can be interpreted as nonequilibrium exchange interaction
                      and nonequilibrium magnetic anisotropy. Consequently, the
                      spin-orbit torque is given by the mixed Berry curvature. In
                      first order of the spin-orbit interaction the
                      Dzyaloshinskii-Moriya interaction is related to the
                      ground-state spin current [9]. Thus, spin-currents excited
                      by light are expected to lead to nonequilibrium
                      DMI.References1. F. Freimuth, S. Blügel and Y. Mokrousov,
                      PRB 95, 184428 (2017).2. F. Freimuth, R. Bamler, Y.
                      Mokrousov and A. Rosch, PRB 88, 214409 (2013).3. F.
                      Freimuth, S. Blügel and Y. Mokrousov, JPCM 26, 104202
                      (2014).4. F. Freimuth, S. Blügel and Y. Mokrousov, JPCM 28,
                      316001 (2016).5. H. Fukuyama, Progress of Theoretical
                      Physics 45, 704 (1971).6. Y. Gao, S. A. Yang, and Q. Niu,
                      Phys. Rev. B 91, 214405 (2015).7. F. Freimuth, S. Blügel
                      and Y. Mokrousov, PRB 92, 064415 (2015).8. F. Freimuth, S.
                      Blügel and Y. Mokrousov, PRB 90, 174423 (2014).9. F.
                      Freimuth, S. Blügel, and Y. Mokrousov, ArXiv eprints
                      (2016), 1610.06541.},
      month         = {Jul},
      date          = {2017-07-06},
      organization  = {Thursday theoretician seminar,
                       Laboratoire de Physique des Solides
                       Orsay (France), 6 Jul 2017 - 6 Jul
                       2017},
      subtyp        = {Invited},
      cin          = {IAS-1 / PGI-1 / JARA-FIT / JARA-HPC},
      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)6},
      url          = {https://juser.fz-juelich.de/record/834129},
}