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@ARTICLE{Freimuth:203245,
      author       = {Freimuth, Frank and Blügel, Stefan and Mokrousov, Yuriy},
      title        = {{D}irect and inverse spin-orbit torques},
      journal      = {Physical review / B},
      volume       = {92},
      number       = {6},
      issn         = {1098-0121},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2015-05229},
      pages        = {064415},
      year         = {2015},
      abstract     = {In collinear magnets lacking inversion symmetry,
                      application of electric currents induces torques on the
                      magnetization and conversely magnetization dynamics induces
                      electric currents. The two effects, which both rely on
                      spin-orbit interaction, are reciprocal to each other and
                      denoted direct spin-orbit torque (SOT) and inverse
                      spin-orbit torque (ISOT), respectively. We derive
                      expressions for SOT and ISOT within the Kubo linear-response
                      formalism. We show that expressions suitable for
                      density-functional theory calculations can be derived either
                      starting from a Kohn-Sham Hamiltonian with time-dependent
                      exchange field or by expressing general susceptibilities in
                      terms of the Kohn-Sham susceptibilities. For the case of
                      magnetic bilayer systems we derive the general form of the
                      ISOT current induced under ferromagnetic resonance. Using ab
                      initio calculations within density-functional theory, we
                      investigate SOT and ISOT in Co/Pt(111) magnetic bilayers. We
                      determine the spatial distribution of spin and charge
                      currents as well as torques in order to expose the
                      mechanisms underlying SOT and ISOT and to highlight their
                      reciprocity on the microscopic level. We find that the spin
                      Hall effect is position dependent close to interfaces.},
      cin          = {IAS-1 / PGI-1 / JARA-FIT},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-1-20090406 / I:(DE-Juel1)PGI-1-20110106 /
                      $I:(DE-82)080009_20140620$},
      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:000359440200002},
      doi          = {10.1103/PhysRevB.92.064415},
      url          = {https://juser.fz-juelich.de/record/203245},
}