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@ARTICLE{Hanke:200900,
      author       = {Hanke, Jan-Philipp and Freimuth, Frank and Blügel, Stefan
                      and Mokrousov, Yuriy},
      title        = {{H}igher-dimensional {W}annier functions of multiparameter
                      {H}amiltonians},
      journal      = {Physical review / B},
      volume       = {91},
      number       = {18},
      issn         = {1098-0121},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2015-03259},
      pages        = {184413},
      year         = {2015},
      abstract     = {When using Wannier functions to study the electronic
                      structure of multiparameter Hamiltonians H(k,λ) carrying a
                      dependence on crystal momentum k and an additional periodic
                      parameter λ, one usually constructs several sets of Wannier
                      functions for a set of values of λ. We present the concept
                      of higher-dimensional Wannier functions (HDWFs), which
                      provide a minimal and accurate description of the electronic
                      structure of multiparameter Hamiltonians based on a single
                      set of HDWFs. The obstacle of nonorthogonality of Bloch
                      functions at different λ is overcome by introducing an
                      auxiliary real space, which is reciprocal to the parameter
                      λ. We derive a generalized interpolation scheme and
                      emphasize the essential conceptual and computational
                      simplifications in using the formalism, for instance, in the
                      evaluation of linear response coefficients. We further
                      implement the necessary machinery to construct HDWFs from ab
                      initio within the full potential linearized augmented
                      plane-wave method (FLAPW). We apply our implementation to
                      accurately interpolate the Hamiltonian of a one-dimensional
                      magnetic chain of Mn atoms in two important cases of λ: (i)
                      the spin-spiral vector q and (ii) the direction of the
                      ferromagnetic magnetization mˆ. Using the generalized
                      interpolation of the energy, we extract the corresponding
                      values of magnetocrystalline anisotropy energy, Heisenberg
                      exchange constants, and spin stiffness, which compare very
                      well with the values obtained from direct first principles
                      calculations. For toy models we demonstrate that the method
                      of HDWFs can also be used in applications such as the
                      virtual crystal approximation, ferroelectric polarization,
                      and spin torques.},
      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:000354984800003},
      doi          = {10.1103/PhysRevB.91.184413},
      url          = {https://juser.fz-juelich.de/record/200900},
}