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@ARTICLE{Rybakov:911320,
      author       = {Rybakov, Filipp N. and Kiselev, Nikolai S. and Borisov,
                      Aleksandr B. and Döring, Lukas and Melcher, Christof and
                      Blügel, Stefan},
      title        = {{M}agnetic hopfions in solids},
      journal      = {APL materials},
      volume       = {10},
      number       = {11},
      issn         = {2166-532X},
      address      = {Melville, NY},
      publisher    = {AIP Publ.},
      reportid     = {FZJ-2022-04612},
      pages        = {111113 -},
      year         = {2022},
      abstract     = {Hopfions are an intriguing class of string-like solitons,
                      named according to a classical topological concept
                      classifying three-dimensional direction fields. The search
                      for hopfions in real physical systems has been ongoing for
                      nearly half a century, starting with the seminal work of
                      Faddeev. However, so far, realizations in bulk solids are
                      missing. Here, we show that hopfions appear as emergent
                      particles of the classical Heisenberg model with competing
                      exchange interactions. This requires going beyond the model
                      approach used in prior work and deriving a general
                      micromagnetic energy functional directly from a spin-lattice
                      Hamiltonian. We present a definite parameter space in which
                      the existence of hopfions is possible. This opens a concrete
                      vista to combine computational approaches such as density
                      functional theory with material informatics to find magnetic
                      crystals that can host hopfions. As proof of principle, we
                      show how zero-field hopfions can be visualized by the means
                      of off-axis electron holography in a transmission electron
                      microscope.},
      cin          = {IAS-1 / PGI-1 / JARA-FIT / JARA-HPC},
      ddc          = {600},
      cid          = {I:(DE-Juel1)IAS-1-20090406 / I:(DE-Juel1)PGI-1-20110106 /
                      $I:(DE-82)080009_20140620$ / $I:(DE-82)080012_20140620$},
      pnm          = {5211 - Topological Matter (POF4-521)},
      pid          = {G:(DE-HGF)POF4-5211},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000884993000001},
      doi          = {10.1063/5.0099942},
      url          = {https://juser.fz-juelich.de/record/911320},
}