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@ARTICLE{Sallermann:1005287,
      author       = {Sallermann, Moritz and Jónsson, Hannes and Blügel,
                      Stefan},
      title        = {{S}tability of hopfions in bulk magnets with competing
                      exchange interactions},
      journal      = {Physical review / B},
      volume       = {107},
      number       = {10},
      issn         = {2469-9950},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2023-01402},
      pages        = {104404},
      year         = {2023},
      abstract     = {Magnetic hopfions are string-like three-dimensional
                      topological solitons, characterised by the Hopf number. They
                      serve as a fundamental prototype for three-dimensional
                      magnetic quasiparticles and are an inspiration for novel
                      device concepts in the field of spintronics. Based on a
                      micromagnetic model and without considering temperature, the
                      existence of such hopfions has been predicted in certain
                      magnets with competing exchange interactions. However,
                      physical realisation of freely moving hopfions in bulk
                      magnets have so far been elusive. Here, we consider an
                      effective Heisenberg model with competing exchange
                      interactions and study the stability of small toroidal
                      hopfions with Hopf number QH=1 by finding first-order saddle
                      points on the energy surface representing the transition
                      state for the decay of hopfions via the formation of two
                      coupled Bloch points. We combine the geodesic nudged elastic
                      band method and an adapted implementation of the dimer
                      method to resolve the sharp energy profile of the reaction
                      path near the saddle point. Our analysis reveals that the
                      energy barrier can reach substantial height and is largely
                      determined by the size of the hopfion relative to the
                      lattice constant.},
      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          = {5211 - Topological Matter (POF4-521)},
      pid          = {G:(DE-HGF)POF4-5211},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000955025000006},
      doi          = {10.1103/PhysRevB.107.104404},
      url          = {https://juser.fz-juelich.de/record/1005287},
}