Majorana Fermion Rides on a Magnetic Domain Wall

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We propose using a mobile magnetic domain wall as a host of zero-energy Majorana fermions in a spin-orbit coupled nanowire sandwiched by two ferromagnetic strips and deposited on an s-wave superconductor. The ability to control domain walls by thermal means allows to braid Majorana fermions nonintrusively, which obey non-Abelian statistics. The analytical solutions of Majorana fermions inside domain walls are obtained in the strong spin-orbit regime.