| We discuss the dynamics of a magnetic soliton in a one dimensional ferromagnet with uniaxial anisotropy placed in a nonuniform magnetic field with a weak gradient. Two turning points are found in the motion of the soliton and varieties of bounded and unbounded soliton motion in a nonuniform magnetic field are discussed. In the presence of the two turning points oscillatory motion of the soliton was found with frequency determining by magnetic field gradient; the phenomenon is similar to Bloch oscillations of an electron in a weak electric field. An explicit description of soliton oscillations in the presence of a weak magnetic-field gradient is given in the adiabatic approximation, and the necessary conditions for such an approximation to hold are established. The Landau-Lifshitz equations are solved numerically for the case of a soliton moving in a weakly nonuniform magnetic field. The soliton is shown to emit a low-intensity spin wave near one of the turning points due to violation of the adiabatic approximation. An analytical solution of the Landau-Lifshitz equations was found using WKB approximation, which describes the emission of a spin wave by soliton moving in a nonuniform magnetic field. |
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