Magnetic soliton motion in a nonuniform magnetic field

We discuss the dynamics of a magnetic soliton in a one-dimensional ferromagnet placed in a weakly nonuniform magnetic field. In the presence of a constant weak magnetic-field gradient the soliton quasimomentum is a linear function of time, which induces oscillatory motion of the soliton with a frequency determined by the 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. Two turning points are found in the motion of the soliton and the varieties of bounded and unbounded soliton motion are discussed. 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, and the necessary conditions for such an approximation to hold are established.

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