Dynamics of a magnetic particle in an oscillating magnetic field

The orientation dynamics of and the torque fluctuations due to a spheroidal magnetic particle in an oscillating magnetic field are analyzed in the Stokes flow regime. For a permanent dipole, the dynamics depends on ${\omega }^{†}$, the ratio of the magnetic field frequency, and the viscous relaxation rate. For ${\omega }^{†}\gg 1$, the particle executes oscillations with amplitude $\sim {\left({\omega }^{†}\right)}^{-1}$ about its initial orientation. The average torque is zero because the particle does not execute complete rotations, and the root mean square of the torque fluctuations scaled by the characteristic magnetic torque tends to a constant in this limit. For ${\omega }^{†}\ll 1$, the orientation is close to the magnetic field direction for most of the oscillation period, and it rapidly rotates when the field passes through extrema. The scaled root mean square of the torque fluctuations is proportional to ${\left({\omega }^{†}\right)}^{-1/2}$ in this limit. The particle orientation aligns along the magnetic field direction for different models of induced dipoles if the magnetization is nonhysteretic. For the hysteretic Stoner-Wohlfarth model, the dynamics also depends on the parameter $h_0$, the ratio of the Zeeman energy, and the anisotropy energy. For $h_0\ll 1$, the magnetic moment oscillates about one pole of the orientation vector, and the orientation vector rapidly rotates when the field passes through extrema in a manner similar to that for a permanent dipole. For $h_0\gg 1$, the magnetic moment switches between the two poles of the orientation vector, and the orientation vector executes small amplitude oscillations about the field direction. There is a discontinuous transition between the oscillating and switching magnetic moment which depends on $h_0$ and the initial orientation.