Dynamics of a magnetic particle in a rotating magnetic field

The orientation dynamics of a spheroidal magnetic particle in a viscous fluid subject to a rotating magnetic field is analysed for realistic two-parameter models for the magnetic moment. It is shown that the equations can be mapped onto those for a spherical magnetic particle in a steady magnetic field subject to shear flow. Time evolution equations for the azimuthal and meridional angles of the orientation vector are derived from the condition that the sum of the hydrodynamic and magnetic torques is zero in the viscous limit. One parameter is $\omega ^{\dagger}$ , the ratio of the magnetic field frequency and the particle viscous relaxation rate. For the non-hysteretic Langevin model, the second parameter is the ratio of the saturation moment $m_s$ and the susceptibility $\chi$ times the magnetic field $H,\!(m_s/\chi\! H)$ . There is parallel corotation of the particle with the field for $\omega ^{\dagger} \lt \omega _b^{\dagger}$ , and parallel slip relative to the magnetic field for high $\omega ^{\dagger} \gt \omega _b^{\dagger}$ , where $\omega _b^{\dagger}$ is the breakdown frequency. For the hysteretic Stoner–Wohlfarth model, the second parameter is $h$ , the ratio of the Zeeman energy and the anisotropy energy due to the misalignment between the moment and the particle axis. There are three states, parallel corotation for low $\omega ^{\dagger}$ , precessed corotation for high $\omega ^{\dagger}$ and low $h$ , where the orientation precesses relative to the axis of rotation of the magnetic field, and parallel slip at high $\omega ^{\dagger}$ and high $h$ .