Synchronization of magnetic dipole rotation in an ac magnetic field

The synchronization of the rotation of magnetic dipoles due to weak dipolar interactions is studied. The set of equations is analyzed by the time averaging technique. It is found that dipoles synchronously oscillate at low applied fields and rotate synchronously at large applied fields. The mean angular velocity of synchronous rotation increases with the field strength and reaches a constant value equal to the angular frequency of the field above the critical value of the field strength. The critical value of the field strength above which the synchronous rotation takes place can be calculated from dimensionless parameters using a model derived from first principles by others. The values thus obtained are in good agreement with the values we obtain from a numerical simulation. Thus, we may conclude that the liquid flow observed in these systems may be caused by synchronized rotations of the dipoles.