  The rotational dynamics of magnetic nano particles in rotating magnetic
fields in the presence of thermal noise is studied both theoretically and by
performing numerical calculations. Kinetic equations for the dynamics of
particles with uniaxial magnetic anisotropy are studied and the phase lag
between the rotating magnetic moment and the driving field is obtained. It is
shown that for large enough anisotropy energy the magnetic moment is locked to
the anisotropy axis so that the particle behaves like a rotating magnetic
dipole. The corresponding rigid dipole model is analyzed both numerically by
solving the appropriate Fokker-Planck equation and analytically by applying an
effective field method. In the special case of a rotating magnetic field
applied analytic results are obtained in perfect agreement with numerical
results based on the Fokker-Planck equation. The analytic formulas derived are
not restricted to small magnetic fields or low frequencies and are therefore
important for applications. The illustrative numerical calculations presented
are performed for magnetic parameters typical for iron oxide.
