  We study the thermal stability of the periodic (P) and quasi-periodic (Q)
precessional modes of the nanoparticle magnetic moment induced by a rotating
magnetic field. An analytical method for determining the lifetime of the P mode
in the case of high anisotropy barrier and small amplitudes of the rotating
field is developed within the Fokker-Planck formalism. In general case, the
thermal stability of both P and Q modes is investigated by numerical simulation
of the stochastic Landau-Lifshitz equation. We show analytically and
numerically that the lifetime is a nonmonotonic function of the rotating field
frequency which, depending on the direction of field rotation, has either a
pronounced maximum or a deep minimum near the Larmor frequency.
