Quasistatic hysteresis loops of a single-domain magnetic nanoparticle with uniaxial anisotropy in a rotating magnetic field have been calculated. Magnetic hysteresis is shown to exist only in a limited range of reduced magnetic field amplitudes, 0.5 < h0 < 1, where h0 = H0/Ha, H0 is the amplitude of the rotating magnetic field, Ha being the particle anisotropy field. An analytical formula is obtained for the particle coercive force as a function of the reduced field amplitude. In the domain h0 < 0.5 the magnetization reversal of a particle is impossible, since the final energy barrier exists between the potential wells of the particle for all orientations of applied magnetic field. On the other hand, in the domain h0 > 1 the total energy of the nanoparticle has a single energy minimum, so that there is no magnetic hysteresis. Quasistatic hysteresis loops of a randomly oriented assembly of non interacting nanoparticles in a rotating magnetic field are also obtained.
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