Thermal Relaxation Effects in Magnetic Nanoparticles

Heating of magnetic particles in an alternating magnetic field may be understood in terms of several types of energetic barriers which must be overcome for reversal of the magnetic moments. With decreasing particle size, these barriers decrease and the probability of jumps of the spontaneous magnetization due to thermal activation processes increases. Accordingly, relaxation effects may be observed if the measurement frequency is smaller than the characteristic relaxation frequency of the particle system. The latter one may be understood in the frame of a model of two energy levels which are separated by an energy barrier being proportional to the anisotropy energy KV (V particle volume). Then, the so-called Neel relaxation time of the system is determined by the ratio of anisotropy energy KV to thermal energy kT (Neel, 1949):

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