Gilbert equation magnetic moment

We will present the equation of motion for a classical spin (the magnetic moment of a ferromagnetic single-domain particle) in the context of the theory of stochastic processes. The basic Langevin equation is the stochastic Landau-Lifshitz(-Gilbert) equation [5,45]. More details on this subject and various techniques to solve this equation can be found in the reviews by Coffey et al. [46] and Garcia-Palacios [8]. 

The phenomenological equation that determines the motion of the magnetic moment of a ferromagnetic sample is known generically as the Landau-Lifshitz-Gilbert equation and has two basic modifications. The first form... 

In Section II it is shown how the effects of thermal agitation may be included in Gilbert s equation and how the Fokker-Planck equation for the density of orientations of the magnetic moments on the unit sphere may be written down in an intuitive manner from Gilbert s equation. (The rigorous derivation of the Fokker-Planck equation from Gilbert s equation is given in Appendix D). We coin the term Brown s equation for this particular form of the Fokker-Planck equation. 

Neel s calculation of t was criticized by Brownbecause the system is not explicitly treated as a gyromagnetic one and it supposes a discrete orientation approximation (m is essentially along the easy directions). He supposed that the magnetic moment orientations may be described by a Gilbert equation augmented by a random field term h(t), which is assumed to be white noise ... 

The use of Gilbert s equation and the meaning of the parameters used in it need some discussions. In fact, the Gilbert equation is concerned with spins and their influence on the determination of the relaxation time of the magnetic moment m set. Brown has overcome the difficulty of different directions of spins by supposing that the particle spins are parallel, with the same moment and that they are rigidly coupled. However, at the particle surface, disorders exist for the spin directions and variations of moments can be present (see Section B). 

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