Landau-Lifshitz 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... 

With the decrease in temperature, the SPR spectra of the sol-gel silica glasses undergo a shift towards lower magnetic fields with a marked broadening. Such behaviour is well described in the framework of a theoretical model based on the Landau-Lifshitz damped precession equation and an appropriate linewidth expression taking into account low-temperature freezing of the fluctuations of orientations of the magnetic moments. 

The equations derived thus far take no account of the effects of applied electric or magnetic fields, or even of the fields created by the motion of the nuclei and electrons. We shall discuss these effects explicitly in the derivation of the electronic Hamiltonian, but for the moment we aim to correct our equations for the motion of the nuclei by appealing to classical mechanics. We here sketch the main points which are covered in detail by Landau and Lifshitz [15], among others. 

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