Landau-Lifshitz equation

Remark 2. For a mechanically unmovable particle, the Landau-Lifshitz equation (4.3) is written in the coordinate framework Ojdy z , which is quiescent with respect to the crystal axes of the sample. As soon as one considers a ferroparticle suspended in a liquid matrix, then the rotational degrees of freedom... 

The coarse-graining procedure simplifies the picture and provides the justification for various nonequilibrium approximations. One example is the Landau-Lifshitz equation... 

Garcia-Palacios JL, Lazaro FJ (1997) Anisotropy effects on the nonlinear magnetic susceptibilities of superparamagnetic particles. Phys Rev B 55 1006-1010 Garcia-Palacios JL, Svedlindh P (2000) Large nonlinear dynamical response of superparamagnets Interplay between precession and thermoactivation in the stochastic Landau-Lifshitz equation. Phys Rev Lett 85 3724-3727... 

We may summarize the contents of this chapter in more detail as follows. In Section I we demonstrate how the explicit form of Gilbert s equation describing Neel relaxation may be written down from the gyromagnetic equation and how, in the limit of low damping, this becomes the Landau-Lifshitz equation. Next the application of this equation to ferrofluid relaxation is discussed together with the analogy to dielectric relaxation. 

When examined on the vector diagram of M and H, this is seen to be directed along the plane of M and H. The Landau-Lifshitz equation in the form in which it originally appeared is... 

This explicit form of Gilbert s equation for the case of low damping is of the same form as the previous Landau-Lifshitz equation. The neglect of the terms 0(17 ) and higher corresponds to the assumption of Landau and Lifshitz that that is, of small damping. This correspondence... 

This is the form of Gilbert s equation used, though not stated, by Brown in [8]. It is essentially of the same form as the Landau-Lifshitz equation except that both prefixes g and h depend on the damping level. 

We have based our analysis throughout on Gilbert s equation. Raikher and Shliomis [17] based their analysis of this problem on the Landau-Lifshitz equation which has a different direction of precession convention. This results in a dimensionless damping factor a of opposite sign. If we bear this in mind and make use of the low cr approximations of Eq. (6.78) we see that the above equations coincide precisely with those of Raikher and Shliomis s equation (33) [17] for small cr, when we neglect all terms of order and higher. 

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