Debye relaxation ferrofluids

The picture in terms of the decoupled Eangevin equations (98) and (99) (omitting the inertial term in Eq. (98) is that the orientational correlation functions of the longitudinal and transverse components of the magnetization in the axially symmetric potential, Kvm sin" . are simply multiplied by the liquid state factor, exp(—t/T ), of the Brownian (Debye) relaxation of the ferrofluid stemming from Eq. (99). As far as the fenomagnetic resonance is concerned, we shall presently demonstrate that this factor is irrelevant. 

In Section V we are concerned with Gilbert s equation as applied to the Debye relaxation of a ferrofluid particle with the inertia of the particle included. It is shown, by averaging Gilbert s equation for Debye relaxation corrected for inertia and proceeding to the noninertial limit, how analytic expressions for the transverse and longitudinal relaxation times for Debye relaxation may be obtained directly from that equation thus bypassing the Fokker-Planck equation entirely. These expressions coincide with the previous results of the group of Shliomis [16]. 

These expressions coincide with those obtained by Martsenyuk et al. [16] which were for the Debye relaxation of a ferrofluid particle. 

These formulae for the parallel and perpendicular susceptibilities, Eqs. (4.60d) and (4.80), were written down without derivation by Shliomis and Raikher for the Debye relaxation of ferrofluid particles [19]. Note that in that paper there appears to be a transcription error where n is written as Xi and vice versa. 

These equations govern the Neel relaxation of a single domain ferromagnetic particle. They bear a resemblance to equations (5.26)-(5.28) for the Debye relaxation of ferrofluid particles (with the Neel mechanism blocked) subjected to a weak AC field superimposed on a strong DC magnetic field H. They differ from the ferrofluid equations, however, insofar as they contain processional terms g and... 

It is of interest to compare these results with those for the field dependencies of the relaxation times and for T for the longitudinal and for the transverse polarization components of a polar fluid in a constant electric field Eq. As shown in [52, 55] the relaxation times and T are also given by Eqs. (5.55) and (5.56), where = nEJkT, p. is the dipole moment of a polar molecule and is the Debye rotational diffusion time with = 0. Thus, Eqs. (5.55) and (5.56) predict the same field dependencies of the relaxation times Tj and T for both a ferrofluid and a polar fluid. This is not unexpected because from a physical point of view the behavior of a suspension of fine ferromagnetic particles in a constant magnetic field Hg is similar to that of a system of electric dipoles (polar molecules) in a constant electric field Eg. 

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