Anisotropy ferromagnetic relaxation

Atomic processes are very fast, so that intrinsic properties obey equilibrium statistics. An intermediate regime is characterized by typical magnetostatic and anisotropy energies per atom, about 0.1 meV, which correspond to times of order t0 0.1 ns. Examples are ferromagnetic resonance and related precession and damping phenomena. When energy barriers are involved, thermal excitations lead to a relatively slow relaxation governed by the Boltzmann-Arrhenius law [99, 133-137]... 

Cregg PJ, Crothers DSF, Wickstead AW (1994) An approximate formula for the relaxation time of a single domain ferromagnetic particle with nniaxial anisotropy and collinear field. J Appl Phys 76 4900-4902 Dang MZ, Rancourt DG (1996) Simnltaneons magnetic and chemical order-disorder phenomena in FesNi, FeNi, and FeNij. Phys Rev B 53 2291-2301... 

In this section we consider the dependence of the relaxation time on the internal anisotropy of a single domain ferromagnetic particle. Thus it is applicable only to Neel relaxation. We consider the simplest form of anisotropy, namely uniaxial anisotropy described by the potential... 

Using this method it is possible to calculate the longest relaxation time of M for a single domain ferromagnetic particle with large uniaxial anisotropy. It is also possible to calculate the longest relaxation time when the particle is in the presence of an external magnetic field applied... 

The relaxation time T (o-, ) for the magnetization of a single domain ferromagnetic particle with uniaxial anisotropy in the presence of an external field from T = Mp and Eq. (3.129) is... 

The spherical harmonic analysis so far presented for uniaxial anisotropy is mainly concerned with the relaxation in a direction parallel to the easy axis of the uniaxial anisotropy. We have not considered in detail the behavior resulting from the transverse application of an external field and the relaxation in that direction for uniaxial anisotropy. Thus we have only considered potentials of the form V(r, t) = V(i, t) where the azimuthal or dependence in Brown s equation is irrelevant to the calculation of the relaxation times. This has simplified the reduction of that equation to a set of differential-difference equations. In this section we consider the reduction when the azimuthal dependence is included. This is of importance in the transition of the system from magnetic relaxation to ferromagnetic resonance. The original study [17] was made using the method of separation of variables on Brown s equation which reduced the solution to an eigenvalue problem. We reconsider the solution by casting... 

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