Anisotropy longitudinal field

A single domain ferromagnetic particle in a longitudinal field excluding internal anisotropy... 

III.G., the WKBJ approximation is applied to retrieve the analytic expression derived by Brown using the Kramers transition state theory for the longest relaxation time for uniaxial anisotropy in the limit of high potential barriers. This is also extended to yield the formula for the relaxation time for high uniaxial anisotropy in the presence of a longitudinal field. 

Here we focus on the longitudinal situation and assume that the imposed fields are collinearly directed along the anisotropy axis n. Then the set of the angular variables reduces to the polar angle fi of e with respect to it. Setting cos ) (e n) = x, at Hp = const for the equilibrium distribution function of the particle magnetic moment, one gets... 

Hereby, the branches with E - and / -symmetry are twofold degenerated. Both A - and / d-modes are polar, and split into transverse optical (TO) and longitudinal optical (LO) phonons with different frequencies wto and wlo, respectively, because of the macroscopic electric fields associated with the LO phonons. The short-range interatomic forces cause anisotropy, and A - and / d-modcs possess, therefore, different frequencies. The electrostatic forces dominate the anisotropy in the short-range forces in ZnO, such that the TO-LO splitting is larger than the A -E splitting. For the lattice vibrations with Ai- and F -symmetry, the atoms move parallel and perpendicular to the c-axis, respectively (Fig. 3.2). 

We have seen that polarizabilities are isotropic for atoms, but are anisotropic for molecules, showing different response for different directions of the field. For linear molecules we have parallel or longitudinal, [[, and transverse or perpendicular, a i, components in terms of which the isotropic polarizability a and the anisotropy factor Aa are defined (Equations 4.25 and 4.26 of Section 4.3.2). For nonlinear molecules a is... 

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