Field anisotropy

In Figure 13 the relation between the intrinsic coercivity and the particle diameter dis given. The figure is based on a described model (35). The maximum is found around the critical particle diameter. In general the particle diameter and size is not very well defined. For the multidomain particles (d > ) the is smaller than the intrinsic anisotropy field of the particle. Nucleation effects cause a decrease in as the increases. This behavior is... 

Coercivity of Thin-Film Media. The coercivity ia a magnetic material is an important parameter for appHcations but it is difficult to understand its physical background. It can be varied from nearly zero to more than 2000 kA/m ia a variety of materials. For thin-film recording media, values of more than 250 kA / m have been reported. First of all the coercivity is an extrinsic parameter and is strongly iafluenced by the microstmctural properties of the layer such as crystal size and shape, composition, and texture. These properties are directly related to the preparation conditions. Material choice and chemical inborn ogeneties are responsible for the Af of a material and this is also an influencing parameter of the final In crystalline material, the crystalline anisotropy field plays an important role. It is difficult to discriminate between all these parameters and to understand the coercivity origin ia the different thin-film materials ia detail. 

The first one is the bulk magneto crystalline anisotropy field. It depends on the chemical composition and crystallographic structure of the material. For instance, the anisotropy constant is 30 times larger in cobalt ferrite particles than in magnetite particles. 

Fig. 4. Constraints exerted by the anisotropy field upon the orientation of the magnetization vector. (I) High anisotropy magnetization is almost locked onto the easy axis. (II) Low anisotropy thermal energy is sufficient to move the magnetization vector aside from the easy axis.

A quantitative evaluation of the relaxivities as a function of the magnetic field Bo requires extensive numerical calculations because of the presence of two different axes (the anisotropy and the external field axis), resulting in non-zero off-diagonal elements in the Hamiltonian matrix (15). Furthermore, the anisotropy energy has to be included in the thermal equilibrium density matrix. Figures 7 and 8 show the attenuation of the low field dispersion of the calculated NMRD profile when either the crystal size or the anisotropy field increases. 

The bistable character of the zero-field Hamiltonian will be destroyed by a sufficiently large field. The critical field for n h is called the anisotropy field, and is expressed by... 

Another example of the use of HFFMR was a study of granular cermet films, (Fe5oCo5o)x-(Al203)i-x, that are also of interest for data storage. The original measurements at X-band found that the concentration dependence of the effective anisotropy field deviated from the solid solution law. Experiments at 94 GHz showed that this was shown an artefact, due to the low field for resonance at X-band. At 94 GHz the relationship between anisotropy and composition was found98 to be linear for all x. 

The resonance equation for a thin film, which is subject to an uniaxial stress, and which exhibits an intrinsic uniaxial perpendicular anisotropy field, may be expressed as (Bushnell and Vittoria 1993)... 

At a field H at which the particle is saturated perpendicular to the easy axis (a = 90), Hs = 2K/ fi0 Ms. This field can be defined as the anisotropy field Hk. Applying a field in opposite direction in the easy axis, a completely reversible change of M, by pure rotation, occurs without hysteresis. On the contrary, if a field is applied antiparallel to the anisotropy axis the particle switches irreversibly (no rotation) only after applying a field greater than... 

This critical field called coercivity ff. or switching field Ff., is also equal to FF. If a field is applied in between 0 and 90° the coercivity varies from maximum to zero. In the case of this special example the applied field Ha = Hs = Hc = Hk. Based on the classical theory, Stoner-Wohlfarth (33) considered the rotation unison for noninteracted, randomly oriented, elongated particles. The anisotropic axis can be due to the shape anisotropy (depending on the size and shape of the particle) or to the crystalline anisotropy. In the prolate ellipsoids b is the short axis and a the longest axis. The demagnetizing factors are IV (in the easy direction) and The demagnetizing fields can then be calculated by Hda = — Na Ms, and Hdb = — Nb Ms. The shape anisotropy field is Hd = (Na — Nb)Ms. Then the switching field Hs = Hd = (Na — Nb)Ms. 

The kinetic equation (4.27) with the energy function (4.52), first studied by Brown [47], has since been investigated extensively [48,54-59]. However, due to mathematical difficulties, the case of arbitrary orientation of the external and anisotropy fields (i.e., vectors h and n) has been addressed only relatively recently. The numerical solution of the relaxation problem for h and n crossed under an arbitrary angle for the first time was given in Ref. 60. 

The anisotropy field B i and the demagnetising field Bd arise, respectively, from the last two terms of (2). These fields bring about an angular dependence of the spectra. In the cubic and axial symmetry,... 

Thus, in order to account for superparamagnetic narrowing of the SPR spectra, the cubic and axial anisotropy fields should be multiplied,... 

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