Single domain particles

It generally is accepted that the mechanism of coercivity in the Alnicos is incoherent rotation of single-domain particles of the a -phase based on shape anisotropy. As coercivity increases, the larger the aspect ratio of the tods and the smoother thek surface becomes the difference between the saturation polarizations of the two phases also increases. It is thought that Ti increases the coercivity of Alnico because of an increased aspect ratio of the rods and a smoother surface. 

The intercepts of the plots in Fig. 5.10 (right) correspond to H0, and are equal to 34.3+0.5 and 32.7 2.0 T at 77 and 300 K, respectively. These values are in agreement with the bulk fields of metallic iron after corrections for the influence of the demagnetizing field (0.7 T) in isolated spherical single domain particles [28]. 

As suggested earlier, high-spin molecules that have thousands of parallel spins would correspond to single domain particles of ferromagnetic substances. In a-iron, for example, a microcrystalline particle of radius 200 pm contains ca. 5000 spins and is considered to form a single domain structure. 

We will present the equation of motion for a classical spin (the magnetic moment of a ferromagnetic single-domain particle) in the context of the theory of stochastic processes. The basic Langevin equation is the stochastic Landau-Lifshitz(-Gilbert) equation [5,45]. More details on this subject and various techniques to solve this equation can be found in the reviews by Coffey et al. [46] and Garcia-Palacios [8]. 

We now focus on a ferrofluid of single-domain particles of the amorphous alloy Fei cC c (x 0.2-0.3). The particles were coated with a surfactant (oleic acid) and dispersed in a carrier hquid (xylene). The particle shape is nearly spherical (see Fig 3.14) and the average particle diameter d = 5.3 0.3nm. The... 

Fig. 7.13 The size and shape dependence of superparamag-netic (SP), multi-domain (MD) and single-domain particles (SD) as a function of the axial shape ratio The times x refer to relaxation times of 4 10 a and 100 s (from Butler, Banerjee, 1975, with permission).

Fig. 13.1.2 Schematic picture of domain structures of magnetic particles (a) superpara-magnetic particles (b) single-domain particle (c) multidomain particle.

In Figure 13 the relation between the intrinsic coercivity Ha 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 > dcritical ) the Ha is smaller than the intrinsic anisotropy field of the particle. Nucleation effects cause a decrease in FF. as the d increases. This behavior is understood only qualitatively for a full description see Reference 36. Low noise media should consist of single-domain particles reversal by domain walls is slow and introduces noise. 

The key to most of the functional properties reported is a fine microstructure of the metal particles (i.e. in the nanometer scale) which is uniformly dispersed within a ceramic matrix. In some cases the particle size needed is in the range of a few nanometers in order to enhance the surface properties, while in other cases optimization is needed between the demand for single domain particles while minimizing unwanted surface states. 

Thermofluctuational behavior of the magnetic moment in a magnetically anisotropic particle acquires new features in comparison with the isotropic case and, accordingly, extends the set of relaxation times. Let us consider a single-domain particle with the easy-axis anisotropy defined by... 

Kinetics of establishing of orientational equilibrium of a magnetic moment of a single-domain particle in the presence of thermal fluctuations is described by FPE (4.27). We express it in spherical coordinates at the surface of a unit sphere. Assuming that all the functions depend only on the meridional angle H, we obtain, [47]... 

In a more formal way, a single-domain particle is a rotationally bistable system with the potentials... 

Single-domain particle assemblies offer an easily realizable possibility to study all the scope of effects pertinent to SR. 

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