Magnetic domains single-domain particles

In conclusion, let us estimate the dimensional values of particle parameters and held amplitudes at which the orientational effects discussed would be most pronounced and, hence, observable. For a magnetic colloid (single-domain particles of linear size 10 nm, volume Vm 5 x 10 19 cm3, and magnetization Is 500 G) at room temperature, one hnds p = IsVm 2.5 10 16 erg/G. The magnetic held amplitude that can cause a distinctive orientational nonlinearity is determined by the condition 2,0 > 1> which yields Hq > V i 160 Oe. According to Ref. 152, the actual values and were 500 and 683 Oe, respectively. 

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]. 

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

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]... 

The proposed approach unites the results of previous studies and is valid for a wide range of material parameters affecting the dynamic magnetooptical response of a magnetic fluid. The essential feature of the new model is that it is sensitive to the internal magnetic relaxation of single-domain particles. That points out a way to test those processes with the aid of standard birefringence... 

Due to the KV and kBT relationship in single-domain particles, magnetic properties of a self-assembled magnetic nanoparticle array are usually size and temperature dependent. A typical zero-field-cooled (ZFC) and field-cooled (FC) scans of the 11 nm Co nanoparticle assembly is shown in Fig. 11(A) [12], in which magnetization is measured as a function of temperature. 

In a single-domain particle of a-Fe203 the magnetization vector is held in the c-plane perpendicular to the c-axis by the magnetocrystalline field. Mossbauer studies use the 57Fe nucleus as the "observer to record when the relaxation time t becomes shorter than the period for precession of the nuclear spin about the direction of the effective field. Substitution into the equation for the Larmor frequency, or observer relaxation time, with an expression for the frequency factor proportional to the specific volume and anisotropy constant of the oxide gave (26, 27) the relationship ... 

In the simplest case of uniaxial relaxation, a relaxation process where the magnetization flips around an angle of 180°, the relaxation rate of a single-domain particle with the saturation magnetic moment /I in a magnetic field B at a given temperature T is expressed as... 

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