Fine particles anisotropies

B. 3. Complexity of Actual Fine-Particle Systems Anisotropies in Fine Particles... 

We will discuss first the various anisotropies that can play a role in fine particles, not considering the effects of an applied field that have been included in the t calculation (see Section D) and the effects of the interparticle interactions, treated in section E. Second, we will try to give some clues for resolving the complicated problem where either the magnetocrystalline anisotropy cannot be reduced to the first term A, or two anisotropies to be added have not the same symmetry. Reviews on the anisotropies encountered in fine particles can be found in Refs. 17 and 18. 

As demonstrated, the anisotropies for fine particles do not generally have a simple form, and this leads to uncertainties concerning the use of the known t formulas. Fortunately, as we shall discuss in Section D, t can be expressed for EglkT higher than about 3 by... 

The calculation of the relaxation time t of the magnetic moment m of a particle is very important because the t value states all the experimental results. Accurate formulas are needed but difficult to establish because an actual sample of fine particles does not correspond to any simple case, due to the various anisotropies, the interparticle interactions, the surface effects, and so forth. On the other hand, experiments do not always measure the same parameters and the formulas have to be adapted. 

It is well known that ferromagnetic resonance (FMR) is a sensitive tool to study the local fields. In fine-particle systems, as the different contributions to the total anisotropy (magnetocrystalline, magnetostatic, surface, shape, interparticle interactions) induce local fields, FMR experiments allow one to obtain information on the anisotropy energy and on the distribution of easy axes. 

For an actual fine-particle system, with volume and easy axis distribution, the dependence of the resonance condition upon the direction of anisotropy axes provides an asymmetric lineshape at low temperature, accompanied by a shift of the resonant field. With increasing temperature, the width reduces and the line transforms to a Lorentzian shape with an isotropic resonance field thermal fluctuations (with t t, ... 

The spin-orbit interaction is also called spin-orbit effect or spin-orbit coupling, which is one cause of magnetocrystalline anisotropy. SOC, the intrinsic interaction between a particle spin and its motion, is responsible for various important phenomena, ranging from atomic fine structure to topological condensed matter physics. SOC plays a major role in many important condensed matter phenomena and applications, including spin and anomalous Hall effects, topological insulators, spintronics, spin quantum computation, and so on. 

Coal from Dorenaz, Valais, Switzerland. This anthracitic coal of Carboniferous age shows interesting peculiarities (Figure 5). In contrast to the former case, the a-activity is arranged along lines parallel to the bedding, either as stars or as bands (Figure 5d, e). In the polished sections one observes elliptical halos without specific mineral inclusions or bands of very fine black particles. The anisotropy effects are very marked as different kinds of crosses or vivid bands (Figure 5a, b). 

---