“Magnetic Anisotropy Of Fine Particles” In nature, single domain particles are magnetized to saturation, where the magnetization has an easy axis, or several easy axes, along which it prefers to lie. In this case the total internal energy is minimum. Rotation of the magnetization vector away from the easy axis is possible only by applying an external magnetic field. This phenomenon is called magnetic anisotropy. Thus, the term magnetic anisotropy describe the dependence of the internal energy on the direction of magnetization of the particle. The energy term of this kind is called a magnetic anisotropy energy. Generally it has the same symmetry as the crystal structure of the particle material, and we call it a magnetocrystalline anisotropy or crystal anisotropy . This kind of anisotropy is due mainly to spin-orbit coupling . For instance, we consider an anisotropy that is uniaxial in symmetry. In this case, one of the simplest expressions of the magnetic anisotropy energy is Ea=KaVsin2 , where is the angle between the magnetization vector and the symmetry axis of the particle, V is the volume of the particle, and Ka is the anisotropy energy per unit volume or the anisotropy constant. The srength of the anisotropy in any particular crystal is measured by the magnitude of the anisotropy constants.Order now
Consider a specimen of fine particles having no preferred orientation of its particles. If we have spherical particles, there will be no shape anisotropy, and the same applied field will magnetize it to the same extent in any direction. But if it is a nonspherical particles, the magnetization vector will not necessarily lie along an easy crystallographic axis, but rather along an axis whose demagnetizating field is a minimum. This is called shape anisotropy and was proposed by (1947).
In real systems, there is always a particle size and shape distributions as well as a distribution of particle enviroments, depending on the topology of the system (e.g. in the case of a dispersion of particles distributed in a hosting matrix). This leads to a distribution of the total energy barriers of particles, P(ED) say, because of the different values of the various contributions ( i.e. magnetocrystalline, surface, stress, shape, etc.) and thus to distributions of the blocking temperatures TB.