Magnetic anisotropy energy

Magnetic Anisotropy Energy. There are several kinds of magnetic anisotropy energy and perhaps the most weU known is the magnetocrystaUine anisotropy. Only a crystalline soHd has this property because the energy is dictated by the symmetry of the crystal lattice. For example, in bcc Fe, the easy axis is in a (100) direction and in fee Ni, it is in a (111) direction. 

Usually, it is assumed that the magnetic anisotropy in nanoparticles is uniaxial with the magnetic anisotropy energy given by the simple expression... 

Fig. 29. Magnetic anisotropy energy barriers for small particles. and K,S are the barriers for shape and magnetosurface anisotropy, respectively, for metallic iron. Figure according to Boudart et al. (215).

When the superparamagnetic theory is applied for interpretation of any measured susceptibility line, it means that some model function x(V,a>,T) depending on several material parameters, is processed through averaging like such as Eq. (4.121) or (1.122). In our case the basic set of the material parameters comprises magnetization /, anisotropy energy density K, relaxation time To, and the particle volume fraction tp. Obviously, for nanosize-dispersed systems the effective values of /, K, and t0 do not coincide with those for a bulk material. The size/volume averaging itself introduces two independent... 

The first term on the right-hand side of eq. (2) is the Zeeman energy. The second term is the magnetic anisotropy energy, i)u and pM being the polar... 

The temperature dependence of the individual linewidth, eq. (21), is rather complicated. At very low temperatures the Langevin function in this equation becomes saturated for the majority of the nanoparticles, so that the main mechanism of this dependence is the thermal modulation of the magnetic anisotropy energy. Indeed, one can see from figure 8 (bottom) that the Ar temperature dependence provides a good estimate of the experimental low-temperature linewidth. As the damping factor linearly depends on the linewidth, it follows the same temperature dependence [11],... 

The most prominent contribution to the magnetic anisotropy energy is determined by the symmetry axis of the local atomic structure (Ch. 3). The free energy density eK of this magnetocrystalline anisotropy can be expressed, for example, by... 

The 3d transition metals have very small magnetic anisotropy energies (MAE), and their calculation is a challenge to ab initio relativistic electronic structure calculations. The MAE may be calculated by means of the so-called Force Theorem,[155-158] (FT) ... 

With sufficiently accurate methods for calculating the magnetic anisotropy energies it should also be possible to treat magnetostriction phenomena in... 

Rado, G. T. Ferrari, J. M. (1975). Electric field dependence of the magnetic anisotropy energy in magnetite (FcjOJ. Physical Review B, 12, 5166-73. 

Tachiki, M. (1960). Origin of the magnetic anisotropy energy of cobalt ferrite. Progress of Theoretical Physics, 23, 1055-72. 

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