Energy magnetocrystalline

As the direction of magnetization of an elongated particle is reversed (from A to C), it must be magnetized in a direction that increases its magnetostatic and magnetocrystalline energies (B). 

Magnetocrystalline energies, (Vc)ioo (V Jni and < Vc)ioo-(V"c)no. can be derived from magnetization measurements in the ferromagnetic state, and from these the crystal-field parameters can also be estimated. 

Magnetocrystalline energy can show various symmetries, but uniaxial and cubic forms cover the majority of cases. For uniaxial symmetry, the energy is given by... 

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

With decreasing particle size, the magnetic contributions from the surface will eventually become more important than those from the bulk of the particle, and hence surface anisotropy energy will dominate over the magnetocrystalline anisotropy and magnetostatic energies. A uniaxial anisotropy energy proportional to the particle surface S... 

Fid. 9. Magnetocrystalline anisotropy. K, V and K2V are the energy barriers for two different directions of relaxation. Figure according to Boudart et al. (215). 

Figure 5. Physical origin of magnetic anisotropy (a) compass-needle analogy of shape anisotropy and (b-c) magnetocrystalline anisotropy. In (b) and (c), the anisotropy energy is given by the electrostatic repulsion between the tripositive rare-earth ions and the negative crystal-field charges.

In 3d atoms, the spin-orbit coupling is much smaller than the crystal-field energy, and the magnetic anisotropy is a perturbative effect [7, 8, 16]. Typical second- and fourth-order transition-metal anisotropies are of the orders of 1 MJ/m3 and 0.01 MJ/m3, respectively. A manifestation of magnetocrystalline anisotropy is magnetoelastic anisotropy, where the crystal field is changed by mechanical strain [5, 16]. 

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