Crystalline anisotropy energy, magnetic

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) ... 

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. 

The effective field includes the applied constant magnetic field Hq and the effect of the crystalline anisotropy [8]. If V(M) is the free energy... 

The value of coefficient B is defined by crystalline fields originated from equilibrium positions of lattice ions. Magnetic spins are coupled with these fields via weak relativistic spin-orbit interaction (giving rise to above magnetic anisotropy energy), while electric dipoles are coupled with electric crystalline field electrostatically. In ferroelastics, the elastic dipoles constituting order parameter interact with elastic strain or gradients of crystalline field. 

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