where is the mass of the electron, is the speed of light in the vacuum, is the distance from the nuclei, and are orbital and spin moments. We would like to note that this form of the SOC term has been used in almost all cases. Although the potential () is not generally central, nevertheless as has its maxim contribution close to the nuclei, where is approximated as the central potential, thus the approximation of SOC (1.5) is generally accepted.

Theoretically the magneto-crystalline anisotropy is determined from the evaluation of the difference of the system's energy when the magnetization is orientated along the easy and hard axes. If other contributions such as the magnetostatic energy can be neglected, then the MCA is given by the anisotropy due to the spin-orbit coupling:

(7) |

where is the spin-orbit coupling constant. This way the magnetization of the system in the hard direction requires an input of energy into the system. The principal difficulty in the study of the MCA is its small size, for example in transition metals MCA is of the order of , which is usually in the limit of accuracy of theoretical calculations.

Rocio Yanes