3 Determination of one-site anisotropy energy

(144) |

where and are matrices . If we assume that the on-site anisotropy is uniaxial and its easy axis is parallel to Z axis, we can rewrite the Hamiltonian as:

In spherical coordinates we can write as a function of the polar and azimuthal angles and , respectively.

(147) |

and evaluate the second derivatives with respect to the polar and azimuthal angles.

If the spin i belongs to the plane XY then Eq. (A.25) is reduced to :

(150) |

Now we evaluate the second derivatives with respect to the polar and azimuthal angles of the energy:

(151) | |||

(152) |

Due to the fact that the spin variables are independent, the equations above can be reduced to:

The free energy of the system is related with the second derivatives above:

(155) |

Taking into account the hypothesis that the on-site anisotropy is uniaxial Eq. (A.22), this expression can be reduced to:

(156) |

Therefore we can calculate the on-site anisotropy constant evaluating the free energy at

(157) |

with

(158) |

Rocio Yanes