As a single ion module, *so1ion* provides to *mcphas* the magnetic properties
of a single rare earth ion subject to the crystal field. Its main duty is
to calculate the magnetic moment given an external magnetic field and an exchange field .
To be more explicit - given the external magnetic and the exchange field by *mcphas*
the module *so1ion*
diagonalises the crystal field and Zeeman Hamiltonian (9):

and calculates the expectation value of the angular momentum according to

(10) |

with

(11) | |||

(12) |

Here is the partition sum, the eigenstate corresponding to
the eigenvalue of the Hamiltonian (9).
^{11}

Martin Rotter 2017-01-10