# ErNiBC - single ion module

The crystal field ground state of the Er ion in ErNiBC can be described by a quasi-quartett consisting of two doublets separated by a energy interval .

In order to calculate efficiently the single ion property (for small effective magnetic fields in comparison to the total CF splitting) the Hamiltonian is projected to the quasi quartett and may be written as

 (133)

with the angular momentum operators given by the 4x4 matrices

 (134)

 (135)

 (136)

The constants - can be computed from the crystal field parameters, if these are known. On the other hand, they are connected to the saturation magnetic moments by the following equations ( denotes the maximum of the argument values)

 (137)

 (138) (139)

 (140) (141)

The module given in /examples/erni2b2c/1ion_mod/quartett.c diagonalises the Hamiltonian (140) and calculates the thermal expectation value of the vector , which is returned to the McPhas program.

Martin Rotter 2017-01-10