Transforming Crystal Field Parameters by Rotation of the Coordinate System

There is a special program *cf2mcphas* for rotating crystal field parameters
(Stevens Notation)
given in the orientation xyz to the *McPhase* notation yzx. The
original crystal field parameters have to be given in a file of the above format of a
single
ion parameter file. Output is written to stdout. Note, there is also a program *mcphas2cf* for transforming parameters back. For more general rotations of
crystal field parameters you can use the program *rotateBlm*(see
chapter 18).

As an example we consider a tetragonal system, where the crystal field parameters
are usually given such that xyz - we denote these parameters as
. For tetragonal symmetry only
and are
not zero. In order to use these parameters in *mocule cfield*, they
have to be transformed to a coordinate system with . Denoting the new
crystal field parameters which are to be used as the transformation
is given by

As a second example we consider an orthorhombic system, where the crystal field
parameters
are given such that xyz - we denote these parameters as
. For orthorhombic symmetry only
and are
not zero. In order to use these parameters in *mocule cfield*, they
have to be transformed to a coordinate system with . Denoting the new
crystal field parameters which are to be used as the transformation
is given by

As a second example we consider an dhcp system with quasi cubic sites, where the crystal
field parameters
are given such that xyz - we denote these parameters as
. Only
and are
not zero. In order to use these parameters in *mocule cfield*, they
have to be transformed to a coordinate system with . Denoting the new
crystal field parameters which are to be used as the transformation
is given by

The general transformation matrices are given by