Hello. I have a question regarding the choice of axes when calculating the eigenenergies of a crystal field Hamiltonian. I am planning to plot the wavefunction of the ground state in real space. To do this, I need to understand how the ( x, y, z ) axes in angular momentum space correspond to the crystal’s ( a, b, c ) axes.
yes and no. The part of the documentation you refer to (in the “Using the point charge model” just above the section on “Calculating Physical Properties”) is only about the point charge calculation - if you are using the point charge calculated crystal field parameters, then yes, the xyz-axes are as you write.
However, if you are not using the point charge model, then the coordinates are such that the z-axis is parallel to the axis with the highest rotational symmetry at that rare site. (This is a general rule for all crystal field calculations, not just in Mantid). Depending on the exact point symmetry there is then still freedom to choose the x and y-axes. E.g. if your rare-earth site just has a single rotation axis (with point group Cn where n is an n-fold rotation) then rotating the crystal field by 360/n about this axis is equivalent and although this will change the Blm parameters it will not affect the eigenvalues (or INS intensities or physical properties like susceptibility), so there is a choice of where the x and y axes can be - however I think that it will affect your plot of the wavefunction (since this is not really an observable).
So it’s a bit tricky working out exactly what the axes are for a given set of CEF parameters unfortunately… In the past I’ve tried to relate the parameters back to the point charge model but this can also be quite hard to do.