Including Quadrupolar and Higher Order Interactions

SIMPLICIUS: The interest of modern solid state physics is in exotic matter - so we need some advanced concepts in order to achieve excellence in our studies. Can you predict the Jahn Teller effect in McPhase ?

ORLANDO: Indeed I would have interest in this subject as well, if we put Pr in our sample, the system becomes nonmagnetic and it shows huge magnetostrictive effects at an ordering temperature, which is most probably a Jahn-Teller transition.

EWALD: So what we need to do such calculations are higher order interactions. Some modules such as so1ion allow to calculate systems with higher order interactions such as quadrupolar interactions. Quadrupolar and higher order interactions can be calculated, which can be described by products of Stevens operators. The general two ion exchange coupling is

  $${\mathcal H}_{JJ}= -\frac{1}{2} \sum_{ij} \sum_ {ll'mm'} {... ...lpha'=(l'm')}} J_{\alpha\alpha'}(ij) \hat I_{\alpha}^i \hat I_{\alpha'}^{j}$$ (85)

For further information on the notation and symmetry restrictions to the parameters in the Hamiltonian refer to [1].