Reverse Rotation Matrices

These matrices rotate a set of crystal field parameters (or Stevens operators) by $\Theta_1$=90$^o$ and $\Phi_1$=90$^o$ and again by $\Theta_2$=90$^o$ and $\Phi_2$=90$^o$.

  $$\stackrel{=}{\mathbf S^{-1}}_2(\pi/2,\pi/2) = \left( \begin{arra... .../2 \\ 2 & 0 & 0 & 0 & 0 \\ 0 & 0 & -3/2 & 0 & -1/2 \\ \end{array} \right)$$ (188)

  $$\stackrel{=}{\mathbf S^{-1}}_4(\pi/2,\pi/2) = \left( \begin{arra... ... & 0 & 0 \\ 0 & 0 & 0 & 0 & 35/8 & 0 & 7/8 & 0 & 1/8 \\ \end{array} \right)$$ (189)

  $$\stackrel{=}{\mathbf S^{-1}}_6(\pi/2,\pi/2) = \left( \begin{arra... ...& 0 &-231/32 & 0 & -33/32 & 0 & %%@ -11/32 & 0 & -1/32 \\ \end{array} \right)$$ (190)