Comparative analysis of energy-level splitting of Pr3+ doped in LiYF4 and LiBiF4 crystals: a complete energy matrix calculation

Based on the combination of Racah's group-theoretical consideration with Slater's wavefunction, a 91 × 91 complete energy matrix is established in tetragonal ligand field D2d for Pr3+ ion. Thus, the Stark energy-levels of Pr3+ ions doped separately in LiYF4 and LiBiF4 crystals are calculated, and our calculations imply that the complete energy matrix method can be used as an effective tool to calculate the energy-levels of the systems doped by rare earth ions. Besides, the influence of Pr3+ on energy-level splitting is investigated, and the similarities and the differences between the two doped crystals are demonstrated in detail by comparing their several pairs of curves and crystal field strength quantities. We see that the energy splitting patterns are similar and the crystal field interaction of LiYF4:Pr3+ is stronger than that of LiBiF4:Pr3+.