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

doi:10.1088/1674-1056/20/1/013102

Abstract 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 D_2d 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⁺.

Keywords: energy levels splitting rare earth ions complete energy matrix

Received: 19 January 2010
Revised: 08 February 2010
Accepted manuscript online:

PACS:	31.15.xp	(Perturbation theory)
	36.20.Kd	(Electronic structure and spectra)
	78.20.Bh	(Theory, models, and numerical simulation)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10774103 and 10974138).

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Duan Mei-Ling(段美玲), Kuang Xiao-Yu(邝小渝), Zhang Cai-Xia(张彩霞), and Chai Rui-Peng(柴瑞鹏) Comparative analysis of energy-level splitting of Pr³⁺ doped in LiYF₄ and LiBiF₄ crystals: a complete energy matrix calculation 2011 Chin. Phys. B 20 013102

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

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