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Crystal-Field Energy Levels of Trivalent Erbium Ion in Cubic Symmetry

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Crystal-Field Energy Levels of Trivalent Erbium Ion in Cubic Symmetry

Said Laachira, Mohamed Moussetadb, Rahma Adhirib, and Ahmed Fahlia

aUFR S.I.R.I, Universit´e Hassan II-Mohammedia Facult´e des Sciences, Ben M’sik, B.P 7955 Casablanca, Morocco

bL.P.S.C.M, Universit´e Hassan II-Mohammedia Facult´e des Sciences, Ben M’sik, B.P 7955 Casablanca, Morocco

Reprint requests to S. L.; E-mail:saidlaachir@yahoo.fr

Z. Naturforsch.66a,457 – 460 (2011); received December 16, 2010

This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term4I15/2of the trivalent erbium ion splits into three Stark quartetsΓ8and two different doubletsΓ6 andΓ7 (irreducible representations). The CF energy matrix of the Er3+ ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors areg=6.8 andg=6.0 forΓ6and Γ7, respectively.

Key words:Crystal Field; Energy Level; Erbium; Rare Earth.

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