Investigations of the spin-Hamiltonian parameters for Er³⁺ions in AlN crystal

Abstract

The spin-Hamiltonian parameters (g factor g // , g ? and hyperfine structure constants A // , A ? ) for Er 3þ ion at the trigonal Al 3þ site of AlN crystal are calculated by diagonalising the 52 Â 52 energy matrix. The matrix are related to the ground mutiplet 4 I 15/2 and the first to third excited multiplets 4 I 13/2 , 4 I 11/2 and 4 I 9/2 for 4f 11 ions in trigonal crystal field under an external magnetic field. The crystal-field parameters used in the matrix are obtained from the superposition model and the local lattice relaxation due to the substitution of Er 3þ for Al 3þ is considered. The calculated spin-Hamiltonian parameters are in reasonable agreement with the experimental values and the signs of hyperfine structure constants are suggested. The results are discussed.