Spin-Hamiltonian parameters and angular distortion for the trigonal Nd3+ center in congruent LiNbO3

The 52 × 52 energy matrix related to the ground multiplet ⁴I_9/2 and the first to third excited multiplets ⁴I_11/2, ⁴I_13/2 and ⁴I_15/2 for 4f³ ions in trigonal crystal field under an external magnetic field is established. By diagonalizing the energy matrix, the spin-Hamiltonian parameters (g factor g_//, g_⊥ and hyperfine structure constants ¹⁴³A_//, ¹⁴³A_⊥, ¹⁴⁵A_//, ¹⁴⁵A_⊥) of the trigonal Nd³⁺ center in congruent LiNbO₃ crystal are calculated. The calculated results are in reasonable agreement with the experimental values. From the calculations, the negative signs of hyperfine structure constants are suggested and the angular distortion of the trigonal Nd³⁺ center in LiNbO₃, which is unable to be determined by EXAFS measurement, is obtained. The results are discussed.