Crystal-field analysis and Zeeman splittings of energy levels of Nd3+ (4f3) in GaN
The crystal-field splitting and Zeeman splitting of energy levels of Nd3+ (4f3) doped into semi-conducting GaN (3.2 eV) grown in the hexagonal (huntite) phase by plasma-assisted molecular beam epitaxy have been modeled using a parameterized Hamiltonian defined to operate within the complete 4f3 electronic configuration of Nd3+ substituted for Ga3+ in the lattice. Zeeman splittings were obtained by applying magnetic fields up to 6.6 T with the fields parallel and perpendicular to the crystallographic c-axis. The experimental energy (Stark) levels were obtained from a recent spectroscopic study on the same samples, where the combined excitation emission spectroscopy (CEES) identified the majority of Nd3+ ions as replacing Ga3+ in sites of C3v symmetry. The manifolds of Nd3+ (4f3)2S+1LJ modeled for the crystal-field splitting include the ground state, 4I9/2, and excited states 4I11/2, 4I13/2, 4F3/2, 4F5/2, 2H9/2, 4F7/2, 4S3/2, 4G5/2, and 4G7/2. The energies of 41 experimental Stark levels from these manifolds were modeled through the use of a Monte Carlo method in which independent crystal-field parameters (CFP) were given random starting values and optimized using standard least-squares fitting between calculated and experimental Stark levels. Irreducible representations (irreps) and crystal field quantum numbers (μ) were assigned to the energy level states of the 4I9/2 and 4F3/2 multiplet manifolds based on an analysis of the Zeeman data. This allows determination of which of the competing local minima should be considered to be the physically significant minimum. Using standard least-squares fitting between calculated and experimental Stark levels for Nd3+ in C3v symmetry, we obtain a final standard deviation of 7.01 cm−1 (rms = 5.48 cm−1).
Journal of Applied Physics
Gruber, John; Burdick, Gary; Woodward, Nathaniel; Dierolf, Volkmar; Chandra, Sreerenjini; and Sardar, Dhiraj, "Crystal-field analysis and Zeeman splittings of energy levels of Nd3+ (4f3) in GaN" (2011). Faculty Publications. 42.