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Crystal-field analysis and Zeeman splittings of energy levels of Nd3+ (4f3) in GaN

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6 Author(s)
Gruber, John B. ; Department of Physics and Astronomy, The University of Texas at San Antonio, San Antonio, Texas 78249–0697, USA ; Burdick, Gary W. ; Woodward, N.T. ; Dierolf, V.
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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 signif- - icant 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).

Published in:

Journal of Applied Physics  (Volume:110 ,  Issue: 4 )

Date of Publication:

Aug 2011

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