Covalent bonding andJ–Jmixing effects on the EPR parameters of Er^{3 +}ions in GaN crystal

Abstract

The EPR parameters of trivalent Er 3+ ions doped in hexagonal GaN crystal have been studied by diagonalizing the 364×364 complete energy matrices. The results indicate that the resonance ground states may be derived from the Kramers doublet Γ 6 . The EPR g-factors may be ascribed to the stronger covalent bonding and nephelauxetic effects compared with other rare-earth doped complexes, as a result of the mismatch of ionic radii of the impurity Er 3+ ion and the replaced Ga 3+ ion apart from the intrinsic covalency of host GaN. Furthermore, the J-J mixing effects on the EPR parameters from the high-lying manifolds have been evaluated. It is found that the dominant J-J mixing contribution is from the manifold 2 K 15/2 , which accounts for about 2.5%. The next important J-J contribution arises from the crystal-field mixture between the ground state 4 I 15/2 and the first excited state 4 I 13/2 , and is usually less than 0.2%. The contributions from the rest states may be ignored.

Determination of charge-compensated C 3υ (II) centers for Er3+ ions in CdF2 and CaF2 crystals*

“…The more charges of the substituted Er 3+ ion and the ligand O 2− ion in the (Er 3+ -F − -O 2− 4 ) structure will bring about the stronger electrostatic interaction between the central Er 3+ ion and ligand ions than the scenario at the cubic site of (Er 3+ -F − 8 ) structure without charge compensation. Since the orbit reduction factor k usually reflects the average covalent effect, [30,50] the less orbit reduction factor k with the (Er 3+ -F − -O 2− 4 ) structure also implies that the stronger covalent bonding effects may exist in the C 3v (II) centers for Er 3+ ions in CaF 2 and CaF 2 , which consists well with the calculated average g-factor g av . The less k of C 3v (II) center in CdF 2 means the stronger covalent bond effect than that in CaF 2 host, which may be ascribed to the less difference in ion radius between the substituted Er 3+ ion (r Er 3+ = 0.881 Å) and the host ion Cd 2+ (r Cd 2+ = 0.97 Å) in CdF 2 compared with the replaced Ca 2+ ion (r Ca 2+ = 0.99 Å) in CaF 2 host.…”

“…In our calculations, in order to reduce the number of adjustable parameters, the wellfitting free-ion parameters of Er 3+ ions doped in LaF 3 are used, [41] because a number of studies have proved that the slight variation of free-ion parameters hardly affects the Stark splitting or the EPR parameters, merely disturbing the centroid of high manifolds. [27][28][29][30] By simulating the Stark energy levels and EPR parameters of Er 3+ ions in CaF 2 and CdF 2 with C 3v (II) centers based on the above distorted models, we determine the values of other intrinsic parameters:…”

“…( 1) are written and defined according to traditional practice. [27][28][29][30] The crystal-field Hamiltonian with the C 3v site symmetry may be expanded as…”

“…[23][24][25][26] In the past several decades, the electron paramagnetic resonance (EPR) as a useful tool has been widely employed to identify the defect sites of paramagnetic ions. [27][28][29][30] For instance, the five different EPR spectra of Er 3+ in CaF 2 have been reported by Ranon and Low, which are associated with cubic or tetragonal or trigonal point symmetry. [31] Subsequently, both of C 3v local symmetry sites were also observed by Ensign and Byer through using correlated EPR and optical spectra for Er 3+ in CdF 2 .…”