Covalent bonding and J-J mixing effects on the EPR parameters of Er³⁺ ions in GaN crystal

The EPR parameters of trivalent Er³⁺ 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 Γ₆. 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 Er³⁺ ion and the replaced Ga³⁺ 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 ²K_15/2, which accounts for about 2.5%. The next important J-J contribution arises from the crystal-field mixture between the ground state ⁴I_15/2 and the first excited state ⁴I_13/2, and is usually less than 0.2%. The contributions from the rest states may be ignored.