Studies on the spin-Hamiltonian parameters of two Cu2+ centers and their defect structures due to Jahn-Teller effect for Cu2+-doped ZnGa2O4 spinel

A complete diagonalization (of energy matrix) method based on the cluster approach (where the covalence effect due to the admixture between the orbitals of the central d(n) ion and that of ligands is considered) was applied to calculate the spin-Hamiltonian parameters (g factors, g(parallel to) and g(perpendicular to), and hyperfine structure constants, A(parallel to) and A(perpendicular to)) for two Cu2+ centers in ZnGa2O4 spinel at the temperature T approximate to 110 K. In both Cu2+ centers, Cu2+ ions occupy the trigonally-distorted octahedral sites 16d and the octahedrons undergo the static Jahn-Teller distortions from trigonal to tetragonally-elongated and tetragonally-compressed, respectively. The calculated spin-Hamiltonian parameters of the elongated Cu2+ center show good agreement with the experimental values and those of the compressed Cu2+ center are close to the observed values. The better agreement of spin-Hamiltonian parameter between calculation and experiment for the compressed Cu2+ center can be acquired by considering a small admixture of vertical bar d(x2-y2)> state to the vertical bar d(z2)> ground state due to the vibrational motion of ligands. The defect structures of both Cu2+ centers (characterized by the ligand displacements a(1) and a(2), respectively) in ZnGa2O4 spinel were also determined from the calculation.