Investigations on the g factors for the Cu2+ sites in YBa1.9Na0.1Cu3O7−δ and YBa2Cu3O7−δ

The anisotropic g factors gi (i=x, y, z ) for the six-fold coordinated orthorhombic Cu2+(1) site in YBa1.9Na0.1Cu3O7−δ and the five-fold coordinated tetragonal Cu2+(2) site in YBa2Cu3O7−δ are theoretically studied from the perturbation formulas of the g factors for a 3d9 ion in orthorhombically and tetragonally elongated octahedra, respectively. The orthorhombic (or tetragonal) field parameters are obtained using the superposition model and the local structures of the Cu2+ sites. In view of covalency, the contributions from the ligand orbital and spin-orbit coupling interactions are taken into account. For the Cu2+(1) site in YBa1.9Na0.1Cu3O7−δ, the axial anisotropy Δg[=gz−(gx−gy)/2] may be ascribed to the moderate (about 3%) elongation of the Cu–O distance along c axis, while the perpendicular anisotropy δg(=gx−gy) can be characterized by the planar bond length deviation difference δR(≈0.083 Å) in the perpendicular (ab) plane. However, for the Cu2+(2) site in YBa2Cu3O7−δ, the anisotropy Δg(=g||−g⊥) is illustrated by the significant elongation of the [CuO5]8− cluster along c axis with about 25% longer axial Cu–O distance than the four planar ones. The theoretical g factors are in good agreement with the experimental data.