4fN-15d energy levels of lanthanides: aquasi-angular-momentum approach and its application to Cs2NaYF6:Er3+

The spin--orbit interaction of the 5d electron needs to be taken intoaccount to give the proper energy structure for the 4f^N-15dconfiguration of heavy lanthanide ions occupying a site with ligandsforming an octahedron. This paper derives theoretical resultsfor the energy structure by treating the t₂ orbitals as quasi porbitals and then using angular-momentum coupling techniques. Ananalytic expression for the electric dipole absorption linestrengths between 4f^N multiplets and 4f^N-15d states isgiven in terms of various angular-momentum quantum numbers andre-coupling coefficients. The result is then applied to interpretthe excitation spectrum of Cs₂NaYF₆:Er³⁺. Thehigh-spin and low-spin states of Cs₂NaYF₆:Er³⁺ arediscussed in terms of the wavefunctions obtained by using thedeveloped theoretical model.