The local geometry of La 3+ in the crystals LaCl 3 , LaBr 3 , and LaNaF 4 is that of a tricapped trigonal prism with C 3h symmetry. If the crystals are doped with cerium, Ca 3+ replaces some of the La 3+ ions. The local geometry changes slightly when Ca 3+ is in the ground state ͑4f͒. However, in the 5d state, the relaxation of the lattice is quite different because the 5d levels experience a pseudo Jahn-Teller coupling with certain lattice displacements. This is because the lowest two 5d states ͑a singlet and a doublet, neglecting spin-orbit interac-tion͒ are very close in energy. We found that the Ca 3+ ion moves away from the centered position, accompanied by a strong deformation of the prism. One of the anions of the triangle of caps moves outward, also because of the pseudo Jahn-Teller distortion, and four anions of the prism move inward. The result is the occurrence of a 0.6-1.0 eV large Stokes shift in the 5d-4f emission. We analyzed the off-center movement of cerium in detail. For this study, we employed a widely used band structure code based on density functional theory. Ionic cluster calculations using the Hartree-Fock method confirm the results obtained and give additional information about the dynamics of the relaxation process.
We address two remarkable features in the optical behavior of Ce 3ϩ defects in LiBaF 3 : the fourfold splitting of the Ce 3ϩ 5d manifold in a cubic system, and the unusually large Stokes shift, of around 1 eV (Ϸ9000 cm Ϫ1 ), between the energy of the lowest Ce 3ϩ 4 f →5d absorption line and its 5d→4 f luminescence energy. To this end we investigated the electronic properties and the structure of several possible luminescence center configurations in LiBaF 3 :Ce 3ϩ , each consisting of a Ce 3ϩ substitution at a Ba or Li site, plus an appropriate charge-compensating defect. Using a plane-wave pseudopotential density-functional-based method to optimize the geometry of a supercell consisting of 3ϫ3ϫ3 LiBaF 3 unit cells, containing a single luminescence center, the equilibrium structures of these defect complexes were determined. We performed ab initio cluster calculations at the Hartree-Fock level to determine the optical-absorption energies of the Ce 3ϩ 4 f →5d transitions in these different geometries. Comparison of these energies with the results of opticalabsorption measurements on LiBaF 3 :Ce 3ϩ shows that the most likely luminescence center configuration consists of Ce 3ϩ at a Ba site, charge compensated by the substitution of one of its nearest-neighboring Ba ions by a Li ϩ ion. For this configuration we have repeated the cluster and supercell calculations with Ce 3ϩ in the ͓Xe͔5d 1 excited-state electronic configuration to determine the Ce 3ϩ 5d→4 f luminescence energy and to study effects that can explain the large Stokes shift in this material. These calculations predict an extensive lattice relaxation, induced by the excitation of the Ce 3ϩ ion, and yield a Stokes shift of 0.61 eV ͑compared to 1 eV found from experiment͒. The origin of this large Stokes shift is identified as a strong coupling of the crystal-field splitting of the Ce 3ϩ 5d manifold to the displacement of four of its F nearest neighbors.
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