D. Kato

G. Gaigalas

L. Rad?i?t?

P. Jonsson

P. Rynkun

National Institute for Fusion Science (NIFS-Repository)

i) Introduction The basic, and novel, idea of thiswork is to calculate the energy spectrum and the tran-sition parameters for the free ion Er3+ in an ab initioapproach and then apply the point charge crystal ﬁeldas a perturbation to obtain the Er2O3 Stark componentsof the [Xe]4f11 4Io15/2 level. The calculations were per-formed using the GRASP2K 1) which is based on themulticonﬁguration Dirac-Hartree-Fock method and rela-tivistic conﬁguration interaction.ii) Calculation and results of Er3+ free ion Thechange of the positions of levels 4S3/2 and4F9/2 when in-creasing the active sets and opening deeper closed shellsis demonstrated in Fig. 1. It is seen that calculationswith the active set n = 6 including single and double sub-stitutions from the valence, core and core-valence shells,when only 4d and 4p excitations are taken from the core(the case SD V+C+CV 4d 4p), lead to energy level po-sitions close to the experimental ones. Further increaseof the active set or opening of deeper core shells do notsigniﬁcantly change the results (see Fig. 1).Fig. 1: Convergence of the energy for 4f11 4S3/2 (ﬁlledsymbols) and 4F9/2 (empty symbols) levels of Er3+: a) open-ing core shells and b) increasing principal quantum numberof the active set in diﬀerent strategies. In one case, notatedV V + CC + CV , SD excitation were made without restric-tions.iii) Method of accounting for the crystal ﬁeldeﬀects In order to calculate the splitting of the ionicenergy levels γJ in solids, the crystal ﬁeld eﬀects mustbe included. Instead of using the simpliﬁed treatment ofthe crystal ﬁeld eﬀects based on the Stevens’ operator-equivalent method we used the fully ab-initio method.In order to be able to perform crystal-ﬁeld calculationsthe GRASP2K 1) relativistic atomic structure programsbeen extended. This extension include programs for thecrystal ﬁeld operator matrix element calculation and di-agonalization of matrix of full atomic Hamiltonian (in-cluding matrix elements between diﬀerent atomic statefunctions).iv) Calculations of the crystal-ﬁeld splitting ofEr3+ ion in the Er2O3 compound Table I comparesthe results obtained in this study with the results of otherauthors using semi-empirical methods as well as withthe experimental results. Experimental data of Starkcomponents were obtained for single crystals Er2O3 andEr3:Y2O32). Semi-empirical Stark levels were calcu-lated using a Hamiltonian containing atomic and crys-tal ﬁeld terms. In other experiments Er2O3 powder wasused 3). Experiment have shown, that powder have alsocubic symmetry. Data from experiment were used insemi-empirical methods to compute crystal ﬁeld param-eters and Stark levels. In another experiment the Starkcomponents of lowest three levels were measured by ab-sorption spectroscopy in Er2O3 and ErF34). As can beseen from the comparative analysis of the results, the ab-initio point charge crystal ﬁeld approximation for Er3+in Er2O3 leads to a bigger splitting compared with theexperimental one. In order to get more accurate theo-retical results, the further development of the theory isneeded.Table I: Comparison of computed energy (Stark) levels (incm−1) of Er3+ (4f11 4Io15/2) in Er2O3 crystal ﬁeld with othertheories and experiment.Experiment Semi-empirical Theoretical2) 3) 4) 2) 3) 4) This work0 0 0 1 2 0 0.0038 36 39.5 36 37 11.6 495.3875 69 75.3 66 65 79.4 797.4188 86 89.0 93 81 107.7 995.97159 162 260.1 169 157 154.8 1287.26265 263 349.6 262 265 176.7 1709.93490 484 488.6 477 483 194.3 2213.95505 503 531.2 502 506 249.8 2609.691) P. Jo¨nsson et al., Comput. Phys. Commun. (2013)vol.184 2197.2) J.B. Gruber et al., J. Appl. Phys. (2010) vol.108023109.3) M. Dammak and De-Long Zhang, Journal of Alloysand Compounds (2006) vol.407 8.4) N. Magnani et al., Phys. Status Solidi C (2007) vol.41209.334§15. Energy Level Structure of Er3+ Free Ion and Er3+ Ion in Er2O3 crystalGaigalas, G., Rynkun, P., Radzˇiu¯te˙, L. (Vilnius Univ.), Jönsson, P. (Malmö Univ.),  Kato, D.

Energy Level Structure of Er3? Free Ion and Er3? Ion in Er2O3 crystal

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