Comparative analysis of free-ion energy levels of Er 3+ (4f 11) in various crystal hosts

Abstract

The best energy level data available in the literature for the trivalent erbium-doped systems of about 30 crystal hosts are analysed in terms of a uniform model free-ion Hamiltonian H fi. H fi consists of 20 free-ion parameters which include the central field E avg, electrostatic repulsion F k ( k = 2, 4, 6), spin-orbit interaction parameter ξ, two-body configuration interaction parameters α, β and γ, three-body configuration interaction parameters T i ( i = 2, 3, 4, 6, 7, 8), spin—other-orbit interaction parameters M j ( j = 0, 2, 4) and electrostatically correlated spin-orbit interaction parameters P k ( k = 2, 4, 6). Our systematic theoretical analysis of crystal free-ion levels results in good correlation between calculated and observed energies. The reanalysis of some systems reported here yields improved fits of calculated to experimental energy levels compared with fits reported previously in the literature. The effects of the crystalline hosts on the empirical parameters are examined.