Semi-empirical and ab-initio calculations of the crystal field interaction in rare earth cuprates

Abstract

Semi-empirical and ab-initio methods useful for theoretical investigations of the crystal field (CF) interaction in rare earth (RE) cuprates are described. Concrete calculations are performed for Sm 1+ x Ba 2− x Cu 3O 6+ y , a system providing detailed data on intermultiplet infrared-active CF transitions for Sm 3+ ions on the regular D 4 h symmetry sites as well as on the substituted C 4 v symmetry Ba sites. Within this study, the main attention is paid to the second order CF parameters calculated using a parameter free first principles method based on the density functional theory (DFT). A general potential linearized augmented plane wave (LAPW) computational method is used to obtain the ground state charge density. The calculated value of B 20=320 cm −1 in D 4 h symmetry sites of Sm is in a good agreement with the phenomenological value of 282 cm −1 obtained from a fit to infrared transmission spectroscopy data. For Sm in the C 4 v symmetry sites, the DFT value of B 20=−227 cm −1 together with the standard superposition model values, B 40=24, B 44=−331, B 60=−427 and B 64=624 cm −1, allow us to interpret the main features of the available infrared absorption data. It is shown that the sign of the B 20 in SmBa 2Cu 3O 6+ y , positive in the regular sites and negative in the Ba sites, is governed by the shape of the crystal potential within the LAPW atomic sphere of Sm atom.