Diagonalization of second-rank crystal field terms for 3d N and 4f N ions at triclinic or monoclinic symmetry sites – case study: Cr 4+ in Li 2MgSiO 4 and Nd 3+ in β-BaB 2O 4

Abstract

Transition ions often occur at triclinic ( C 1 and C i) symmetry sites in crystals. Proper understanding of spectroscopic, magnetic, and structural properties of such crystals require consideration of low symmetry aspects in crystal field (CF) theory, which are not yet well understood. In this paper a method of extracting information from CF parameters (CFPs) for 3d N and 4f N ions at low symmetry sites is developed. The method is based on three-dimensional diagonalization (3DD) of a 3 × 3 matrix, which enables determination of the principal axis system and principal values of the 2nd-rank CFPs. Our approach incorporates monoclinic and, for the first time, triclinic standardization, including the 4th- and 6th-rank CF terms. These features, not included in earlier studies, enable more comprehensive analysis of low symmetry aspects. Major focus is on extracting information inherent in the principal axis system and principal values of the 2nd-rank CFPs for transition ions at low symmetry sites. Computations are facilitated by the recently developed computer package DPC, which comprises the module 3DD and other modules suitable for the tasks in question. As a case study, spectroscopic and structural data for two technologically important materials exhibiting triclinic site symmetry: Li 2MgSiO 4 doped with Cr 4+ ions and β-BaB 2O 4 doped with Nd 3+ ions are considered. Due to the ascent in symmetry method, the module 3DD can also be used for monoclinic symmetry cases.