Ab initio simulation of the absorption spectrum of Ruby and the role of vibronic coupling

Abstract

Context

Ruby is a material commonly found in Nature. Its red color is due to chromium impurity in the lattice of \(\alpha \)-alumina. It has several technological applications, such as lasers, thermometers, and radiation dosimeters. The study of its absorption spectrum is relevant in this context. On the other hand, vibronic coupling in solids is an important phenomenon since it can change the features of the absorption spectrum, especially when involving transition metal d-d electronic transitions in a quasi-octahedral environment, as in the case considered here. This work provides insight into the role of the vibronic coupling mechanism in the profile of the absorption spectrum of Ruby in the visible region.

Methods

The spectrum of Ruby, i.e., \(\alpha \)-alumina doped with chromium, is calculated within the linear response regime applied to a PBE DFT initial calculation. Intensities are taken as the imaginary part of the frequency-dependent dielectric function, obtained by the Green-Kubo formula. The model is composed of an \(\alpha \)-alumina supercell in which an aluminum atom is replaced by a chromium atom. Periodic boundary conditions were applied throughout. The vertical spectrum at the equilibrium geometry was first reported. Then, vibronic coupling effects were evaluated by carrying out distortions of the geometry along the normal modes related to the motions of chromium and its first neighbors. In addition, the effect of distortions involving combined modes was also assessed. In the last case, the modes are combined in pairs, generating hundreds of possibilities, all of which were carefully calculated. Modes (pure and combined) that change the absorption profile are clearly identified, and it is shown that they were able to change both position and intensity of the absorption peak in the visible region.