DFT computations combined with semiempirical modeling of variations with temperature of spectroscopic and magnetic properties of Gd3+-doped PbTiO3

Abstract

The rare-earth or 3d transition metal dopants in perovskites have potential to induce interesting features, thus opening opportunities for investigations and applications. Hence, understanding some features, i.e., defect structure, site of incorporation, valence state, and mechanism of charge compensation, in a wide range of temperature is crucial for their technological applications. A comprehensive understanding of the mechanism of structural changes in PbTiO₃ doped with trivalent rare-earths is significant for their potential applications in photonics. To unravel the structural changes, we utilize the density functional theory (DFT) to optimize structural data, which then serve as input for the semiempirical superposition model (SPM) analysis of spectroscopic and magnetic properties of Gd³⁺-doped PbTiO₃. We compute the formation energies of the doped compounds with and without O-vacancy to determine the stable composition. Analysis of the Bader electron charges computed using DFT plus quantum theory of atoms in molecules enables elucidating the effects of the Gd dopant and O-vacancy on the ionic and covalent bonds and, thereby, chemical stability of the compositions. To explain and corroborate the zero-field splitting parameters (ZFSPs) measured by EMR and the lattice parameter changes obtained from XRD, we employ SPM. The optimized structures obtained from ab initio computations for various structural models of Gd³⁺ doped PbTiO₃ are utilized as input data for SPM calculations of ZFPs. This enables theoretical analysis of variations of ZFSPs from 5 to 780 K. The results were fine-tuned by matching with available experimental EMR data for Gd³⁺ probes in PbTiO₃ nanoparticles. Modeling has been carried out considering several possible structural models and the role of an O-vacancy around Gd³⁺ centers. The results show that the two-fold modeling approach, combining DFT and SPM, provides a reliable description of experimental data. Comparative analysis indicates that the Ti-site is less favorable for being replaced by Gd³⁺ with/without O-vacancy. This analysis confirms the plausibility of the Pb²⁺ site for Gd³⁺ dopants and sheds light on the changes of crystal structure during the phase transitions occurring in PbTiO₃ with decreasing temperature.