Optical and theoretical study of NaCr(P2O7): a look through the Neuhauser model and Racah theory

Abstract

A sample of NaCr(P₂O₇) was synthesized using the solid-state reaction method. X-ray diffraction and Rietveld refinement confirmed the formation of a monoclinic structure with the P2₁/a space group. Scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) analysis identified the morphology and homogeneity of the chemical composition. The optical absorption spectrum revealed a direct optical band gap of 2.9 eV and an Urbach energy of 0.44 eV. Notably, the absorption spectrum showed an interference dip on the lowest energy band ⁴T_2g(⁴F), attributed to spin–orbit coupling between states ²E_g(²G) and ⁴T_2g(⁴F). This phenomenon was analyzed using the Neuhauser model based on coupled potential energy surfaces. From this analysis, the electronic structure of Cr³⁺ (3d³) ions in the NaCr(P₂O₇) sample was determined, enabling a reliable calculation of Racah and crystal-field parameters. The results showed good agreement between experimental and theoretical energy levels. The study demonstrates the impact of spin–orbit interactions using the coupled potential energy surface model.