Extension of Judd-Ofelt theory: Application on Eu$^{3+}$, Nd$^{3+}$ and Er$^{3+}$

TL;DR

This paper extends the Judd-Ofelt theory to better model f-f transition intensities in lanthanide ions, incorporating atomic-structure calculations and perturbative effects of crystal fields, validated on Eu$^{3+}$, Nd$^{3+}$, and Er$^{3+}$.

Contribution

The paper introduces a modified Judd-Ofelt model that includes perturbative spin-orbit interactions and wavelength-dependent refractive index effects, improving accuracy for lanthanide ions.

Findings

Accurately reproduces experimental oscillator strengths.

Provides physical insights into electronic transitions.

Results align well with existing literature.

Abstract

We present a modified version of the Judd-Ofelt theory, which describes the intensities of f-f transitions for trivalent lanthanide ions (Ln$^{3+}$) in solids. In our model, the properties of the dopant are calculated with well-established atomic-structure techniques, while the influence of the crystal-field potential is described as a perturbation, by three adjustable parameters. Compared to our previous work [G. Hovhannesyan \textit{et al.}, J. Lumin. \textbf{241}, 118456 (2022)], the spin-orbit interaction within the first excited configuration 4f$^{w-1}$5d is described in a perturbative way, whereas it is exactly taken into account in the ground configuration 4f$^w$, using all the eigenvector components of the free-ion levels. Moreover, the wavelength-dependence of the refractive index of the host material is also accounted for. We test the validity of our model on three ions: Eu$^{3+}$, Nd$^{3+}$ and Er$^{3+}$. The results of the extension are satisfactory, we are able to give a physical insight into all the transitions within the ground electronic configuration, and also to reproduce quantitatively experimental absorption oscillator strengths. We also performed calculations of standard JO parameters, and the results are in good agreement with the values reported in the literature. The code used to make the calculations is available on GitLab.