First-principles method justifying the Dieke diagram and beyond

TL;DR

This paper introduces a first-principles approach to derive model Hamiltonians for rare-earth ions in solids, validating the Dieke diagram's applicability and exploring its limitations due to crystal field effects.

Contribution

The method connects quasiparticle extit{GW} calculations with model Hamiltonians, providing a theoretical basis for understanding rare-earth multiplets in solids.

Findings

Dieke diagram is justified for ions in solids.

Crystal fields significantly break Russell-Saunders coupling.

The approach clarifies the limitations of traditional models.

Abstract

We present a method to determine the model Hamiltonians to treat rare-earth multiplets in solids from the results of the quasiparticle self-consistent \textit{GW} (QSGW) method. We apply the method to trivalent Eu compounds EuCl$_3$, EuN, and Eu-doped GaN after examining free rare-earth ions. We solve the model Hamiltonian by the exact diagonalization. Our results justify applying the Dieke diagram to ions in solid, while its limitation is clarified. In particular, we show that the crystal fields cause sizable breaking of the Russell-Saunders coupling.