Model analysis of multiplet excitation of RE ions using QSGW

The multiplet property of rare-earth (RE) atoms is one of the most important phenomena. However, it is difficult to discuss the properties of multiplet states using density functional theory (DFT). The reason for this difficulty comes from underestimation of the electron correlations in LDA/GGA correlation functional which is usually used in DFT calculation. Generally, LDA+U is used in strongly correlated systems like the f-orbital system. However, this "U" is an empirical parameter and it is difficult to define uniquely. In order to solve this problem, we focus on quasi-particle self-consistent GW (QSGW) approximation, and try to reproduce multiplet states of RE ions in the framework of DFT. We focus on free RE ions from Ce to Yb, and obtain electronic properties of them using QSGW. After that, we determine the parameters of the many-body Hamiltonian for the local f-orbitals of RE ions by comparing the mean field Hamiltonian of this one with QSGW Hamiltonian. Using these parameters, we obtain multiplet excited states and compare them with previous studies. Finally, we discuss the evolution of multiplet properties of trivalent Eu ions in materials using this framework. In this presentation, we discuss the trends in the multiplet states of each RE ion and the influence of the crystal field of Eu ions in materials.