# A RIXS investigation of the crystal-field splitting of Sm$^{3+}$ in SmB$_6$

## TL;DR

This study uses high-resolution RIXS to precisely measure the crystal-field splitting of Sm$^{3+}$ in SmB$_6$, revealing a small splitting that suggests significant mass renormalization of 4f electrons in this topological insulator.

## Contribution

The paper provides the first high-resolution RIXS measurement of the crystal-field splitting of Sm$^{3+}$ in SmB$_6$, isolating the multiplet contributions and analyzing high-energy multiplets to determine the splitting.

## Key findings

- Crystal-field splitting of 20±10 meV for Sm$^{3+}$ in SmB$_6$
- Large mass renormalization of 4f electrons indicated
- High-energy multiplet analysis avoids elastic tail ambiguities

## Abstract

The crystal-field (CF) splitting of the $^6H_{5/2}$ Hund's rule ground state of Sm$^{3+}$ in the strongly correlated topological insulator SmB$_6$ has been determined with high resolution resonant inelastic x-ray scattering (RIXS) at the Sm M$_5$ edge. The valence selectivity of RIXS allows isolating the crystal-field-split excited multiplets of the Sm$^{3+}$ (4$f^5$) configuration from those of Sm$^{2+}$ (4$f^6$) in intermediate valent SmB$_6$. The very large energy range of RIXS allows the crystal-field analysis of a high lying multiplet at about 2.4\,eV that has the same total angular momentum $J$ as the ground state so that ambiguities due to the elastic tail can be avoided. We find that the $\Gamma_7$ doublet and $\Gamma_8$ quartet of the $^6H_{5/2}$ Hund's rule ground state are split by $\Delta^{CF}_{^6H_{5/2}}$\,=\,20$\pm$10\,meV which sets an upper limit for the 4$f$ band width. This indicates an extremely large mass renormalization from the band structure value, pointing out the need to consider the coefficients of fractional parentage for the hopping of the 4$f$ electrons.