# Spin-Orbital-Intertwined Nematic State in FeSe

## TL;DR

This study uncovers a nontrivial spin-orbit coupling effect in FeSe's nematic state, revealing orbital-dependent spin susceptibility, orbital reconstruction, and a spin-orbital-intertwined nematicity that advances understanding of its nematic transition mechanism.

## Contribution

It demonstrates the role of spin-orbit coupling and Hund's coupling in the nematic state of FeSe, highlighting orbital-dependent effects and spin-orbital interplay.

## Key findings

- Orbital-dependent spin susceptibility dominated by 3dxy orbital.
- Orbital reconstruction occurs on 3dxy, 3dxz, and 3dyz orbitals below Tnem.
- Development of in-plane anisotropy indicating spin-orbital-intertwined nematicity.

## Abstract

The importance of the spin-orbit coupling (SOC) effect in Fe-based superconductors (FeSCs) has recently been under hot debate. Considering the Hund's coupling-induced electronic correlation, the understanding of the role of SOC in FeSCs is not trivial and is still elusive. Here, through a comprehensive study of 77Se and 57Fe nuclear magnetic resonance, a nontrivial SOC effect is revealed in the nematic state of FeSe. First, the orbital-dependent spin susceptibility, determined by the anisotropy of the 57Fe Knight shift, indicates a predominant role from the 3dxy orbital, which suggests the coexistence of local and itinerant spin degrees of freedom (d.o.f.) in the FeSe. Then, we reconfirm that the orbital reconstruction below the nematic transition temperature (Tnem ~ 90 K) happens not only on the 3dxz and 3dyz orbitals but also on the 3dxy orbital, which is beyond a trivial ferro-orbital order picture. Moreover, our results also indicate the development of a coherent coupling between the local and itinerant spin d.o.f. below Tnem, which is ascribed to a Hund's coupling-induced electronic crossover on the 3dxy orbital. Finally, due to a nontrivial SOC effect, sizable in-plane anisotropy of the spin susceptibility emerges in the nematic state, suggesting a spin-orbital-intertwined nematicity rather than simply spin- or orbital-driven nematicity}. The present work not only reveals a nontrivial SOC effect in the nematic state but also sheds light on the mechanism of nematic transition in FeSe.