# Competing itinerant and local spin interactions in kagome metal FeGe

**Authors:** Lebing Chen, Xiaokun Teng, Hengxin Tan, Barry L. Winn, Garrett E. Granorth, Feng Ye, D. H. Yu, R. A. Mole, Bin Gao, Binghai Yan, Ming Yi, Pengcheng Dai  
**arXiv:** [2308.04815](https://arxiv.org/abs/2308.04815)  
**Date:** 2023-08-09  
**Summary page:** https://www.summarizepaper.com/en/paper/2308.04815v1/

## Key points

- Two-dimensional kagome metals with corner-sharing triangles are studied for strong electron correlations and band topology
- These systems exhibit competing quantum phases such as CDW, magnetic order, and superconductivity
- FeGe is used as a model system in this study
- FeGe exhibits A-type collinear antiferromagnetic (AFM) order at T_N (~400 K)
- Below T_N, FeGe undergoes a phase transition and establishes a CDW phase coupled with AFM ordered moment at T_CDW (~100 K)
- At even lower temperatures around T_Canting (~60 K), FeGe forms a unique $c$-axis double cone AFM structure
- Neutron scattering techniques were used to investigate the magnetic excitations in FeGe
- Gapless incommensurate spin excitations associated with the double cone AFM structure were observed at temperatures above T_Canting and T_CDW
- These incommensurate spin excitations merge into gapped commensurate spin waves originating from the A-type AFM order
- The intensity of these incommensurate spin excitations peaks at T_Canting indicating critical scattering associated with a second-order magnetic phase transition as temperature decreases
- Density functional theory calculations were performed to understand these findings further
- The researchers concluded that the incommensurate magnetic structure arises from nested Fermi surfaces of itinerant electrons and formation of a spin density wave order likely due to flat electronic bands near the Fermi level around T_N and associated electron correlation effects

## Summary

Two-dimensional kagome metals with corner-sharing triangles have become a fascinating platform for studying strong electron correlations and band topology due to their geometrically frustrated lattice structure. These systems exhibit similar energy scales between spin, lattice, and electronic degrees of freedom, leading to the emergence of competing quantum phases such as charge density wave (CDW), magnetic order, and superconductivity. In this study, the researchers focused on the kagome metal FeGe as a model system. They observed that FeGe initially exhibits A-type collinear antiferromagnetic (AFM) order at a transition temperature (T_N) of around 400 K. Below T_N, FeGe undergoes a phase transition and establishes a CDW phase coupled with AFM ordered moment at T_CDW (~100 K). At even lower temperatures, around T_Canting (~60 K), FeGe forms a unique $c$-axis double cone AFM structure. Using neutron scattering techniques, the researchers investigated the magnetic excitations in FeGe. They discovered the presence of gapless incommensurate spin excitations associated with the double cone AFM structure at temperatures well above T_Canting and T_CDW. These incommensurate spin excitations merge into gapped commensurate spin waves originating from the A-type AFM order which follow the Bose population factor and can be accurately described by a local moment Heisenberg Hamiltonian. Interestingly, these incommensurate spin excitations first appear below T_N when AFM order is still commensurate but start to deviate from the Bose population factor around T_CDW. The intensity of these incommensurate spin excitations peaks at T_Canting indicating critical scattering associated with a second-order magnetic phase transition as temperature decreases. To understand these findings further, density functional theory calculations were performed and compared with experimental results. The researchers concluded that the incommensurate magnetic structure arises from nested Fermi surfaces of itinerant electrons and formation of a spin density wave order likely due to flat electronic bands near the Fermi level around T_N and associated electron correlation effects. This suggests coupling between spin density wave and CDW orders which could explain various quantum phases observed in kagome metals like FeGe. Overall, this study provides valuable insights into complex interplay between itinerant and local spin interactions in these systems.