Spin-Charge-Lattice Coupling across the Charge Density Wave Transition in a Kagome Lattice Antiferromagnet

Xiaokun Teng, David W. Tam, Lebing Chen, Hengxin Tan, Yaofeng Xie, Bin Gao, Garrett E. Granroth, Alexandre Ivanov, Philippe Bourges, Binghai Yan, Ming Yi, and Pengcheng Dai

Phys. Rev. Lett. 133, 046502 – Published 25 July 2024

Abstract

Understanding spin and lattice excitations in a metallic magnetic ordered system forms the basis to unveil the magnetic and lattice exchange couplings and their interactions with itinerant electrons. Kagome lattice antiferromagnet FeGe is interesting because it displays a rare charge density wave (CDW) deep inside the antiferromagnetic ordered phase that interacts with the magnetic order. We use neutron scattering to study the evolution of spin and lattice excitations across the CDW transition $T_{CDW}$ in FeGe. While spin excitations below $\sim 100 meV$ can be well described by spin waves of a spin-1 Heisenberg Hamiltonian, spin excitations at higher energies are centered around the Brillouin zone boundary and extend up to $\sim 180 meV$ consistent with quasiparticle excitations across spin-polarized electron-hole Fermi surfaces. Furthermore, $c$ -axis spin wave dispersion and Fe-Ge optical phonon modes show a clear hardening below $T_{CDW}$ due to spin-charge-lattice coupling but with no evidence of a phonon Kohn anomaly. By comparing our experimental results with density functional theory calculations in absolute units, we conclude that FeGe is a Hund’s metal in the intermediate correlated regime where magnetism has contributions from both itinerant and localized electrons arising from spin polarized electronic bands near the Fermi level.

Received 6 February 2024
Accepted 25 June 2024

DOI:https://doi.org/10.1103/PhysRevLett.133.046502

Physics Subject Headings (PhySH)

Charge density waves Magnetic coupling Magnetic order

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xiaokun Teng ¹, David W. Tam², Lebing Chen¹, Hengxin Tan ³, Yaofeng Xie¹, Bin Gao ¹, Garrett E. Granroth ⁴, Alexandre Ivanov ⁵, Philippe Bourges⁶, Binghai Yan ³, Ming Yi¹, and Pengcheng Dai ^1,*

¹Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
²Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, 5232 Villigen, Switzerland
³Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
⁴Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁵Institut Laue-Langevin, 71 avenue des Martyrs CS 20156, 38042 Grenoble Cedex 9, France
⁶Laboratoire Léon Brillouin, CEA-CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette, France

^*Contact author: pdai@rice.edu

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Issue

Vol. 133, Iss. 4 — 26 July 2024

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Images

Figure 1
(a) In-plane lattice structure of FeGe with red and gray denoting Fe and Ge atoms, respectively. Magnetic structure of FeGe at (b) $T > T_{canting}$ and (c) $T < T_{canting}$ . (d) Reciprocal space of FeGe. The thick red line denotes the momentum path along the $[H, - 0.5 H, - 1.5]$ direction. (e) DFT (with no spin orbit coupling) calculation. The red and blue bands represent spin up and down bands, respectively. Thick arrows indicate particle-hole ( $p − h$ ) scattering. (f) Dynamic susceptibility calculated from $p − h$ scattering of the set of bands in (e), where the energy axis has been renormalized by 1.7 [19].
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Figure 2
(a) Constant energy slices at $E = 30 \pm 10$ , $50 \pm 10$ , $70 \pm 10$ , $90 \pm 10$ , $110 \pm 10$ , $130 \pm 10$ , $150 \pm 10$ , $170 \pm 10 meV$ . The white lines are Brillouin zone boundaries, and high symmetry points are labeled with black points. (b) In-plane magnetic excitation along the $[H, - 0.5 H, - 1.5]$ direction. The black solid lines and gray dashed lines indicate simulated acoustic and optical spin wave branches, respectively, using a Heisenberg model (SpinW) [43]. Data in (a) and (b) are taken at 120 K. (c) Spin wave dispersions extracted by Gaussian fitting with a linear background of the symmetrized spectra along the $[H, - 0.5 H, - 1.5]$ direction. The vertical error bars indicate the energy integration range. Horizontal error bars are from fitting. Integration along the orthogonal in-plane direction is [ $- 0.1$ , 0.1]. (d) Integrated magnetic intensity in the first in-plane Brillouin zone and averaged between $L = [- 2.5, - 0.5]$ . The black line indicates the calculated spin wave intensity in absolute units assuming $S = 1$ in the $SpinW + Horace$ program [43]. Red, green, and blue symbols represent 120 K, 70 K, and 8 K data, respectively [44]. The red-dashed line is the DFT estimated spin susceptibility from the two electronic bands in Figs. 1 and 1.
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Figure 3
High energy magnetic excitations along (a) $[0, K]$ with $[H, - 0.5 H] = [- 0.1, 0.1]$ and (b) $[H, - 0.5 H]$ with $K = [- 0.1, 0.1]$ , $L = [- 4, 0]$ (r.l.u.) measured with $E_{i} = 300 meV$ . The dashed lines indicate the $M$ points in (a) and $K$ points in (b). Constant energy slices at (c) $E = 130 \pm 10$ , (d) $150 \pm 10$ , (e) $170 \pm 10 meV$ , and (f) $190 \pm 10 meV$ . The solid black lines mark the Brillouin zone boundaries. Data are taken at 120 K.
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Figure 4
Temperature dependent spin excitations along the $c$ axis ( $L$ direction) at (a) 8 K, (b) 70 K, and (c) 120 K measured with $E_{i} = 45 meV$ . (d) Spin wave dispersions determined by fitting constant momentum cuts taken from (a)–(c) with the Lorentzian on a constant background. Red and blue arrows in (a) and (d) mark $L = 1.35$ and $L = 1.25$ , respectively. (e) Temperature dependent spin wave energy at $L = 1.35$ (blue dots) and 1.25 (red dots), obtained from IN8. Gray and blue dashed lines mark $T_{canting}$ and $T_{CDW}$ respectively. Thick blue and red lines are guides to the eye.
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Figure 5
(a) In-plane phonon dispersion at $L = [- 3.1, - 2.9]$ and 120 K. The solid black lines are DFT calculations. Two separate optical phonon branches are labeled as OP1 and OP2, corresponding to Fe-Ge $A_{2 u}$ and Fe out-of-plane vibrations, respectively. Phonon dispersions of (b) the OP1 and (c) OP2 at 10 K, 50 K, 120 K, 200 K, and 300 K. (d) Temperature dependence of the OP1 energy shift throughout the Brillouin zone at 10 K, 50 K, 80 K, 120 K, 140 K, 160 K, and 300 K. The phonon energy at the base temperature (10 K) is subtracted. Temperature dependence of the OP1 phonon mode at (e) $Γ$ , (f) $M$ points, and the OP2 phonon mode at $M$ point. The thick colored lines in (b)–(d) and the gray lines in (e)–(g) are guides to the eye. Temperature dependence of phonon full width half maximum (FWHM) at the OP1 $Γ$ (h), OP1 $M$ (i), and OP2 $M$ (j).
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