Damped Dirac magnon in the metallic kagome antiferromagnet FeSn

Letter

Damped Dirac magnon in the metallic kagome antiferromagnet FeSn

Seung-Hwan Do, Koji Kaneko, Ryoichi Kajimoto, Kazuya Kamazawa, Matthew B. Stone, Jiao Y. Y. Lin, Shinichi Itoh, Takatsugu Masuda, German D. Samolyuk, Elbio Dagotto, William R. Meier, Brian C. Sales, Hu Miao, and Andrew D. Christianson

Phys. Rev. B 105, L180403 – Published 6 May 2022

Abstract

The kagome lattice is a fertile platform to explore topological excitations with both Fermi-Dirac and Bose-Einstein statistics. While relativistic Dirac fermions and flat bands have been discovered in the electronic structure of kagome metals, the spin excitations have received less attention. Here, we report inelastic neutron scattering studies of the prototypical kagome magnetic metal FeSn. The spectra display well-defined spin waves extending to 120 meV. Above this energy, the spin waves become progressively broadened, reflecting interactions with the Stoner continuum. Using linear spin-wave theory, we determine an effective spin Hamiltonian that reproduces the measured dispersion. This analysis indicates that the Dirac magnon at the $K$ point remarkably occurs on the brink of a region where well-defined spin waves become unobservable. Our results emphasize the influential role of itinerant carriers on the topological spin excitations of metallic kagome magnets.

Received 18 July 2021
Revised 18 January 2022
Accepted 6 April 2022
Corrected 1 August 2022

DOI:https://doi.org/10.1103/PhysRevB.105.L180403

Physics Subject Headings (PhySH)

Magnetism Magnons Quasiparticles & collective excitations Spin dynamics

Kagome lattice Strongly correlated systems

Neutron scattering Neutron techniques

Condensed Matter, Materials & Applied Physics

Corrections

1 August 2022

Correction: The previously published Ref. [27] contained an error and has been fixed.

Authors & Affiliations

Seung-Hwan Do ¹, Koji Kaneko ^2,3, Ryoichi Kajimoto ², Kazuya Kamazawa⁴, Matthew B. Stone ⁵, Jiao Y. Y. Lin⁶, Shinichi Itoh ^2,7, Takatsugu Masuda ^8,7, German D. Samolyuk¹, Elbio Dagotto^1,9, William R. Meier¹, Brian C. Sales¹, Hu Miao¹, and Andrew D. Christianson¹

¹Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Materials and Life Science Division, J-PARC Center, Tokai, Ibaraki 319-1195, Japan
³Materials Sciences Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
⁴Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society, Tokai, Ibaraki 319-1106, Japan
⁵Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁶Second Target Station, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁷Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Ibaraki 305-0081, Japan
⁸Institute for Solid State Physics, The University of Tokyo, Chiba 277-8581, Japan
⁹Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

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Issue

Vol. 105, Iss. 18 — 1 May 2022

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Figure 1
(a), (b) Crystal and magnetic structure of FeSn. The exchange paths between Fe spins are indicated. (c), (d) The spin-wave dispersions of a ferromagnetic kagome lattice with $J_{1} = - 1$ meV and (c) $J_{2} = 0$ and (d) $J_{2} = 0.2 J_{1}$ ( $J_{2} = - 0.2 J_{1}$ ), are displayed with black and gray (blue) curves, respectively. High-symmetry points are indicated in the inset to (d). (e) Schematic of a Stoner excitation spectra (continuum) and magnon (sharp dispersion) as a function of momentum ( $Q$ ) and energy ( $E$ ). The spin-wave mode decays into a particle-hole pair near the Fermi energy ( $E_{F}$ ) when it enters the Stoner continuum. The continuum boundary shifts with gap $Δ$ ( $δ$ ), reflecting the direct (indirect) electronic transitions, as shown in the inset.
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Figure 2
(a) Contour map of the INS intensity along high-symmetry directions [given in (f)]. The data [(a), (c)] were measured using HRC with $E_{i} = 153$ meV. The spectrum above (below) the horizontal line at 30 meV was obtained from the BZ for $Γ$ at $Q = (0, 0, 1 / 2)$ $[(0, 0, 3 / 2)]$ , integrating over $Q = \pm 0.22$ Å $^{- 1}$ along the vertical direction. Horizontal (vertical) error bars of pink (green) circles indicate the fitted peaks full width at half maxima (FWHM), and vertical (horizontal) error bars indicate the range of energy (momentum) integration. (b) INS data (left) and spin-wave calculations (right) as described in the text along the out-of-plane direction through the Zone Center (ZC), measured using the 4SEASONS spectrometer with $E_{i} = 46$ meV. The solid line is the calculated magnon dispersion. (c) Constant energy slice of the magnon spectra in the $[H, 0, L]$ plane and the calculated spectra. (d) Low-energy spectrum of $I (Q, E)$ near the ZC measured using $E_{i} = 27$ meV at 4SEASONS, and (e) the corresponding calculation including an easy-plane anisotropy of $S D_{z} = 0.1$ meV.
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Figure 3
(a) High-energy INS spectra [plotted as $E \times I (Q, E)]$ and (b) spin-wave calculations, along the high-symmetry directions as indicated in the right panel of the $H K$ -reciprocal space map. Data were obtained by integrating over $Q = \pm 0.19$ Å $^{- 1}$ and $- 4 \leq L \leq 4$ . The calculation was performed for an identical $Q$ -integration range and convoluted with the instrumental resolution of SEQUOIA. The black solid lines display the magnon dispersion for $L = 0.5$ . Horizontal (vertical) error bars of white solid circles indicate the fitted peaks FWHM (range of energy integration). (c) Constant energy cut along the high-symmetry directions, integrated over energy $\pm 5$ meV. Solid lines are Gaussian fits described in the text with fitted values displayed in (a). (d) INS spectra obtained from HRC ( $E_{i} = 153$ meV), integrated over $- 3 \leq L \leq 3$ .
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Figure 4
(a)–(d) Constant energy slices of the INS data $[E \times I (Q, E)]$ and spin-wave calculations. Dashed lines indicate the first BZ in the $H K$ plane. The color bar for (a) and (b) [(c) and (d)] is shown in the right-hand side of (b) [(d)]. INS spectra through the $K$ point along (e) transverse and (f) radial directions (see arrows in insets). (g) Momentum scans at constant energy through the $K$ point along the transverse direction. The dispersion was extracted by fitting the spectra to Gaussian functions (solid lines) and the results are displayed as circles in (e). The lines in (e) and (f) represent the linearly crossing magnons for $L = 0.5$ at the Dirac node. Horizontal (vertical) error bars in (e) and (f) indicate the fitted FWHM (range of energy integration). (h) Constant wave-vector scan at the Dirac point. Data are shown as symbols and the spectral weight from LSWT (shaded region) is described in the text. The line is a guide to eye. Green bar indicates instrumental resolution ( $FWHM = 28.6$ meV) at $E = 120$ meV. The data were obtained by integrating over the momentum region $[0, H, 0] = \pm 0.05$ , $[2 K, - K, 0] = \pm 0.06$ , and $[0, 0, L] = \pm 4$ . (e), (f), (h) The nonmagnetic background was obtained from the scattering at $Q = (2 / 3, 2 / 3, 0)$ and subtracted from the measured intensities (see Supplemental Material for the background subtraction [29]).
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