Spin excitations in the kagome-lattice metallic antiferromagnet ${\mathrm{Fe}}_{0.89}{\mathrm{Co}}_{0.11}\mathrm{Sn}$

Spin excitations in the kagome-lattice metallic antiferromagnet ${Fe}_{0.89} {Co}_{0.11} Sn$

Tao Xie, Qiangwei Yin, Qi Wang, A. I. Kolesnikov, G. E. Granroth, D. L. Abernathy, Dongliang Gong, Zhiping Yin, Hechang Lei, and A. Podlesnyak

Phys. Rev. B 106, 214436 – Published 26 December 2022

Abstract

Kagome-lattice materials have attracted tremendous interest due to the broad prospect for seeking superconductivity, quantum spin liquid states, and topological electronic structures. Among them, the transition-metal kagome lattices are high-profile objects for the combination of topological properties, rich magnetism, and multiple-orbital physics. Here we report an inelastic neutron scattering study on the spin dynamics of a kagome-lattice antiferromagnetic metal ${Fe}_{0.89} {Co}_{0.11} Sn$ . Although the magnetic excitations can be observed up to $\sim 250$ meV, well-defined spin waves are only identified below $\sim 90$ meV and can be modeled using Heisenberg exchange with ferromagnetic in-plane nearest-neighbor coupling $J_{1}$ , in-plane next-nearest-neighbor coupling $J_{2}$ , and antiferromagnetic (AFM) interlayer coupling $J_{c}$ under linear spin-wave theory. Above $\sim 90$ meV, the spin waves enter the itinerant Stoner continuum and become highly damped particle-hole excitations. At the $K$ point of the Brillouin zone, we reveal a possible band crossing of the spin wave, which indicates a potential Dirac magnon. Our results uncover the evolution of the spin excitations from the planar AFM state to the axial AFM state in ${Fe}_{0.89} {Co}_{0.11} Sn$ , solve the magnetic Hamiltonian for both states, and confirm the significant influence of the itinerant magnetism on the spin excitations.

Received 7 September 2022
Revised 24 October 2022
Accepted 15 December 2022

DOI:https://doi.org/10.1103/PhysRevB.106.214436

Physics Subject Headings (PhySH)

Magnetic order Spin dynamics

Antiferromagnets Kagome lattice

Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tao Xie ^1,*,†, Qiangwei Yin^2,*, Qi Wang², A. I. Kolesnikov ¹, G. E. Granroth¹, D. L. Abernathy ¹, Dongliang Gong³, Zhiping Yin⁴, Hechang Lei^2,‡, and A. Podlesnyak ^1,§

¹Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Laboratory for Neutron Scattering, and Beijing Key Laboratory of Optoelectronic Functional Materials MicroNano Devices, Department of Physics, Renmin University of China, Beijing 100872, China
³Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA
⁴Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, Beijing 100875, China

^*These authors contributed equally to this work.
^†Corresponding author: xiet@ornl.gov
^‡Corresponding author: hlei@ruc.edu.cn
^§Corresponding author: podlesnyakaa@ornl.gov

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Vol. 106, Iss. 21 — 1 December 2022

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Figure 1
(a) The Fe-Co kagome layer with the hexagonal holes filled with Sn in ${Fe}_{1 - x} {Co}_{x} Sn$ . The in-plane nearest-neighbor and next-nearest-neighbor exchange couplings are indicated by the red and green arrows, respectively. (b) and (c) The magnetic structures for the planar and axial AFM states in ${Fe}_{1 - x} {Co}_{x} Sn$ . The orange arrows represent the interlayer nearest-neighbor exchange coupling $J_{c}$ . (d) A schematic of the 2D Brillouin zone of ${Fe}_{1 - x} {Co}_{x} Sn$ . (e) A schematic of the spin wave and Stoner continuum in some metallic magnets. (f) A typical photo of ${Fe}_{0.89} {Co}_{0.11} Sn$ single crystals on 1-mm grid paper. The long axis of the rodlike crystals is the crystallographic $c$ axis. (g) The magnetization as a function of temperature of our ${Fe}_{0.89} {Co}_{0.11} Sn$ sample. FC, field cooled; ZFC, zero-field cooled. (h) and (i) Zero-energy ( $E$ = 0 $\pm$ 0.2 meV) 2D slices in ( $H$ 0 $L$ ) with $E_{i}$ = 10 meV at 18 K (planar AFM state) and 280 K (axial AFM state), respectively. The arcs at the lower right corner and the upper right corner are the scattering intensity from the aluminum sampler holder. (j) and (k) Zero-energy ( $E$ = 0 $\pm$ 1 meV) 2D slices in ( $H K$ 0.5) with $E_{i}$ = 80 meV at 10 K (planar AFM state) and 280 K (axial AFM state), respectively. The dashed lines indicate the boundary of the Brillouin zones in the ( $H K$ 0) plane.
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Figure 2
Dispersion of the spin wave. (a) and (b) Spin-wave dispersion along the [ $H$ , 0, 0.5] direction [the red path in Fig. 1] measured with $E_{i}$ = 80 meV, $T$ = 10 K, and along the [0, 0, $L$ ] direction measured with $E_{i}$ = 150 meV, $T$ = 10 K. (c) Spin-wave dispersion along the [0, 0, $L$ ] direction measured with $E_{i}$ = 3.32 meV, $T$ = 10 K. (d) and (e) Spin-wave dispersion along the [ $H$ , 0, 0.5] and [0, 0, $L$ ] directions, respectively, measured with $E_{i}$ = 80 meV, $T$ = 280 K. (f) Spin-wave dispersion along the [0, 0, $L$ ] direction measured with $E_{i}$ = 3.32 meV, $T$ = 280 K. The extra intensities in (a) and (d) around 10 and 30 meV in the high- $Q$ region are the phonon signal. (g) Spin-wave dispersion along the [ $H$ , 0] $\to [H, H$ ] path at 10 K measured with $E_{i}$ = 150 meV. The extra intensity around 10 meV is the intensity of phonon scattering. (h) and (i) 1D constant-energy curves along the [ $H$ , 0, 0.5] direction and the [0, 0, $L$ ] direction at different energies in both planar and axial AFM states. The solid lines are fittings with the Gaussian function. (j) 1D constant-momentum cuts at $Q$ = (0, 0, 0.5) in both planar and axial AFM states. The integration range along the [ $- K$ /2 $K$ 0] direction for all the panels is $K$ = [ $- 0.1$ , 0.1]. The dashed lines in (a), (b), (d), (e), and (g) are results of LSWT fittings (see details in Sec. 4). The data points with error bars in (a), (d), and (g) are the peak positions of the 1D constant-energy curves shown in (h) and (i). The vertical error bars are the energy resolution of the instrument, and the horizontal error bars are the full width at half maximum (FWHM) of the Gaussian fittings there. The data points in (b) and (e) are peak positions of the 1D constant-momentum curves. The vertical error bars are the line width (FWHM) of spectra, and the horizontal error bars are the integration momentum range.
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Figure 3
Constant-energy 2D slices in the ( $H K$ ) plane and the ( $H$ 0 $L$ ) plane. (a)–(e) The evolution of the spin wave with the increasing energy in the ( $H K$ ) plane at $T$ = 10 and 18 K (planar AFM state). (f) Constant-energy slice in the ( $H$ 0 $L$ ) plane at $T$ = 10 K and $E$ = 50 $\pm$ 1 meV. (g)–(k) The evolution of the spin wave with the increasing energy in the ( $H K$ ) plane at $T$ = 280 K (axial AFM state). (l) Constant-energy slice in the ( $H$ 0 $L$ ) plane at $T$ = 280 K and $E$ = 50 $\pm$ 1 meV. The white dashed lines represent the boundary of the Brillouin zones.
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Figure 4
The high-energy spin wave and LSWT fittings with spinw. (a)–(d) Experimental INS spectra along the [ $H$ , 0] [the red path in Fig. 1] and [ $H, H$ ] [the green path in Fig. 1] directions measured with $E_{i}$ = 300 meV, $T$ = 18 K and the corresponding LSWT calculations. (e) Comparison of the experimental spin-wave dispersion and the LSWT calculation of the spin-wave dispersion along [0, 0, $L$ ] for the planar AFM state. (f)–(i) INS spectra along the [ $H$ , 0] and [ $H, H$ ] directions measured with $E_{i}$ = 250 meV, $T$ = 280 K and the corresponding LSWT calculations. (j) Comparison of the experimental spin-wave dispersion and the LSWT calculation of the spin-wave dispersion along [0, 0, $L$ ] for the axial AFM state. Some extra intensities that are away from the main dispersion around 50 meV in (a), (c), (f), and (h) are residual intensities due to the imperfect background subtraction. The gray data points with error bars in (a), (c), (f), and (h) are fitted peak positions of constant-energy curves. The vertical error bars are the energy resolution of the instrument, and the horizontal error bars are the FWHM of the Gaussian fittings. The dashed lines are LSWT calculations with the best fitting parameters in Table 1. The black dashed lines indicate the acoustic magnons, and the red and white dashed lines indicate the optical magnons.
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Figure 5
(a) and (b) Spin-excitation dispersion along the [ $H - 1 / 3, 2 / 3$ ] direction [the blue path in Fig. 1] in planar (a) and axial (b) AFM states. The gray data points with error bars are fitted peak positions of constant-energy curves. The vertical error bars are the energy resolution of the instrument, and the horizontal error bars are the FWHM of the Gaussian fittings. The black solid lines are the calculated spin-wave dispersion using the LSWT with the parameters in Table 1. (c) and (d) High-energy spin excitations measured with $E_{i}$ = 400 meV.
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Physical Review B

covering condensed matter and materials physics

Spin excitations in the kagome-lattice metallic antiferromagnet ${Fe}_{0.89} {Co}_{0.11} Sn$

Tao Xie, Qiangwei Yin, Qi Wang, A. I. Kolesnikov, G. E. Granroth, D. L. Abernathy, Dongliang Gong, Zhiping Yin, Hechang Lei, and A. Podlesnyak

Phys. Rev. B 106, 214436 – Published 26 December 2022

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Physical Review B

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Spin excitations in the kagome-lattice metallic antiferromagnet Fe0.89Co0.11Sn

Tao Xie, Qiangwei Yin, Qi Wang, A. I. Kolesnikov, G. E. Granroth, D. L. Abernathy, Dongliang Gong, Zhiping Yin, Hechang Lei, and A. Podlesnyak

Phys. Rev. B 106, 214436 – Published 26 December 2022

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Spin excitations in the kagome-lattice metallic antiferromagnet ${Fe}_{0.89} {Co}_{0.11} Sn$