Stripe order and spin dynamics in the triangular-lattice antiferromagnet ${\mathrm{KErSe}}_{2}$: A single-crystal study with a theoretical description

Letter

Stripe order and spin dynamics in the triangular-lattice antiferromagnet ${KErSe}_{2}$ : A single-crystal study with a theoretical description

Gaofeng Ding, Hongliang Wo, Rui Leonard Luo, Yimeng Gu, Yiqing Gu, Robert Bewley, Gang Chen, and Jun Zhao

Phys. Rev. B 107, L100411 – Published 15 March 2023

Abstract

The rare-earth triangular-lattice chalcogenide is a great platform for exploring both spin liquids and novel magnetic orders with anisotropic spin interactions and magnetic frustrations. Here, we report the thermodynamic and neutron-scattering measurements of rare-earth triangular-lattice chalcogenide ${KErSe}_{2}$ , using single-crystal samples. Our experiments revealed a long-range stripe order below 0.2 K. Although the magnetic order was three dimensional, magnetic excitations exhibited negligible modulation along the $z$ direction, indicating very weak interlayer coupling. Furthermore, magnetic excitation developed a well-defined spin-wave dispersion with a gap of $\sim 0.03 meV$ at $M$ points. Both the stripe order and spin-wave excitations could be quantitatively understood from the anisotropic spin interactions of the ${Er}^{3 +}$ Kramers doublets.

Received 27 October 2022
Accepted 3 March 2023

DOI:https://doi.org/10.1103/PhysRevB.107.L100411

Physics Subject Headings (PhySH)

Magnetic anisotropy Magnetic interactions Magnetic order Spin dynamics Spin-orbit coupling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Gaofeng Ding ^1,2,*, Hongliang Wo^1,2,*, Rui Leonard Luo ^3,*, Yimeng Gu ^1,2, Yiqing Gu ^1,2, Robert Bewley⁴, Gang Chen ^3,†, and Jun Zhao ^1,2,5,6,‡

¹State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
²Shanghai Qi Zhi Institute, Shanghai 200232, China
³Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China
⁴ISIS Facility, Rutherford Appleton Laboratory, STFC, Chilton, Didcot, Oxon OX11 0QX, United Kingdom
⁵Institute of Nanoelectronics and Quantum Computing, Fudan University, Shanghai 200433, China
⁶Shanghai Research Center for Quantum Sciences, Shanghai 201315, China

^*These authors contributed equally to this work
^†gangchen@hku.hk
^‡zhaoj@fudan.edu.cn

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Vol. 107, Iss. 10 — 1 March 2023

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Figure 1
(a) Crystallographic structure of ${KErSe}_{2}$ . Edge-sharing ${ErSe}_{6}$ octahedra form the 2D triangular lattice of ${Er}^{3 +}$ ions, stacking along the $c$ axis and separated by potassium layers. (b) (0 0 $l$ ) Bragg peaks in single-crystalline ${KErSe}_{2}$ . Asterisks indicate the background signals from the sample stage. (c) Temperature dependence of heat capacity from 0.1 to 1 K measured under a zero field for ${KErSe}_{2}$ single crystals. (d) Field-cooling (FC) and zero-field-cooling (ZFC) measurements of magnetic susceptibility under an external magnetic field of 0.1 T applied parallel and perpendicular to the $c$ axis of ${KErSe}_{2}$ . The inset shows the Curie-Weiss fit of inversed magnetic susceptibility below 10 K. (e) Isothermal magnetization for $H ∥ c$ and $H ⊥ c$ at $T = 1.8 K$ .
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Figure 2
(a) Sketch of the reciprocal lattice of ${KErSe}_{2}$ . The Г, $M$ , and $K$ points are in red, cyan, and purple, respectively. (b) Elastic neutron-scattering signals in the ( $H$ , $K$ , 0.5) plane at $T = 20 mK$ . Red line indicates the Brillouin-zone boundaries. Yellow arrow marks the direction of $Q$ cuts across the $M_{1}$ point in (d). (c) $L$ cuts and (d) ( $H$ , $H$ ) cuts for the magnetic Bragg peaks at the indicated temperatures. Solid lines are the fitting results of the Gaussian profile. Weak peak at $L = - 0.5$ in (c) originates from the misalignment of minor single crystals. (e) Magnetic structure of ${KErSe}_{2}$ with $k = (1 / 2, 0, 1 / 2)$ . Only half of the doubled magnetic unit cell along the $c$ axis is shown for clarity. Magnetic moments lying in the $a b$ plane are represented by red arrows.
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Figure 3
Measured and calculated momentum dependence of spin excitations in ${KErSe}_{2}$ at indicated energies. (a), (b) ( $H$ , $K$ , 0.5) contour plots with energy transfer $E = 0.2$ and 0.3 meV measured at $T = 20 mK$ . (c), (d) Corresponding calculated spin excitations using the model specified in the text. Dashed lines indicate the zone boundaries. Color bars indicate the scattering intensity of arbitrary units on a linear scale.
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Figure 4
Measured and calculated spin-wave dispersions in ${KErSe}_{2}$ . (a) and (b) show the dispersive behaviors of the spin excitations along the two high-symmetry directions marked by the black and red arrows in Fig. 2. Data were collected at $T = 20 mK$ . (c), (d) Corresponding calculated spin excitation dispersions using the model mentioned in the main text. Color bars indicate the scattering intensity of arbitrary units on a linear scale. (e) $L$ dependence of spin excitations at $Г_{2}$ point. (f), (g) Constant $Q$ cuts at $K_{2}$ and $M_{2}$ points demonstrating the energy gap. Blue solid line shows the Gaussian fitting of the data. The data in (a) and (e) were measured with incident energy $E_{i} = 1.8 meV$ , and those in (b), (f), and (g) were measured with $E_{i} = 0.8 meV$ .
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Physical Review B

covering condensed matter and materials physics

Stripe order and spin dynamics in the triangular-lattice antiferromagnet ${KErSe}_{2}$ : A single-crystal study with a theoretical description

Gaofeng Ding, Hongliang Wo, Rui Leonard Luo, Yimeng Gu, Yiqing Gu, Robert Bewley, Gang Chen, and Jun Zhao

Phys. Rev. B 107, L100411 – Published 15 March 2023

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Physical Review B

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Stripe order and spin dynamics in the triangular-lattice antiferromagnet KErSe2: A single-crystal study with a theoretical description

Gaofeng Ding, Hongliang Wo, Rui Leonard Luo, Yimeng Gu, Yiqing Gu, Robert Bewley, Gang Chen, and Jun Zhao

Phys. Rev. B 107, L100411 – Published 15 March 2023

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Stripe order and spin dynamics in the triangular-lattice antiferromagnet ${KErSe}_{2}$ : A single-crystal study with a theoretical description