Weakly coupled alternating $S=\frac{1}{2}$ chains in the distorted honeycomb lattice compound ${\mathrm{Na}}_{2}{\mathrm{Cu}}_{2}{\mathrm{TeO}}_{6}$

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Weakly coupled alternating $S = \frac{1}{2}$ chains in the distorted honeycomb lattice compound ${Na}_{2} {Cu}_{2} {TeO}_{6}$

Shang Gao, Ling-Fang Lin, Andrew F. May, Binod K. Rai, Qiang Zhang, Elbio Dagotto, Andrew D. Christianson, and Matthew B. Stone

Phys. Rev. B 102, 220402(R) – Published 2 December 2020

Abstract

Spin- $\frac{1}{2}$ chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement as the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb lattice compound ${Na}_{2} {Cu}_{2} {TeO}_{6}$ , but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here, we employ neutron scattering to study the spin dynamics in ${Na}_{2} {Cu}_{2} {TeO}_{6}$ and accurately determine the coupling strengths through the random phase approximation and density functional theory approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish ${Na}_{2} {Cu}_{2} {TeO}_{6}$ as a weakly coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.

Received 3 October 2020
Accepted 17 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.220402

Physics Subject Headings (PhySH)

Exchange interaction

1-dimensional spin chains Honeycomb lattice

Density functional theory Neutron scattering Random phase approximation

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shang Gao^1,2, Ling-Fang Lin ³, Andrew F. May ¹, Binod K. Rai ¹, Qiang Zhang², Elbio Dagotto^1,3, Andrew D. Christianson¹, and Matthew B. Stone ²

¹Materials Science & Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

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Vol. 102, Iss. 22 — 1 December 2020

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Figure 1
(a), (b) Crystal structure of ${Na}_{2} {Cu}_{2} {TeO}_{6}$ viewed along the (a) $b$ and (b) $c^{*}$ axes with the ${Cu}^{2 +}$ ions forming chains along the $b$ axis. The size of the unit cell is indicated by black lines. The ${Cu}^{2 +}$ spins are coupled through alternating $J_{1}$ (red) and $J_{2}$ (blue) interactions along the chain and $J_{3}$ interactions (gray) between the chains. Cu-O bonds of different lengths are indicated in the ${CuO}_{6}$ octahedron at the left bottom corner of (b), with $b 1 = 1.978 (1)$ Å, $b 2 = 1.999 (1)$ Å, and $b 3 = 2.533 (1)$ Å.
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Figure 2
(a) Scattering intensity of ${Na}_{2} {Cu}_{2} {TeO}_{6}$ measured along $(- 1 0.5 Q_{l})$ at $T = 5$ K with integration widths of $Δ Q_{h} = 0.2$ and $Δ Q_{k} = 0.1$ . Measurements were performed in the high-resolution configuration. (b) Intensity map in the $(Q_{h} Q_{k} 0)$ plane integrated over ranges of $[17, 28]$ meV in $E$ and $[- 2, 2]$ in $Q_{l}$ . Measurements were performed in the high-intensity setup at $T = 5$ K. (c) Scattering intensity along $Q_{k}$ integrated from the map in (b) over the range of $[- 2.1, 1.9]$ in $Q_{h}$ . The intensity can be described by the structure factor of the $r_{1}$ -dimer model (red solid line) instead of the $r_{2}$ -dimer model (blue dashed line), where $r_{1} \approx 2 b / 3$ and $r_{2} \approx b / 3$ are the bond distances for $J_{1}$ and $J_{2}$ , respectively.
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Figure 3
(a)–(d) Intensity maps of ${Na}_{2} {Cu}_{2} {TeO}_{6}$ measured along $(1 Q_{k} 0)$ , $(2 Q_{k} 0)$ , $(Q_{h} 0.5 0)$ , and $(Q_{h} 1 0)$ at $T = 5$ K using the high-intensity configuration. The integration widths are $Δ Q_{h} = 0.1$ , $Δ Q_{k} = 0.1$ , and $Δ Q_{l} = 2$ . (e)–(h) Intensity maps calculated through the random phase approximation with fitted coupling strengths $J_{1} = 22.78 (2)$ meV, $J_{2} = - 8.73 (4)$ meV, and $J_{3} = 1.34 (3)$ meV. An instrumental energy resolution of 3.0 meV was convolved with the calculated spectrum. (a)–(d) and (e)–(h) are shown on the identical intensity scale, respectively.
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Figure 4
(a) Energy dependence of the scattering intensity at $(1 0.5 0)$ measured at $T = 5$ (circles), 50 (squares), 100 (diamonds), 150 (up-pointing triangles), and 250 (right-pointing triangles) K. Solid lines are Gaussian fits. (b) Temperature dependence of the fitted gap size $Δ$ (circles, right axis) and full width at half maximum FWHM (squares, left axis). Solid lines are fits using the empirical formula in Eq. (3). The fitted parameters are $α = 2.3 (8)$ meV, $γ = 6 (2)$ meV, and $Γ_{0} = 2.8 (2)$ meV. At low temperatures, the FWHM is close to the instrumental energy resolution.
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Figure 5
(a) Wannier functions of the Cu $3 d_{x^{2} - y^{2}}$ orbital, an antibonding combination of the Cu $3 d_{x^{2} - y^{2}}$ and O $2 p$ states, viewed along the $c$ axis. Different colors represent the $+ / -$ signs of the Wannier function. (b) Diagrams for the supersuperexchange and superexchange couplings between the nearest-neighbor Cu $3 d_{x^{2} - y^{2}}$ orbitals via oxygen $2 p$ ligands. For the $J_{1}$ path, the Cu-O⋯O-Cu supersuperexchange leads to the AF alignment of the nearest-neighbor Cu ions. For the $J_{2}$ path, Cu-O-Cu superexchange with a bonding angle of $90^{\circ}$ results in a FM exchange between the nearest-neighbor Cu ions.
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Physical Review B

covering condensed matter and materials physics

Weakly coupled alternating $S = \frac{1}{2}$ chains in the distorted honeycomb lattice compound ${Na}_{2} {Cu}_{2} {TeO}_{6}$

Shang Gao, Ling-Fang Lin, Andrew F. May, Binod K. Rai, Qiang Zhang, Elbio Dagotto, Andrew D. Christianson, and Matthew B. Stone

Phys. Rev. B 102, 220402(R) – Published 2 December 2020

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Physical Review B

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Weakly coupled alternating S=12 chains in the distorted honeycomb lattice compound Na2Cu2TeO6

Shang Gao, Ling-Fang Lin, Andrew F. May, Binod K. Rai, Qiang Zhang, Elbio Dagotto, Andrew D. Christianson, and Matthew B. Stone

Phys. Rev. B 102, 220402(R) – Published 2 December 2020

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Weakly coupled alternating $S = \frac{1}{2}$ chains in the distorted honeycomb lattice compound ${Na}_{2} {Cu}_{2} {TeO}_{6}$