Gapless spinons and a field-induced soliton gap in the hyperhoneycomb Cu oxalate framework compound [(${\mathrm{C}}_{2}{\mathrm{H}}_{5}{)}_{3}{\mathrm{NH}]}_{2}{\mathrm{Cu}}_{2}{({\mathrm{C}}_{2}{\mathrm{O}}_{4})}_{3}$

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Gapless spinons and a field-induced soliton gap in the hyperhoneycomb Cu oxalate framework compound [( $C_{2} H_{5})_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$

C. Dissanayake, A. C. Jacko, K. Kumarasinghe, R. Munir, H. Siddiquee, W. J. Newsome, F. J. Uribe-Romo, E. S. Choi, S. Yadav, X.-Z. Hu, Y. Takano, S. Pakhira, D. C. Johnston, Q.-P. Ding, Y. Furukawa, B. J. Powell, and Y. Nakajima

Phys. Rev. B 108, 134418 – Published 13 October 2023

Abstract

We report a detailed study of the specific heat and magnetic susceptibility of single crystals of a spin-liquid candidate: the hyperhoneycomb Cu oxalate framework compound $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ . The specific heat shows no anomaly associated with a magnetic transition at low temperatures down to $T \sim 180 mK$ in zero magnetic field. We observe a large linear-in- $T$ contribution to the specific heat $γ T, γ = 98 (1) mJ / mol K^{2}$ , at low temperatures, indicative of the presence of fermionic excitations despite the Mott insulating state. The low- $T$ specific heat is strongly suppressed by applied magnetic fields $H$ , which induce an energy gap, $Δ (H)$ , in the spin-excitation spectrum. We use the four-component relativistic density-functional theory (DFT) to calculate the magnetic interactions, including the Dzyaloshinskii-Moriya antisymmetric exchange, which causes an effective staggered field acting on one copper sublattice. The magnitude and field dependence of the field-induced gap, $Δ (H) \propto H^{2 / 3}$ , are accurately predicted by the soliton mass calculated from the sine-Gordon model of weakly coupled antiferromagnetic Heisenberg chains with all parameters determined by our DFT calculations. Thus our experiment and calculations are entirely consistent with a model of $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ in which anisotropic magnetic exchange interactions due to Jahn-Teller distortion cause one copper sublattice to dimerize, leaving a second sublattice of weakly coupled antiferromagnetic chains. We also show that this model quantitatively accounts for the measured temperature-dependent magnetic susceptibility. Thus $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ is a canonical example of a one-dimensional spin-1/2 Heisenberg antiferromagnet and not a resonating-valence-bond quantum spin liquid, as previously proposed.

Received 23 June 2023
Revised 15 September 2023
Accepted 26 September 2023

DOI:https://doi.org/10.1103/PhysRevB.108.134418

Physics Subject Headings (PhySH)

Exchange interaction Frustrated magnetism Jahn-Teller effect Magnetism Quantum spin liquid Specific heat Spin liquid Spinon

Metal-organic framework Mott insulators

DC susceptibility measurements Density functional theory Specific heat measurements Torque magnetometry

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

C. Dissanayake¹, A. C. Jacko^2,*, K. Kumarasinghe¹, R. Munir¹, H. Siddiquee¹, W. J. Newsome³, F. J. Uribe-Romo^3,4, E. S. Choi⁵, S. Yadav^6,†, X.-Z. Hu ^6,‡, Y. Takano ⁶, S. Pakhira ^7,8, D. C. Johnston ^7,9, Q.-P. Ding ^7,9, Y. Furukawa^7,9, B. J. Powell ², and Y. Nakajima ^1,§

¹Department of Physics, University of Central Florida, Orlando, Florida 32816, USA
²School of Mathematics and Physics, The University of Queensland, Brisbane, Queensland 4072, Australia
³Department of Chemistry, University of Central Florida, Orlando, Florida 32816, USA
⁴REACT: Renewable Energy and Chemical Transformations Cluster, University of Central Florida, Orlando, Florida 32816, USA
⁵National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA
⁶Department of Physics, University of Florida, Gainesville, Florida 32611, USA
⁷Ames National Laboratory, Iowa State University, Ames, Iowa 50011, USA
⁸Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, D-76021 Karlsruhe, Germany
⁹Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

^*Deceased.
^†Present address: Walmart Global Tech, Sunnyvale, California 94086, USA.
^‡Present address: Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
^§Corresponding author: yasuyuki.nakajima@ucf.edu

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Vol. 108, Iss. 13 — 1 October 2023

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Figure 1
Crystal structure of $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ [12]. Views are shown along (a) the $a$ axis and (b) the $c$ axis. Cu1 ions form chains along the $c$ axis, while Cu2 ions form chains along the $a$ axis. (c) Schematic diagram of Cu network in $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ forming a hyperhoneycomb structure, also known as the ths net in O'Keeffe's three-letter RCSR codes [10]. Due to Jahn-Teller distortion, magnetic interactions between ${Cu}^{2 +}$ ions ( $J_{1}, J_{2}, J_{3}$ , and $J_{4}$ ) are anisotropic (see the main text). The inset shows a photo image of a single crystal of $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ .
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Figure 2
Specific heat $C_{p}$ divided by temperature, $C_{p} / T$ , of $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ as a function of $T$ . Magnetic fields are applied along the $b$ axis. The red solid line is a fit to the data for $H = 0 T$ from 1 to 5 K using $C_{p} / T = γ + β T^{2} + δ T^{4}$ . The $γ$ value is obtained to be 98(1) mJ/mol $K^{2}$ . Inset: Temperature dependence of $C_{p}$ at $H = 0 T$ . Below about 2 K, $C_{p} (H = 0 T)$ is approximately proportional to $T$ .
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Figure 3
Temperature dependence of the magnetic contribution to the specific heat of $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ where $C_{mag} = C_{p} - C_{ph}$ and $C_{p}$ is the phonon contribution. The curves are successively shifted upward by 150 mJ/mol K for clarity. The red dashed lines are fits to the sine-Gordon model (see the main text). A clear development of an energy gap is observed upon applying magnetic fields parallel to the $b$ axis.
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Figure 4
Magnetic field $H$ dependence of the magnetic contribution to the specific heat $C_{mag} (T) / T$ of $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ at four temperatures. The magnetic fields are applied along the $b$ axis. The peak position in $C_{mag} (T) / T$ shifts to a higher magnetic field with increasing temperature.
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Figure 5
Temperature dependence of magnetic susceptibility $χ$ in magnetic field $H = 0.1$ T. The magnetic field is applied parallel to the $b$ axis. The red line is a fit to the data from 2 to 140 K using $χ_{fit} = χ_{BF} + χ_{CW} + χ_{dimer} + χ_{0}$ , where $χ_{BF}$ is the magnetic susceptibility for one-dimensional AFHCs (the blue dashed line), $χ_{CW}$ is a contribution from impurities/defects (the purple dashed line), $χ_{dimer}$ is a contribution from AFHDs (the green dashed line), and $χ_{0}$ is a diamagnetic susceptibility estimated from the Pascal's constants [11, 22]. The arrow indicates an anomaly associated with an order-disorder transition of ( $C_{2} H_{5})_{3} {NH}^{+}$ cations at $\sim 170 K$ [11]. Inset: Field dependence of magnetic torque divided by magnetic field, $τ / H = M_{⊥} V$ , where $M_{⊥}$ is the magnetization perpendicular to applied magnetic field and $V$ is the sample volume, of $[{(C_{2} H_{5})}_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$ at $T = 0.4 K$ . The magnetic field is applied along the $b$ axis. No discernible anomaly associated with a magnetic transition is observed.
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Figure 6
Field dependence of the soliton gap extracted from the magnetic specific heat and NMR data [16]. The solid line is the soliton gap predicted [17] from the sine-Gordon model, Eq. (13), for the DMI and exchange interaction obtained from our DFT calculations. This curve contains no adjustable parameters once $U$ and $J_{H}$ are fixed and depends only extremely weakly on the choice of these parameters.
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Physical Review B

covering condensed matter and materials physics

Gapless spinons and a field-induced soliton gap in the hyperhoneycomb Cu oxalate framework compound [( $C_{2} H_{5})_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$

C. Dissanayake, A. C. Jacko, K. Kumarasinghe, R. Munir, H. Siddiquee, W. J. Newsome, F. J. Uribe-Romo, E. S. Choi, S. Yadav, X.-Z. Hu, Y. Takano, S. Pakhira, D. C. Johnston, Q.-P. Ding, Y. Furukawa, B. J. Powell, and Y. Nakajima

Phys. Rev. B 108, 134418 – Published 13 October 2023

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Gapless spinons and a field-induced soliton gap in the hyperhoneycomb Cu oxalate framework compound [(C2H5)3NH]2Cu2(C2O4)3

C. Dissanayake, A. C. Jacko, K. Kumarasinghe, R. Munir, H. Siddiquee, W. J. Newsome, F. J. Uribe-Romo, E. S. Choi, S. Yadav, X.-Z. Hu, Y. Takano, S. Pakhira, D. C. Johnston, Q.-P. Ding, Y. Furukawa, B. J. Powell, and Y. Nakajima

Phys. Rev. B 108, 134418 – Published 13 October 2023

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Gapless spinons and a field-induced soliton gap in the hyperhoneycomb Cu oxalate framework compound [( $C_{2} H_{5})_{3} {NH]}_{2} {Cu}_{2} {(C_{2} O_{4})}_{3}$