Possible gapless quantum spin liquid behavior in the triangular-lattice Ising antiferromagnet ${\mathrm{PrMgAl}}_{11}{\mathrm{O}}_{19}$

Possible gapless quantum spin liquid behavior in the triangular-lattice Ising antiferromagnet ${PrMgAl}_{11} O_{19}$

Zhen Ma, Shuhan Zheng, Yingqi Chen, Ruokai Xu, Zhao-Yang Dong, Jinghui Wang, Hong Du, Jan Peter Embs, Shuaiwei Li, Yao Li, Yongjun Zhang, Meifeng Liu, Ruidan Zhong, Jun-Ming Liu, and Jinsheng Wen

Phys. Rev. B 109, 165143 – Published 23 April 2024

Abstract

Quantum spin liquids (QSLs) represent a novel state where spins are highly entangled but do not order even at zero temperature due to strong quantum fluctuations. Such a state is mostly studied in Heisenberg models defined on geometrically frustrated lattices. Here, we turn to a new triangular-lattice antiferromagnet ${PrMgAl}_{11} O_{19}$ , in which the interactions are believed to be of Ising type. Magnetic susceptibility measured with an external field along the $c$ axis is two orders of magnitude larger than that with a field in the $a b$ plane, displaying an ideal easy-axis behavior. Meanwhile, there is no magnetic phase transition or spin freezing observed down to 1.8 K. Ultralow-temperature specific heat measured down to 50 mK does not capture any phase transition either, but a hump at 4.5 K, below which the magnetic specific heat exhibits a quasiquadratic temperature dependence that is consistent with a Dirac QSL state. The inelastic neutron scattering technique is also employed to elucidate the nature of its ground state. In the magnetic excitation spectra, there is a gapless broad continuum at the base temperature 55 mK, in favor of the realization of a gapless QSL. Our results provide a scarce example for the QSL behaviors observed in an Ising-type magnet, which can serve as a promising platform for future research on QSL physics based on an Ising model.

Received 12 October 2023
Revised 19 March 2024
Accepted 9 April 2024

DOI:https://doi.org/10.1103/PhysRevB.109.165143

Physics Subject Headings (PhySH)

Frustrated magnetism Magnetic anisotropy Magnetism Quantum spin liquid Spin-orbit coupling Spinon

Antiferromagnets

Inelastic neutron scattering Specific heat measurements Susceptibility measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zhen Ma ^1,2,*, Shuhan Zheng¹, Yingqi Chen ¹, Ruokai Xu¹, Zhao-Yang Dong^3,†, Jinghui Wang⁴, Hong Du⁵, Jan Peter Embs ⁶, Shuaiwei Li¹, Yao Li¹, Yongjun Zhang¹, Meifeng Liu¹, Ruidan Zhong⁵, Jun-Ming Liu^7,8, and Jinsheng Wen^7,8,‡

¹Hubei Key Laboratory of Photoelectric Materials and Devices, School of Materials Science and Engineering, Hubei Normal University, Huangshi 435002, China
²State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
³Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, China
⁴ShanghaiTech Laboratory for Topological Physics and School of Physical Science and Technology, ShanghaiTech University, Shanghai 200031, China
⁵Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
⁶Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, 5232 Villigen, Switzerland
⁷National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
⁸Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

^*zma@hbnu.edu.cn
^†zhydong@njust.edu.cn
^‡jwen@nju.edu.cn

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Vol. 109, Iss. 16 — 15 April 2024

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Figure 1
(a) Schematic crystal structure of ${PrMgAl}_{11} O_{19}$ . (b) Top view of the triangular layer consisting of magnetic $\Pr^{3 +}$ ions. Dashed lines in (a) and (b) denote the crystalline unit cell and the triangular unit, respectively. (c) X-ray Laue pattern of the (001) plane of a single crystal. Inset shows a photograph of chartreuse single crystals with several typical pieces. (d) Rietveld refinement results for the powder XRD data collected at room temperature. Red circles and black solid line indicate the measured data and calculated results upon Rietveld refinement, respectively. Green ticks denote Bragg peak positions of ${PrMgAl}_{11} O_{19}$ with space group $P 6_{3} / mmc$ . Blue solid line represents the difference between the experiments and calculations for this compound.
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Figure 2
(a) Temperature dependence of the magnetic susceptibility ( $χ$ ) for ${PrMgAl}_{11} O_{19}$ single crystals with the external fields parallel and perpendicular to the $c$ axis, respectively. The measurements were performed in both zero-field-cooling (ZFC) and field-cooling (FC) conditions with a field of 0.1 T down to 1.8 K. The inset shows the inverse magnetic susceptibility data with the field along $c$ axis. The dashed line is the fit with the Curie-Weiss law. (b) Magnetic-field dependence of the magnetization for the single-crystal sample with two different directions at 2 and 15 K, respectively.
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Figure 3
(a) Ultralow-temperature specific heat ( $C_{p}$ ) results of ${PrMgAl}_{11} O_{19}$ at various magnetic fields. The specific heat of a nonmagnetic reference compound ${LaMgAl}_{11} O_{19}$ at zero field is also shown for comparison, which can be nicely fitted by a Debye model as $C_{p} \propto T^{3}$ . The dashed line denotes such a fitting. (b) Magnetic specific heat ( $C_{m}$ ) of ${PrMgAl}_{11} O_{19}$ obtained by subtracting the lattice contribution using an isostructural nonmagnetic sample ${LaMgAl}_{11} O_{19}$ . The solid lines denote the fit to the data with a power-law function $C_{m} / T \propto T^{α - 1}$ . The inset shows the extracted exponent values of $α$ at different fields. The solid in the inset is the guide to the eye. (c) Temperature dependence of magnetic entropy ( $S_{m}$ ) obtained by integrating $C_{m} / T$ data.
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Figure 4
[(a)–(d)] Inelastic neutron scattering spectra of ${PrMgAl}_{11} O_{19}$ measured with an incident neutron energy $E_{i}$ = 3.7 meV at several temperatures. To distinguish the possible low-energy magnetic excitations covered by the strong signals from low-lying crystal electric field excitations, the data at a higher temperature of 50 K were used for background subtraction.
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Figure 5
(a) Wave-vector $Q$ dependence of the energy-integrated neutron scattering intensity in the range from 0.25 to 2.5 meV at several temperatures. (b) Energy dependence of the integrated intensity in the $Q$ range from 0 to $2.5 Å^{- 1}$ . The solid lines in (a) and (b) are guides to the eye. The dashed line in (b) denotes the instrumental resolution. (c) Elastic neutron scattering data were obtained by integrating the intensity in an energy window of $[- 0.1, 0.1]$ meV. Errors of the neutron scattering data represent one standard deviation.
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Physical Review B

covering condensed matter and materials physics

Possible gapless quantum spin liquid behavior in the triangular-lattice Ising antiferromagnet ${PrMgAl}_{11} O_{19}$

Zhen Ma, Shuhan Zheng, Yingqi Chen, Ruokai Xu, Zhao-Yang Dong, Jinghui Wang, Hong Du, Jan Peter Embs, Shuaiwei Li, Yao Li, Yongjun Zhang, Meifeng Liu, Ruidan Zhong, Jun-Ming Liu, and Jinsheng Wen

Phys. Rev. B 109, 165143 – Published 23 April 2024

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Physical Review B

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Possible gapless quantum spin liquid behavior in the triangular-lattice Ising antiferromagnet PrMgAl11O19

Zhen Ma, Shuhan Zheng, Yingqi Chen, Ruokai Xu, Zhao-Yang Dong, Jinghui Wang, Hong Du, Jan Peter Embs, Shuaiwei Li, Yao Li, Yongjun Zhang, Meifeng Liu, Ruidan Zhong, Jun-Ming Liu, and Jinsheng Wen

Phys. Rev. B 109, 165143 – Published 23 April 2024

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Possible gapless quantum spin liquid behavior in the triangular-lattice Ising antiferromagnet ${PrMgAl}_{11} O_{19}$