- Editors' Suggestion
- Open Access
Coupled dimerized alternating-bond quantum spin chains in the distorted honeycomb-lattice magnet
Phys. Rev. Research 8, 013247 – Published 6 March, 2026
DOI: https://doi.org/10.1103/vdgg-d128
Abstract
We analyze powder-averaged inelastic neutron scattering and magnetization data for the distorted honeycomb compound using a first-order dimer expansion calculation and quantum Monte Carlo simulations. We show that, in contrast to the previously proposed honeycomb-lattice model, accommodates interacting dimerized spin chains with alternating ferromagnetic-antiferromagnetic couplings along the chain. Moreover, unlike the typical couplings observed in other -based distorted honeycomb magnets, the spin chains in primarily couple through an antiferromagnetic coupling that arises between the honeycomb layers, rather than the expected interchain coupling in the layers. This finding reveals a different magnetic coupling scheme for . In addition, utilizing x-ray spectroscopy and transmission electron microscopy, we also refine the crystal structure and stacking-fault model of the compound.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (76)
- S. Sachdev, Quantum magnetism and criticality, Nat. Phys. 4, 173 (2008).
- A. Vasiliev, O. Volkova, E. Zvereva, and M. Markina, Milestones of low-D quantum magnetism, npj Quantum Mater. 3, 18 (2018).
- T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka, Bose-Einstein condensation of dilute magnons in , Phys. Rev. Lett. 84, 5868 (2000).
- C. Rüegg, N. Cavadini, A. Furrer, H.-U. Gudel, K. Krämer, H. Mutka, A. Wildes, K. Habicht, and P. Vorderwisch, Bose–Einstein condensation of the triplet states in the magnetic insulator , Nature (London) 423, 62 (2003).
- M. Jaime, V. F. Correa, N. Harrison, C. D. Batista, N. Kawashima, Y. Kazuma, G. A. Jorge, R. Stein, I. Heinmaa, S. A. Zvyagin, Y. Sasago, and K. Uchinokura, Magnetic-field-induced condensation of triplons in Han Purple pigment , Phys. Rev. Lett. 93, 087203 (2004).
- V. S. Zapf, D. Zocco, B. R. Hansen, M. Jaime, N. Harrison, C. D. Batista, M. Kenzelmann, C. Niedermayer, A. Lacerda, and A. Paduan-Filho, Bose-Einstein condensation of nickel spin degrees of freedom in -4SC(, Phys. Rev. Lett. 96, 077204 (2006).
- T. Giamarchi, C. Rüegg, and O. Tchernyshyov, Bose–Einstein condensation in magnetic insulators, Nat. Phys. 4, 198 (2008).
- A. A. Aczel, Y. Kohama, C. Marcenat, F. Weickert, M. Jaime, O. E. Ayala-Valenzuela, R. D. McDonald, S. D. Selesnic, H. A. Dabkowska, and G. M. Luke, Field-induced Bose-Einstein condensation of triplons up to 8 K in , Phys. Rev. Lett. 103, 207203 (2009).
- V. Zapf, M. Jaime, and C. D. Batista, Bose-Einstein condensation in quantum magnets, Rev. Mod. Phys. 86, 563 (2014).
- E. C. Samulon, Y. Kohama, R. D. McDonald, M. C. Shapiro, K. A. Al-Hassanieh, C. D. Batista, M. Jaime, and I. R. Fisher, Asymmetric quintuplet condensation in the frustrated spin dimer compound , Phys. Rev. Lett. 103, 047202 (2009).
- S. E. Sebastian, N. Harrison, C. D. Batista, L. Balicas, M. Jaime, P. A. Sharma, N. Kawashima, and I. R. Fisher, Dimensional reduction at a quantum critical point, Nature (London) 441, 617 (2006).
- C. Rüegg, B. Normand, M. Matsumoto, A. Furrer, D. F. McMorrow, K. W. Krämer, H.-U. Güdel, S. N. Gvasaliya, H. Mutka, and M. Boehm, Quantum magnets under pressure: Controlling elementary excitations in , Phys. Rev. Lett. 100, 205701 (2008).
- P. A. McClarty, F. Krüger, T. Guidi, S. F. Parker, K. Refson, A. W. Parker, D. Prabhakaran, and R. Coldea, Topological triplon modes and bound states in a Shastry–Sutherland magnet, Nat. Phys. 13, 736 (2017).
- A. Koga and N. Kawakami, Quantum phase transitions in the Shastry-Sutherland model for , Phys. Rev. Lett. 84, 4461 (2000).
- M. E. Zayed et al., 4-spin plaquette singlet state in the Shastry–Sutherland compound , Nat. Phys. 13, 962 (2017).
- E. Fogh, M. Nayak, O. Prokhnenko, M. Bartkowiak, K. Munakata, J.-R. Soh, A. A. Turrini, M. E. Zayed, E. Pomjakushina, H. Kageyama, H. Nojiri, K. Kakurai, B. Normand, F. Mila, and H. M. Rønnow, Field-induced bound-state condensation and spin-nematic phase in revealed by neutron scattering up to 25.9 T, Nat. Commun. 15, 442 (2024).
- M. Takigawa, M. Horvatić, T. Waki, S. Krämer, C. Berthier, F. Lévy-Bertrand, I. Sheikin, H. Kageyama, Y. Ueda, and F. Mila, Incomplete Devil’s staircase in the magnetization curve of , Phys. Rev. Lett. 110, 067210 (2013).
- P. Corboz and F. Mila, Crystals of bound states in the magnetization plateaus of the Shastry-Sutherland model, Phys. Rev. Lett. 112, 147203 (2014).
- D. A. Tennant, B. Lake, A. J. A. James, F. H. L. Essler, S. Notbohm, H.-J. Mikeska, J. Fielden, P. Kögerler, P. C. Canfield, and M. T. F. Telling, Anomalous dynamical line shapes in a quantum magnet at finite temperature, Phys. Rev. B 85, 014402 (2012).
- E. S. Klyushina, A. T. M. N. Islam, J. T. Park, E. A. Goremychkin, E. Wheeler, B. Klemke, and B. Lake, Hamiltonian of the dimerized antiferromagnetic-ferromagnetic quantum spin chain , Phys. Rev. B 98, 104413 (2018).
- K. Kodama, H. Harashina, H. Sasaki, M. Kato, M. Sato, K. Kakurai, and M. Nishi, Neutron scattering study on the quasi-one-dimensional spin-gap system , J. Phys. Soc. Jpn. 68, 237 (1999).
- M. B. Stone, W. Tian, M. D. Lumsden, G. E. Granroth, D. Mandrus, J.-H. Chung, N. Harrison, and S. E. Nagler, Quantum spin correlations in an organometallic alternating-sign chain, Phys. Rev. Lett. 99, 087204 (2007).
- Y. Miura, R. Hirai, Y. Kobayashi, and M. Sato, Spin-gap behavior of with distorted honeycomb structure, J. Phys. Soc. Jpn. 75, 084707 (2006).
- Y. Miura, Y. Yasui, T. Moyoshi, M. Sato, and K. Kakurai, Magnetic excitations of spin-gap system with distorted honeycomb structure, J. Phys. Soc. Jpn. 77, 104709 (2008).
- H.-J. Koo and M.-H. Whangbo, Analysis of the spin lattice model for the spin-gapped layered compounds and on the basis of electronic structure calculations, Inorg. Chem. 47, 128 (2008).
- C. N. Kuo, T. S. Jian, and C. S. Lue, Characterization of the spin gap nature in using NMR, J. Alloys Compd. 531, 1 (2012).
- M. Schmitt, O. Janson, S. Golbs, M. Schmidt, W. Schnelle, J. Richter, and H. Rosner, Microscopic magnetic modeling for the alternating-chain compounds and , Phys. Rev. B 89, 174403 (2014).
- C. Koo, E. A. Zvereva, I. L. Shukaev, M. Richter, M. I. Stratan, A. N. Vasiliev, V. B. Nalbandyan, and R. Klingeler, Static and dynamic magnetic response of fragmented Haldane-like spin chains in layered , J. Phys. Soc. Jpn. 85, 084702 (2016).
- E. Vavilova, S. Nishimoto, T. Salikhov, T. Vasilchikova, V. Nalbandyan, A. Vasiliev, and E. Zvereva, Spin dynamics in the alternating chain system with defects probed by nuclear magnetic resonance, Phys. Rev. B 103, 094415 (2021).
- S. Gao, L.-F. Lin, A. F. May, B. K. Rai, Q. Zhang, E. Dagotto, A. D. Christianson, and M. B. Stone, Weakly coupled alternating chains in the distorted honeycomb lattice compound , Phys. Rev. B 102, 220402(R) (2020).
- Y. Shangguan, S. Bao, Z.-Y. Dong, Z. Cai, W. Wang, Z. Huang, Z. Ma, J. Liao, X. Zhao, R. Kajimoto, K. Iida, D. Voneshen, S.-L. Yu, J.-X. Li, and J. Wen, Evidence for strong correlations at finite temperatures in the dimerized magnet , Phys. Rev. B 104, 224430 (2021).
- L.-F. Lin, R. Soni, Y. Zhang, S. Gao, A. Moreo, G. Alvarez, A. D. Christianson, M. B. Stone, and E. Dagotto, Electronic structure, magnetic properties, and pairing tendencies of the copper-based honeycomb lattice , Phys. Rev. B 105, 245113 (2022).
- J. M. S. Skakle, M. A. Castellanos R., S. T. Tovar, and A. R. West, Synthesis of , a new partially ordered rock salt structure, J. Solid State Chem. 131, 115 (1997).
- V. B. Nalbandyan, M. Avdeev, and M. A. Evstigneeva, Crystal structure of and revision of , J. Solid State Chem. 199, 62 (2013).
- K. Momma and F. Izumi, VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data, J. Appl. Crystallogr. 44, 1272 (2011).
- V. Kumar, A. Gupta, and S. Uma, Formation of honeycomb ordered monoclinic (, Ni) and disordered orthorhombic oxides, Dalton Trans. 42, 14992 (2013).
- O. A. Smirnova, V. B. Nalbandyan, A. A. Petrenko, and M. Avdeev, Subsolidus phase relations in –CuO– system and crystal structure of new sodium copper antimonate , J. Solid State Chem. 178, 1165 (2005).
- J. Xu, A. Assoud, N. Soheilnia, S. Derakhshan, H. L. Cuthbert, J. E. Greedan, M. H. Whangbo, and H. Kleinke, Synthesis, structure, and magnetic properties of the layered copper(II) oxide , Inorg. Chem. 44, 5042 (2005).
- R. Sankar, I. P. Muthuselvam, G. J. Shu, W. T. Chen, S. K. Karna, R. Jayavel, and F. C. Chou, Crystal growth and magnetic ordering of with honeycomb layers and with Cu spin dimers, CrystEngComm. 16, 10791 (2014).
- T. Murtaza, R. Kalaivanan, G. Madeswaran, K. Bayikadi, and R. Sankar, Magnetic properties of honeycomb spin lattice compounds (M = Co, Ni) and spin dimer compound single crystals by flux-growth, J. Mater. Res. Technol. 14, 1601 (2021).
- K. Morimoto, Y. Itoh, K. Yoshimura, M. Kato, and K. Hirota, Hole doping effects on spin-gapped via topochemical Na deficiency, J. Phys. Soc. Jpn. 75, 083709 (2006).
- S. Derakhshan, H. L. Cuthbert, J. E. Greedan, B. Rahaman, and T. Saha-Dasgupta, Electronic structures and low-dimensional magnetic properties of the ordered rocksalt oxides and , Phys. Rev. B 76, 104403 (2007).
- S. Patil and S. D. Kaushik, Investigating structure and physical properties of quaternary layered transition metal oxide , arXiv:2508.16219.
- P. W. Anderson, Antiferromagnetism. Theory of superexchange interaction, Phys. Rev. 79, 350 (1950).
- J. B. Goodenough, Theory of the role of covalence in the perovskite-type manganites [La, ], Phys. Rev. 100, 564 (1955).
- J. B. Goodenough, An interpretation of the magnetic properties of the perovskite-type mixed crystals , J. Phys. Chem. Solids 6, 287 (1958).
- A. S. Moskvin, N. S. Ovanesyan, and V. A. Trukhtanov, Angular dependence of the superexchange interaction , Hyperfine Interact. 1, 265 (1975).
- E. Climent-Pascual, P. Norby, N. H. Andersen, P. W. Stephens, H. W. Zandbergen, J. Larsen, and R. J. Cava, Spin 1/2 delafossite honeycomb compound , Inorg. Chem. 51, 557 (2012).
- P. Sae-Fu et al. (unpublished).
- K. Nakajima et al., AMATERAS: A cold-neutron disk chopper spectrometer, J. Phys. Soc. Jpn. 80, SB028 (2011).
- J. W. Lynn, Y. Chen, S. Chang, Y. Zhao, S. Chi, W. Ratcliff, B. G. Ueland, and R. W. Erwin, Double-focusing thermal triple-axis spectrometer at the NCNR, J. Res. Natl. Inst. Stand. Technol. 117, 61 (2012).
- Y. Inamura, T. Nakatani, J. Suzuki, and T. Otomo, Development status of software “Utsusemi” for Chopper spectrometers at MLF, J-PARC, J. Phys. Soc. Jpn. 82, SA031 (2013).
- V. Petříček, M. Dušek, and L. Palatinus, Crystallographic computing system JANA2006: General features, Z. Kristallogr.—Cryst. Mater. 229, 345 (2014).
- H. M. Rietveld, A profile refinement method for nuclear and magnetic structures, J. Appl. Crystallogr. 2, 65 (1969).
- J. Rodríguez-Carvajal, Recent advances in magnetic structure determination by neutron powder diffraction, Physica B 192, 55 (1993).
- B. Ravel and M. Newville, ATHENA, ARTEMIS, HEPHAESTUS: data analysis for x-ray absorption spectroscopy using IFEFFIT, J. Synchrotron Radiat. 12, 537 (2005).
- M. Newville, Fundamentals of XAFS, Rev. Mineral. Geochem. 78, 33 (2014).
- J. Bréger, M. Jiang, N. Dupré, Y. S. Meng, Y. Shao-Horn, G. Ceder, and C. P. Grey, High-resolution X-ray diffraction, DIFFaX, NMR and first principles study of disorder in the solid solution, J. Solid State Chem. 178, 2575 (2005).
- S. K. Choi, R. Coldea, A. N. Kolmogorov, T. Lancaster, I. I. Mazin, S. J. Blundell, P. G. Radaelli, Y. Singh, P. Gegenwart, K. R. Choi, S.-W. Cheong, P. J. Baker, C. Stock, and J. Taylor, Spin waves and revised crystal structure of honeycomb iridate , Phys. Rev. Lett. 108, 127204 (2012).
- M. M. J. Treacy, J. M. Newsam, and M. W. Deem, A general recursion method for calculating diffracted intensities from crystals containing planar faults, Proc. R. Soc. London, Ser. A 433, 499 (1991).
- M. Casas-Cabanas, J. Rodríguez-Carvajal, and M. Palacín, Faults, a new program for refinement of powder diffraction patterns from layered structures, in Ninth European Powder Diffraction Conference (Oldenbourg Wissenschaftsverlag, München, 2006), pp. 243–248.
- M. Casas-Cabanas, M. Reynaud, J. Rikarte, P. Horbach, and J. Rodríguez-Carvajal, FAULTS: A program for refinement of structures with extended defects, J. Appl. Crystallogr. 49, 2259 (2016).
- S. Todo and K. Kato, Cluster algorithms for general- quantum spin systems, Phys. Rev. Lett. 87, 047203 (2001).
- H. G. Evertz, The loop algorithm, Adv. Phys. 52, 1 (2003).
- B. Bauer, L. D. Carr, H. G. Evertz, A. Feiguin, J. Freire, S. Fuchs, L. Gamper, J. Gukelberger, E. Gull, S. Guertler, A. Hehn, R. Igarashi, S. V. Isakov, D. Koop, P. N. Ma, P. Mates, H. Matsuo, O. Parcollet, G. Pawłowski, J. D. Picon, et al., The ALPS project release 2.0: Open source software for strongly correlated systems, J. Stat. Mech. (2011) P05001.
- D. C. Johnston, R. K. Kremer, M. Troyer, X. Wang, A. Klümper, S. L. Bud’ko, A. F. Panchula, and P. C. Canfield, Thermodynamics of spin antiferromagnetic uniform and alternating-exchange Heisenberg chains, Phys. Rev. B 61, 9558 (2000).
- O. F. Syljuåsen and A. W. Sandvik, Quantum Monte Carlo with directed loops, Phys. Rev. E 66, 046701 (2002).
- O. F. Syljuåsen, Directed loop updates for quantum lattice models, Phys. Rev. E 67, 046701 (2003).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/vdgg-d128 for raw inelastic neutron scattering data at 4 and 200 K, integrated magnetic scattering intensity, density of states for the model, and details of the powder inelastic neutron scattering simulation.
- G. Xu, C. L. Broholm, Y.-A. Soh, G. Aeppli, J. F. Ditusa, Y. Chen, M. Kenzelmann, C. D. Frost, T. Ito, K. Oka, and H. Takagi, Mesoscopic phase coherence in a quantum spin fluid, Science 317, 1049 (2007).
- F. H. L. Essler and R. M. Konik, Finite-temperature lineshapes in gapped quantum spin chains, Phys. Rev. B 78, 100403(R) (2008).
- I. Exius, K. P. Schmidt, B. Lake, D. A. Tennant, and G. S. Uhrig, Vertex corrections in the dynamic structure factor in spin ladders, Phys. Rev. B 82, 214410 (2010).
- B. Normand and C. Rüegg, Complete bond-operator theory of the two-chain spin ladder, Phys. Rev. B 83, 054415 (2011).
- F. Verstraete, M. Popp, and J. I. Cirac, Entanglement versus correlations in spin systems, Phys. Rev. Lett. 92, 027901 (2004).
- B.-Q. Jin and V. E. Korepin, Localizable entanglement in antiferromagnetic spin chains, Phys. Rev. A 69, 062314 (2004).
- Č. Brukner, V. Vedral, and A. Zeilinger, Crucial role of quantum entanglement in bulk properties of solids, Phys. Rev. A 73, 012110 (2006).