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Quantum spin ladder with ferromagnetic rungs in Bi2CuO3(SO4)

Rodolfo A. Rangel Hernandez1, Kirill Yu. Povarov2, Sergei Zvyagin2, Oleg I. Siidra3, Alexander A. Tsirlin1,*, and Victoria A. Ginga1,†

  • *Contact author: altsirlin@gmail.com
  • †Contact author: victoria.ginga@uni-leipzig.de
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Phys. Rev. B 114, 034402 – Published 6 July, 2026

DOI: https://doi.org/10.1103/nwlh-vnyp

Abstract

We introduce Bi2CuO3(SO4) as a rare example of a spin-ladder magnet with ferromagnetic interactions on the rungs. Its magnetic response is studied through measurements of temperature-dependent magnetic susceptibility and heat capacity, field-dependent magnetization, and electron spin resonance spectroscopy. These experiments are complemented by density-functional-theory calculations combined with the construction of maximally localized Wannier functions and an analysis of the relevant superexchange pathways. Quantum Monte Carlo simulations are employed to model thermodynamic properties and to quantitatively determine the magnetic exchange parameters. Our combined approach identifies Bi2CuO3(SO4) as a two-leg spin-ladder system with ferromagnetic rungs (J′ ≈−208K) and antiferromagnetic legs (J≈258K). These interactions of similar magnitude arise from remarkably different superexchange pathways, with the Cu–Cu distance along the leg being almost twice as long as the respective distance along the rung. The antiferromagnetic leg coupling represents the strongest oxygen-mediated long-range superexchange in a Cu2+ compound and sets a benchmark for the role of complex superexchange pathways in quantum magnets.

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References (62)

  1. F. D. M. Haldane, Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model, Phys. Lett. A 93, 464 (1983).
  2. E. Dagotto and T. M. Rice, Surprises on the way from one- to two-dimensional quantum magnets: The ladder materials, Science 271, 618 (1996).
  3. D. S. Inosov, Quantum magnetism in minerals, Adv. Phys. 67, 149 (2018).
  4. H. Zhang, Z. Zhao, D. Gautreau, M. Raczkowski, A. Saha, V. O. Garlea, H. Cao, T. Hong, H. O. Jeschke, S. D. Mahanti, T. Birol, F. F. Assaad, and X. Ke, Coexistence and interaction of spinons and magnons in an antiferromagnet with alternating antiferromagnetic and ferromagnetic quantum spin chains, Phys. Rev. Lett. 125, 037204 (2020).
  5. P. Lemmens, G. Güntherodt, and C. Gros, Magnetic light scattering in low-dimensional quantum spin systems, Phys. Rep. 375, 1 (2003).
  6. S. Lebernegg, O. Janson, I. Rousochatzakis, S. Nishimoto, H. Rosner, and A. A. Tsirlin, Frustrated spin chain physics near the Majumdar-Ghosh point in szenicsite Cu3(MoO4)(OH)4, Phys. Rev. B 95, 035145 (2017).
  7. A. A. Kulbakov, D. Y. Kononenko, S. Nishimoto, Q. Stahl, A. M. Chakkingal, M. Feig, R. Gumeniuk, Y. Skourski, L. Bhaskaran, S. A. Zvyagin, J. P. Embs, I. Puente-Orench, A. Wildes, J. Geck, O. Janson, D. S. Inosov, and D. C. Peets, Coupled frustrated ferromagnetic and antiferromagnetic quantum spin chains in the quasi-one-dimensional mineral antlerite Cu3SO4(OH)4, Phys. Rev. B 106, L020405 (2022).
  8. A. Glamazda, Y. S. Choi, S.-H. Do, S. Lee, P. Lemmens, A. N. Ponomaryov, S. A. Zvyagin, J. Wosnitza, D. P. Sari, I. Watanabe, and K.-Y. Choi, Quantum criticality in the coupled two-leg spin ladder Ba2CuTeO6, Phys. Rev. B 95, 184430 (2017).
  9. A. A. Tsirlin, I. Rousochatzakis, D. Kasinathan, O. Janson, R. Nath, F. Weickert, C. Geibel, A. M. Läuchli, and H. Rosner, Bridging frustrated-spin-chain and spin-ladder physics: Quasi-one-dimensional magnetism of BiCu2PO6, Phys. Rev. B 82, 144426 (2010).
  10. M. Azuma, Z. Hiroi, M. Takano, K. Ishida, and Y. Kitaoka, Observation of a spin gap in SrCu2O3 comprising spin-½ quasi-1D two-leg ladders, Phys. Rev. Lett. 73, 3463 (1994).
  11. V. Kiryukhin, Y. J. Kim, K. J. Thomas, F. C. Chou, R. W. Erwin, Q. Huang, M. A. Kastner, and R. J. Birgeneau, Magnetic properties of the S=12 quasi-one-dimensional antiferromagnet CaCu2O3, Phys. Rev. B 63, 144418 (2001).
  12. S. Sugai, T. Shinoda, N. Kobayashi, Z. Hiroi, and M. Takano, Anisotropic exchange integrals in the two-leg spin ladder LaCuO2.5, Phys. Rev. B 60, R6969(R) (1999).
  13. B. Koteswararao, S. Salunke, A. V. Mahajan, I. Dasgupta, and J. Bobroff, Spin-gap behavior in the two-leg spin-ladder BiCu2PO6, Phys. Rev. B 76, 052402 (2007).
  14. O. Mentré, E. Janod, P. Rabu, M. Hennion, F. Leclercq-Hugeux, J. Kang, C. Lee, M.-H. Whangbo, and S. Petit, Incommensurate spin correlation driven by frustration in BiCu2PO6, Phys. Rev. B 80, 180413(R) (2009).
  15. K.-Y. Choi, J. W. Hwang, P. Lemmens, D. Wulferding, G. J. Shu, and F. C. Chou, Evidence for dimer crystal melting in the frustrated spin-ladder system BiCu2PO6, Phys. Rev. Lett. 110, 117204 (2013).
  16. K. W. Plumb, K. Hwang, Y. Qiu, L. W. Harriger, G. E. Granroth, A. I. Kolesnikov, G. J. Shu, F. C. Chou, Ch. Rüegg, Y. B. Kim, and Y.-J. Kim, Quasiparticle-continuum level repulsion in a quantum magnet, Nat. Phys. 12, 224 (2016).
  17. Y. Kohama, S. Wang, A. Uchida, K. Prsa, S. Zvyagin, Y. Skourski, R. D. McDonald, L. Balicas, H. M. Rønnow, C. Rüegg, and M. Jaime, Anisotropic cascade of field-induced phase transitions in the frustrated spin-ladder system BiCu2PO6, Phys. Rev. Lett. 109, 167204 (2012).
  18. F. Casola, T. Shiroka, A. Feiguin, S. Wang, M. S. Grbić, M. Horvatić, S. Krämer, S. Mukhopadhyay, K. Conder, C. Berthier, H.-R. Ott, H. M. Rønnow, Ch. Rüegg, and J. Mesot, Field-induced quantum soliton lattice in a frustrated two-leg spin-1/2 ladder, Phys. Rev. Lett. 110, 187201 (2013).
  19. L. Splinter, N. A. Drescher, H. Krull, and G. S. Uhrig, Minimal model for the frustrated spin ladder system BiCu2PO6, Phys. Rev. B 94, 155115 (2016).
  20. K. Hwang and Y. B. Kim, Theory of triplon dynamics in the quantum magnet BiCu2PO6, Phys. Rev. B 93, 235130 (2016).
  21. P. Pilch, K. Amelin, G. Schmiedinghoff, A. Reinold, C. Zhu, K. Yu. Povarov, S. Zvyagin, H. Engelkamp, Y.-P. Lan, G.-J. Shu, F. C. Chou, U. Nagel, T. Rõõm, G. S. Uhrig, B. Fauseweh, and Z. Wang, Low-energy spin excitations in field-induced phases of the spin-ladder antiferromagnet BiCu2PO6, Phys. Rev. B 111, 024423 (2025).
  22. O. Siidra, D. Charkin, I. Plokhikh, E. Nazarchuk, A. Holzheid, and G. Akimov, Expanding family of litharge-derived sulfate minerals and synthetic compounds: Preparation and crystal structures of [Bi2CuO3]SO4 and [Ln2O2]SO4 (Ln=Dy and Ho), Minerals 10, 887 (2020).
  23. M. Lü, M. Colmont, H. Kabbour, S. Colis, and O. Mentré, Revised Bi/M layered oxo-sulfate (M = Co, Cu): A structural and magnetic study, Inorg. Chem. 53, 6969 (2014).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/nwlh-vnyp for additional details of the crystal structure, comparison between the different batches, and for the simulated magnetization curves.
  25. A. Fitch, C. Dejoie, E. Covacci, G. Confalonieri, O. Grendal, L. Claustre, P. Guillou, J. Kieffer, W. de Nolf, S. Petitdemange, M. Ruat, and Y. Watier, ID22—the high-resolution powder-diffraction beamline at ESRF, J. Synchrotron Rad. 30, 1003 (2023).
  26. V. Petříček, M. Dušek, and L. Palatinus, Crystallographic computing system JANA2006: General features, Z. Krist. 229, 345 (2014).
  27. B. Aurivillius, Pyrolysis products of Bi2(SO4)3. Crystal structures of Bi26O27(SO4)12 and Bi14O16(SO4)5, Acta Chem. Scand. 41a, 415 (1987).
  28. S. A. Zvyagin, J. Krzystek, P. H. M. van Loosdrecht, G. Dhalenne, and A. Revcolevschi, High-field ESR study of the dimerized-incommensurate phase transition in the spin-Peierls compound CuGeO3, Physica B 346-347, 1 (2004).
  29. K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
  30. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  31. H. Eschrig and K. Koepernik, Tight-binding models for the iron-based superconductors, Phys. Rev. B 80, 104503 (2009).
  32. V. V. Mazurenko, S. L. Skornyakov, A. V. Kozhevnikov, F. Mila, and V. I. Anisimov, Wannier functions and exchange integrals: The example of LiCu2O2, Phys. Rev. B 75, 224408 (2007).
  33. V. V. Mazurenko, M. V. Valentyuk, R. Stern, and A. A. Tsirlin, Nonfrustrated interlayer order and its relevance to the Bose-Einstein condensation of magnons in BaCuSi2O6, Phys. Rev. Lett. 112, 107202 (2014).
  34. P. Bag, N. Ahmed, V. Singh, M. Sahoo, A. A. Tsirlin, and R. Nath, Low-dimensional magnetism of BaCuTe2O6, Phys. Rev. B 103, 134410 (2021).
  35. H. J. Xiang, E. J. Kan, S.-H. Wei, M.-H. Whangbo, and X. G. Gong, Predicting the spin-lattice order of frustrated systems from first principles, Phys. Rev. B 84, 224429 (2011).
  36. S. Todo and K. Kato, Cluster algorithms for general-S quantum spin systems, Phys. Rev. Lett. 87, 047203 (2001).
  37. A. F. Albuquerque, F. Alet, P. Corboz, P. Dayal, A. Feiguin, S. Fuchs, L. Gamper, E. Gull, S. Gürtler, A. Honecker, R. Igarashi, M. Körner, A. Kozhevnikov, A. Läuchli, S. Manmana, M. Matsumoto, I. P. McCulloch, F. Michel, R. M. Noack, G. Pawłowski, et al., The ALPS project release 1.3: Open-source software for strongly correlated systems, J. Magn. Magn. Mater. 310, 1187 (2007).
  38. A. F. Albuquerque, M. Troyer, and J. Oitmaa, Quantum phase transition in a Heisenberg antiferromagnet on a square lattice with strong plaquette interactions, Phys. Rev. B 78, 132402 (2008).
  39. 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 S=1/2 antiferromagnetic uniform and alternating-exchange Heisenberg chains, Phys. Rev. B 61, 9558 (2000).
  40. M. Sigrist and A. Furusaki, Low-temperature properties of the randomly depleted Heisenberg ladder, J. Phys. Soc. Jpn. 65, 2385 (1996).
  41. H.-J. Mikeska, U. Neugebauer, and U. Schollwöck, Spin ladders with nonmagnetic impurities, Phys. Rev. B 55, 2955 (1997).
  42. D. Schmidiger, K. Yu. Povarov, S. Galeski, N. Reynolds, R. Bewley, T. Guidi, J. Ollivier, and A. Zheludev, Emergent interacting spin islands in a depleted strong-leg Heisenberg ladder, Phys. Rev. Lett. 116, 257203 (2016).
  43. A. A. Tsirlin, O. Janson, and H. Rosner, β−Cu2V2O7: A spin-12 honeycomb lattice system, Phys. Rev. B 82, 144416 (2010).
  44. A. A. Tsirlin and H. Rosner, Uniform spin-chain physics arising from N—C—N bridges in CuNCN, the nitride analog of the copper oxides, Phys. Rev. B 81, 024424 (2010).
  45. A. A. Tsirlin, R. Zinke, J. Richter, and H. Rosner, Spiral ground state in the quasi-two-dimensional spin-12 system Cu2GeO4, Phys. Rev. B 83, 104415 (2011).
  46. D. C. Johnston, M. Troyer, S. Miyahara, D. Lidsky, K. Ueda, M. Azuma, Z. Hiroi, M. Takano, M. Isobe, Y. Ueda, M. A. Korotin, V. I. Anisimov, A. V. Mahajan, and L. L. Miller, Magnetic susceptibilities of spin-1/2 antiferromagnetic Heisenberg ladders and applications to ladder oxide compounds, arXiv:cond-mat/0001147.
  47. M. Troyer, H. Tsunetsugu, and D. Würtz, Thermodynamics and spin gap of the Heisenberg ladder calculated by the look-ahead Lanczos algorithm, Phys. Rev. B 50, 13515 (1994).
  48. G. N. Rao, R. Sankar, A. Singh, I. P. Muthuselvam, W. T. Chen, V. N. Singh, G.-Y. Guo, and F. C. Chou, Tellurium-bridged two-leg spin ladder in Ba2CuTeO6, Phys. Rev. B 93, 104401 (2016).
  49. A. S. Gibbs, A. Yamamoto, A. N. Yaresko, K. S. Knight, H. Yasuoka, M. Majumder, M. Baenitz, P. J. Saines, J. R. Hester, D. Hashizume, A. Kondo, K. Kindo, and H. Takagi, S=12 quantum critical spin ladders produced by orbital ordering in Ba2CuTeO6, Phys. Rev. B 95, 104428 (2017).
  50. W. E. A. Lorenz, R. O. Kuzian, S.-L. Drechsler, W.-D. Stein, N. Wizent, G. Behr, J. Málek, U. Nitzsche, H. Rosner, A. Hiess, W. Schmidt, R. Klingeler, M. Loewenhaupt, and B. Büchner, Highly dispersive spin excitations in the chain cuprate Li2CuO2, Europhys. Lett. 88, 37002 (2009).
  51. J. Philippe, F. Elson, T. Arh, S. Sanz, M. Metzelaars, D. W. Tam, O. K. Forslund, O. Shliakhtun, C. Jiang, J. Lass, M. D. Le, J. Ollivier, P. Bouillot, T. Giamarchi, M. Bartkowiak, D. G. Mazzone, P. Kögerler, M. Månsson, A. M. Läuchli, Y. Sassa, et al., Magnetic and phononic dynamics in the two-ladder quantum magnet (C5H9NH3)2CuBr4, Phys. Rev. B 113, 134438 (2026).
  52. B. C. Watson, V. N. Kotov, M. W. Meisel, D. W. Hall, G. E. Granroth, W. T. Montfrooij, S. E. Nagler, D. A. Jensen, R. Backov, M. A. Petruska, G. E. Fanucci, and D. R. Talham, Magnetic spin ladder (C5H12N)2CuBr4: High-field magnetization and scaling near quantum criticality, Phys. Rev. Lett. 86, 5168 (2001).
  53. A. T. Savici, G. E. Granroth, C. L. Broholm, D. M. Pajerowski, C. M. Brown, D. R. Talham, M. W. Meisel, K. P. Schmidt, G. S. Uhrig, and S. E. Nagler, Neutron scattering evidence for isolated spin-12 ladders in (C5D12N)2CuBr4, Phys. Rev. B 80, 094411 (2009).
  54. T. Hong, K. P. Schmidt, K. Coester, F. F. Awwadi, M. M. Turnbull, Y. Qiu, J. A. Rodriguez-Rivera, M. Zhu, X. Ke, C. P. Aoyama, Y. Takano, H. Cao, W. Tian, J. Ma, R. Custelcean, H. D. Zhou, and M. Matsuda, Magnetic ordering induced by interladder coupling in the spin-12 Heisenberg two-leg ladder antiferromagnet C9H18N2CuBr4, Phys. Rev. B 89, 174432 (2014).
  55. T. Fischer, S. Duffe, and G. S. Uhrig, Microscopic model for Bose-Einstein condensation and quasiparticle decay, Europhys. Lett. 96, 47001 (2011).
  56. A. A. Tsirlin, O. Janson, and I. Rousochatzakis, One-dimensional physics of the frustrated quantum magnet PHCC, Z. Naturforsch. A 81, 335 (2026).
  57. T. Hong, Y. H. Kim, C. Hotta, Y. Takano, G. Tremelling, M. M. Turnbull, C. P. Landee, H.-J. Kang, N. B. Christensen, K. Lefmann, K. P. Schmidt, G. S. Uhrig, and C. Broholm, Field-induced Tomonaga-Luttinger liquid phase of a two-leg spin-1/2 ladder with strong leg interactions, Phys. Rev. Lett. 105, 137207 (2010).
  58. D. Schmidiger, P. Bouillot, S. Mühlbauer, S. Gvasaliya, C. Kollath, T. Giamarchi, and A. Zheludev, Spectral and thermodynamic properties of a strong-leg quantum spin ladder, Phys. Rev. Lett. 108, 167201 (2012).
  59. L. V. Shvanskaya, T. D. Bushneva, D. A. Chareev, P. A. Maksimov, A. A. Sudakov, E. I. Kornienko, A. V. Ushakov, S. V. Streltsov, and A. N. Vasiliev, Peculiar crystal structure and strong-rung spin ladders in KCu2BiO2(SO4)2, Inorg. Chem. 65, 395 (2026).
  60. 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 S=12 chains in the distorted honeycomb lattice compound Na2Cu2TeO6, Phys. Rev. B 102, 220402(R) (2020).
  61. 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 Na2Cu2TeO6, Phys. Rev. B 104, 224430 (2021).
  62. R. A. R. Hernandez, K. Yu. Povarov, S. Zvyagin, O. I. Siidra, A. A. Tsirlin, and V. A. Ginga, Supplemental Materials for the manuscript “Quantum spin ladder with ferromagnetic rungs in Bi2CuO3(SO4)” [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.19241586.

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Phys. Rev. B 114, 034402– Published 6 July, 2026
  • Received 26 March 2026
  • Revised 2 June 2026
  • Accepted 10 June 2026
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