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Cluster spin glass state in Ba3Sb1+xCo2−xO9−δ: Cation disorder and mixed-valence Co dimers

Anzar Ali1,*,†, Guratinder Kaur1,2,*, Lukas Keller3, and Masahiko Isobe1,‡

  • *These authors contributed equally to this work.
  • †Contact author: a.ali@fkf.mpg.de
  • ‡Contact author: m.isobe@fkf.mpg.de
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Phys. Rev. B 112, 024409 – Published 7 July, 2025

DOI: https://doi.org/10.1103/k7mm-g2zc

Abstract

We investigate the structural, magnetic, and thermodynamic properties of Ba3Sb1+xCo2−xO9−δ (x=0.04,δ=0.54), a hexagonal perovskite featuring face-sharing CoO6 octahedra that form Co dimers. DC and AC magnetization measurements reveal a frequency-dependent spin-freezing transition consistent with glassy dynamics. AC susceptibility fits best to the Vogel-Fulcher model, indicating collective freezing of interacting spin clusters. Isothermal magnetization follows the Langevin function, suggesting finite-sized magnetic clusters rather than isolated paramagnetic moments. Nonequilibrium dynamics, evidenced by thermoremanent magnetization and memory effects, further support a spin-glass-like state. Heat capacity shows no sharp anomalies, and neutron powder diffraction confirms the absence of magnetic Bragg peaks down to 1.5 K, ruling out long-range magnetic order. Rietveld refinement reveals significant Co/Sb intersite disorder (∼30%) and oxygen nonstoichiometry, introducing exchange randomness and frustration that drive the spin-glass-like behavior. Electrical resistivity exhibits Arrhenius-type temperature dependence with an activation energy of 0.173 eV, consistent with semiconducting behavior. Temperature-dependent x-ray diffraction shows no structural phase transitions, confirming that the spin-glass-like state is not lattice driven. Our results establish Ba3Sb1+xCo2−xO9−δ as a cluster spin-glass candidate, where Co dimers, disorder, and geometric frustration prevent long-range order, leading to slow spin dynamics. These findings highlight the role of cation disorder and oxygen vacancies in stabilizing unconventional magnetic states in cobalt-based hexagonal perovskites.

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References (74)

  1. L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
  2. C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020).
  3. R. Moessner and A. P. Ramirez, Geometrical frustration, Phys. Today 59(2), 24 (2006).
  4. K. Binder and A. P. Young, Spin glasses: Experimental facts, theoretical concepts, and open questions, Rev. Mod. Phys. 58, 801 (1986).
  5. K. Binder and W. Kob, Glassy Materials and Disordered Solids (World Scientific, Singapore, 2005).
  6. V. M. Katukuri, S. Nishimoto, I. Rousochatzakis, H. Stoll, J. van den Brink, and L. Hozoi, Strong magnetic frustration and anti-site disorder causing spin-glass behavior in honeycomb Li2RhO3, Sci. Rep. 5, 14718 (2015).
  7. R. C. Sahoo, S. Das, and T. K. Nath, Influence of magnetic frustration and structural disorder on magnetocaloric effect and magneto-transport properties in La1.5Ca0.5CoMnO6 double perovskite, J. Appl. Phys. 123, 013902 (2018).
  8. C. A. Bridges, T. Hansen, A. S. Wills, G. M. Luke, and J. E. Greedan, Frustrated magnetism and the effects of titanium substitution in the mixed-valence oxide BaV10−xTixO15, Phys. Rev. B 74, 024426 (2006).
  9. L. T. Nguyen and R. J. Cava, Hexagonal perovskites as quantum materials, Chem. Rev. 121, 2935 (2021).
  10. L. T. Nguyen and R. J. Cava, Trimer-based spin liquid candidate Ba4NbIr3O12, Phys. Rev. Mater. 3, 014412 (2019).
  11. A. Bandyopadhyay, S. Lee, D. T. Adroja, G. B. G. Stenning, A. Berlie, M. R. Lees, R. A. Saha, D. Takegami, A. Meléndez-Sans, G. Poelchen, M. Yoshimura, K. D. Tsuei, Z. Hu, C.-W. Kao, Y.-C. Huang, T.-S. Chan, and K.-Y. Choi, Quantum spin liquid ground state in the trimer rhodate Ba4NbRh3O12, Phys. Rev. B 109, 184403 (2024).
  12. A. Ali, H.-S. Kim, P. Yadav, S. Lee, D. Yoon, and S. Choi, Partial molecular orbitals in face-sharing 3d manganese trimer: Comparative studies on Ba4TaMn3O12 and Ba4NbMn3O12, Phys. Rev. Res. 6, 013231 (2024).
  13. J. A. Quilliam, F. Bert, A. Manseau, C. Darie, C. Guillot-Deudon, C. Payen, C. Baines, A. Amato, and P. Mendels, Gapless quantum spin liquid ground state in the spin-1 antiferromagnet 6H-Ba3NiSb2O9, Phys. Rev. B 93, 214432 (2016).
  14. H. D. Zhou, E. S. Choi, G. Li, L. Balicas, C. R. Wiebe, Y. Qiu, J. R. D. Copley, and J. S. Gardner, Spin liquid state in the S=1/2 triangular lattice Ba3CuSb2O9, Phys. Rev. Lett. 106, 147204 (2011).
  15. S. Middey, S. Ray, K. Mukherjee, P. L. Paulose, E. V. Sampathkumaran, C. Meneghini, S. D. Kaushik, V. Siruguri, K. Kovnir, and D. D. Sarma, Glasslike ordering and spatial inhomogeneity of magnetic structure in Ba3FeRu2O9: Role of Fe/Ru site disorder, Phys. Rev. B 83, 144419 (2011).
  16. L. Savary and L. Balents, Disorder-induced quantum spin liquid in spin ice pyrochlores, Phys. Rev. Lett. 118, 087203 (2017).
  17. J.-J. Wen, S. M. Koohpayeh, K. A. Ross, B. A. Trump, T. M. McQueen, K. Kimura, S. Nakatsuji, Y. Qiu, D. M. Pajerowski, J. R. D. Copley, and C. L. Broholm, Disordered route to the Coulomb quantum spin liquid: Random transverse fields on spin ice in Pr2Zr2O7, Phys. Rev. Lett. 118, 107206 (2017).
  18. A. Smerald and F. Mila, Disorder-driven spin-orbital liquid behavior in the Ba3XSb2O9 materials, Phys. Rev. Lett. 115, 147202 (2015).
  19. S. Kundu, A. Hossain, P. K. S., R. Das, M. Baenitz, P. J. Baker, J.-C. Orain, D. C. Joshi, R. Mathieu, P. Mahadevan, S. Pujari, S. Bhattacharjee, A. V. Mahajan, and D. D. Sarma, Signatures of a spin-12 cooperative paramagnet in the diluted triangular lattice of Y2CuTiO6, Phys. Rev. Lett. 125, 117206 (2020).
  20. S. Kundu, A. Shahee, A. Chakraborty, K. M. Ranjith, B. Koo, J. Sichelschmidt, M. T. F. Telling, P. K. Biswas, M. Baenitz, I. Dasgupta, S. Pujari, and A. V. Mahajan, Gapless quantum spin liquid in the triangular system Sr3CuSb2O9, Phys. Rev. Lett. 125, 267202 (2020).
  21. S.-H. Baek, H. W. Yeo, S.-H. Do, K.-Y. Choi, L. Janssen, M. Vojta, and B. Büchner, Observation of a random singlet state in a diluted Kitaev honeycomb material, Phys. Rev. B 102, 094407 (2020).
  22. R. Kumar and A. Sundaresan, Antisite disorder driven cluster glass state and colossal magnetoresistance in MnSb2Se4, Phys. Rev. B 106, 134423 (2022).
  23. K. Pal and I. Das, Exploring the origin of exchange bias and spin glass behavior in 6H hexagonal perovskite structure: Structural and magnetic analysis, Appl. Mater. Today 39, 102316 (2024).
  24. V. Petříček, M. Dušek, and L. Palatinus, Crystallographic computing system JANA2006: General features, Z. Kristallogr. - Cryst. Mater. 229, 345 (2014).
  25. S. Istomin, V. A. Koutcenko, E. V. Antipov, F. Lindberg, and G. Svensson, Synthesis and characterization of novel 6-H perovskites Ba2Co2−xSbxO6−y, 0.6≤x≤0.8 and x=1.33 (Ba3CoSb2O9), Mater. Res. Bull. 39, 1013 (2004).
  26. Y. Doi, Y. Hinatsu, and K. Ohoyama, Structural and magnetic properties of pseudo-two-dimensional triangular antiferromagnets Ba3MSb2O9 (M = Mn, Co, and Ni), J. Phys.: Condens. Matter 16, 8923 (2004).
  27. C. Darie, P. Bordet, M. Viaud, C. Guillot-Deudon, P. Deniard, E. Gautron, C. Colin, F. Porcher, G. Berlanda, F. Bert, P. Mendels, and C. Payen, Two new cubic perovskite oxides Ba3CoSb2O9 and Ba2SrCoSb2O9: Syntheses, crystal structures and magnetic properties, J. Solid State Chem. 317, 123701 (2023).
  28. P. Kearins, E. Solana-Madruga, K. Ji, C. Ritter, and J. P. Attfield, Cluster spin glass formation in the double double perovskite CaMnFeTaO6, J. Phys. Chem. C 125, 9550 (2021).
  29. T. Murakami, M. Avdeev, R. Morikawa, J. R. Hester, and M. Yashima, High proton conductivity in β−Ba2ScAlO5 enabled by octahedral and intrinsically oxygen-deficient layers, Adv. Funct. Mater. 33, 2206777 (2023).
  30. M. I. Gómez, G. Lucotti, J. A. de Morán, P. J. Aymonino, S. Pagola, P. Stephens, and R. E. Carbonio, Ab initio structure solution of BaFeO2.8−δ, a new polytype in the system BaFeOy(2.5≤y≤3.0) prepared from the oxidative thermal decomposition of BaFe[(CN)5NO]·3H2O, J. Solid State Chem. 160, 17 (2001).
  31. D. C. Sinclair, J. M. S. Skakle, F. D. Morrison, R. I. Smith, and T. P. Beales, Structure and electrical properties of oxygen-deficient hexagonal BaTiO3, J. Mater. Chem. 9, 1327 (1999).
  32. C. de la Calle, J. A. Alonso, A. Aguadero, and M. T. Fernández-Díaz, Phase transformations in Sr0.8Ba0.2CoO2.5 brownmillerite: Correlation between structure and transport properties, Dalton Trans. 2009, 4104 (2009).
  33. S. Mugiraneza and A. M. Hallas, Tutorial: A beginner's guide to interpreting magnetic susceptibility data with the Curie-Weiss law, Commun. Phys. 5, 95 (2022).
  34. M. A. Korotin, S. Y. Ezhov, I. V. Solovyev, V. I. Anisimov, D. I. Khomskii, and G. A. Sawatzky, Intermediate-spin state and properties of LaCoO3, Phys. Rev. B 54, 5309 (1996).
  35. G. Maris, Y. Ren, V. Volotchaev, C. Zobel, T. Lorenz, and T. T. M. Palstra, Evidence for orbital ordering in LaCoO3, Phys. Rev. B 67, 224423 (2003).
  36. N. A. A. M. Amin, S. M. Said, N. M. J. N. Ibrahim, M. M. I. M. Hasnan, M. F. M. Salleh, and A. M. Afifi, Comparative analysis between solution-phase and thin films of cobalt(II) spin crossover (SCO) complexes with 8, 10, 12-carbon alkyl chains based on structural, optical and electrical properties, J. Mater. Sci.: Mater. Electron. 35, 1930 (2024).
  37. Y.-Y. Chin, H.-J. Lin, Z. Hu, C.-Y. Kuo, D. Mikhailova, J.-M. Lee, S.-C. Haw, S.-A. Chen, W. Schnelle, H. Ishii, N. Hiraoka, Y.-F. Liao, K.-D. Tsuei, A. Tanaka, L. Hao Tjeng, C.-T. Chen, and J.-M. Chen, Relation between the Co-O bond lengths and the spin state of Co in layered cobaltates: A high-pressure study, Sci. Rep. 7, 3656 (2017).
  38. Y. M. Oey and R. Cava, The effective magnetic moments of Co2+ and Co3+ in SrTiO3 investigated by temperature-dependent magnetic susceptibility, Mater. Res. Bull. 122, 110667 (2020).
  39. A. Podlesnyak, M. Russina, A. Furrer, A. Alfonsov, E. Vavilova, V. Kataev, B. Büchner, T. Strässle, E. Pomjakushina, K. Conder, and D. I. Khomskii, Spin-state polarons in lightly-hole-doped LaCoO3, Phys. Rev. Lett. 101, 247603 (2008).
  40. T. Burnus, Z. Hu, H. H. Hsieh, V. L. J. Joly, P. A. Joy, M. W. Haverkort, H. Wu, A. Tanaka, H.-J. Lin, C. T. Chen, and L. H. Tjeng, Local electronic structure and magnetic properties of LaMn0.5Co0.5O3 studied by x-ray absorption and magnetic circular dichroism spectroscopy, Phys. Rev. B 77, 125124 (2008).
  41. S. V. Streltsov and D. I. Khomskii, Cluster magnetism of Ba4NbMn3O12: Localized electrons or molecular orbitals? JETP Lett. 108, 686 (2018).
  42. L. T. Nguyen, T. Halloran, W. Xie, T. Kong, C. L. Broholm, and R. J. Cava, Geometrically frustrated trimer-based Mott insulator, Phys. Rev. Mater. 2, 054414 (2018).
  43. G. S. Thakur, S. Chattopadhyay, T. Doert, T. Herrmannsdörfer, and C. Felser, Crystal growth of spin-frustrated Ba4Nb0.8Ir3.2O12: A possible spin liquid material, Cryst. Growth Des. 20, 2871 (2020).
  44. S. Shibasaki, I. Terasaki, E. Nishibori, H. Sawa, J. Lybeck, H. Yamauchi, and M. Karppinen, Magnetic and transport properties of the spin-state disordered oxide La0.8Sr0.2Co1−xRhxO3−δ, Phys. Rev. B 83, 094405 (2011).
  45. C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, 2004).
  46. S. J. Sebastian, K. Somesh, M. Nandi, N. Ahmed, P. Bag, M. Baenitz, B. Koo, J. Sichelschmidt, A. A. Tsirlin, Y. Furukawa, and R. Nath, Quasi-one-dimensional magnetism in the spin-12 antiferromagnet BaNa2Cu(VO4)2, Phys. Rev. B 103, 064413 (2021).
  47. C. A. M. Mulder, A. J. van Duyneveldt, and J. A. Mydosh, Frequency and field dependence of the ac susceptibility of the AuMn spin-glass, Phys. Rev. B 25, 515 (1982).
  48. J. Mydosh, Disordered magnetism and spin glasses, J. Magn. Magn. Mater. 157-158, 606 (1996).
  49. J. A. Mydosh, Spin Glasses: An Experimental Introduction (Taylor & Francis, 1993).
  50. P. Bag, P. R. Baral, and R. Nath, Cluster spin-glass behavior and memory effect in Cr0.5Fe0.5Ga, Phys. Rev. B 98, 144436 (2018).
  51. J. Lago, S. J. Blundell, A. Eguia, M. Jansen, and T. Rojo, Three-dimensional Heisenberg spin-glass behavior in SrFe0.90Co0.10O3.0, Phys. Rev. B 86, 064412 (2012).
  52. J. Souletie and J. L. Tholence, Critical slowing down in spin glasses and other glasses: Fulcher versus power law, Phys. Rev. B 32, 516 (1985).
  53. S. Shtrikman and E. Wohlfarth, The theory of the Vogel-Fulcher law of spin glasses, Phys. Lett. A 85, 467 (1981).
  54. P. Beauvillain, C. Chappert, J. Renard, and J. Seiden, Critical scaling laws in insulating spin glasses, J. Magn. Magn. Mater. 54-57, 127 (1986).
  55. R. Mathieu, M. Hudl, and P. Nordblad, Memory and rejuvenation in a spin glass, Europhys. Lett. 90, 67003 (2010).
  56. R. Kumar, P. Yanda, and A. Sundaresan, Cluster-glass behavior in the two-dimensional triangular lattice Ising-spin compound Li2Mn3O7, Phys. Rev. B 103, 214427 (2021).
  57. G. H. McCabe, T. Fries, M. T. Liu, Y. Shapira, L. R. Ram-Mohan, R. Kershaw, A. Wold, C. Fau, M. Averous, and E. J. McNiff, Bound magnetic polarons in p-type Cu2Mn0.9Zn0.1SnS4, Phys. Rev. B 56, 6673 (1997).
  58. P. Anil Kumar, A. Nag, R. Mathieu, R. Das, S. Ray, P. Nordblad, A. Hossain, D. Cherian, D. A. Venero, L. DeBeer-Schmitt, O. Karis, and D. D. Sarma, Magnetic polarons and spin-glass behavior in insulating La1−xSrxCoO3 (x=0.125 and 0.15), Phys. Rev. Res. 2, 043344 (2020).
  59. A. Kumar, A. Senyshyn, and D. Pandey, Evidence for cluster spin glass phase with precursor short-range antiferromagnetic correlations in the B-site disordered Ca(Fe1/2Nb1/2)O3 perovskite, Phys. Rev. B 99, 214425 (2019).
  60. K. Jonason, E. Vincent, J. Hammann, J. P. Bouchaud, and P. Nordblad, Memory and chaos effects in spin glasses, Phys. Rev. Lett. 81, 3243 (1998).
  61. R. S. Freitas, L. Ghivelder, F. Damay, F. Dias, and L. F. Cohen, Magnetic relaxation phenomena and cluster glass properties of La0.7−xYxCa0.3MnO3 manganites, Phys. Rev. B 64, 144404 (2001).
  62. R. V. Chamberlin, G. Mozurkewich, and R. Orbach, Time decay of the remanent magnetization in spin-glasses, Phys. Rev. Lett. 52, 867 (1984).
  63. C. A. Cardoso, F. M. Araujo-Moreira, V. P. S. Awana, E. Takayama-Muromachi, O. F. de Lima, H. Yamauchi, and M. Karppinen, Spin glass behavior in RuSr2Gd1.5Ce0.5Cu2O10−δ, Phys. Rev. B 67, 020407(R) (2003).
  64. D. Chu, G. G. Kenning, and R. Orbach, Dynamic measurements in a Heisenberg spin glass: CuMn, Phys. Rev. Lett. 72, 3270 (1994).
  65. A. Bhattacharyya, S. Giri, and S. Majumdar, Spin-glass-like state in GdCu: Role of phase separation and magnetic frustration, Phys. Rev. B 83, 134427 (2011).
  66. S. Pakhira, C. Mazumdar, R. Ranganathan, S. Giri, and M. Avdeev, Large magnetic cooling power involving frustrated antiferromagnetic spin-glass state in R2NiSi3(R=Gd,Er), Phys. Rev. B 94, 104414 (2016).
  67. H. Mamiya, Universal memory effects in Heisenberg spin glasses and spontaneous restoration of the spin configuration, Phys. Procedia 75, 711 (2015).
  68. J.-H. Yuan, B. Zhang, Y.-Q. Song, J.-F. Wang, K.-H. Xue, and X.-S. Miao, Planar penta-transition metal phosphide and arsenide as narrow-gap semiconductors with ultrahigh carrier mobility, J. Mater. Sci. 54, 7035 (2019).
  69. G. Liu, X. Q. Liu, and X. M. Chen, Contribution of oxygen vacancies to the giant dielectric response in Sm1.5Sr0.5NiO4−δ ceramics, Appl. Phys. A 116, 1421 (2014).
  70. R. M. Hill, Variable-range hopping, Phys. Status Solidi A 34, 601 (1976).
  71. J. Chen, X. Wu, and A. Selloni, Electronic structure and bonding properties of cobalt oxide in the spinel structure, Phys. Rev. B 83, 245204 (2011).
  72. M. W. Haverkort, Z. Hu, J. C. Cezar, T. Burnus, H. Hartmann, M. Reuther, C. Zobel, T. Lorenz, A. Tanaka, N. B. Brookes, H. H. Hsieh, H.-J. Lin, C. T. Chen, and L. H. Tjeng, Spin state transition in LaCoO3 studied using soft x-ray absorption spectroscopy and magnetic circular dichroism, Phys. Rev. Lett. 97, 176405 (2006).
  73. A. Ali, Raw data for the article entited “Cluster spin glass state in Ba3Sb1+xCo2−xO9−δ: Cation disorder and mixed-valence Co dimers” [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.15789706.
  74. A. Altomare, C. Cuocci, C. Giacovazzo, A. Moliterni, R. Rizzi, N. Corriero, and A. Falcicchio, EXPO2013: A kit of tools for phasing crystal structures from powder data, J. Appl. Crystallogr. 46, 1231 (2013).

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Phys. Rev. B 112, 024409– Published 7 July, 2025
  • Received 10 March 2025
  • Accepted 23 June 2025
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