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Long-ranged spin-glass phase boundary in quasicrystal approximants

Fernand Denoel1,*, Karthika K. Thilakan2,†, Yu-Chin Huang2,‡, Takayuki Shiino1,§, Girma Hailu Gebresenbut2, Huibo Cao3, Ulrich Häussermann4, Cesar Pay Gómez2, Martin Sahlberg2 et al.

Roland Mathieu1,∥

  • *Contact author: fernand.denoel@gmail.com
  • †Contact author: karthika.kariattukarakaran-thilakan@kemi.uu.se
  • ‡Present address: Department of Materials and Manufacturing, Jönköping University, Box 1026, 551 11 Jönköping, Sweden.
  • §Present address: Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Carrer dels Til·lers, 08193 Cerdanyola del Vallès, Spain.
  • ∥Contact author: roland.mathieu@angstrom.uu.se

Phys. Rev. B 114, 084404 – Published 4 August, 2026

DOI: https://doi.org/10.1103/n3yq-b937

Abstract

We report the magnetic structure of the pseudo-Tsai Tb-Au-Si 1/1 approximant crystal (AC), a periodic crystal where the Tb3+ magnetic ions are arranged in a bcc packing as icosahedron nodes plus center decoration. While looking seemingly long ranged in dc magnetometry and neutron diffraction experiments, this crystal shows dynamical magnetic behavior consistent with a spin glass, including aging and memory effects. The relevance of the spin chirality subtended by three noncoplanar magnetic moments, and its order and disorder is discussed. The results are compared to those obtained for the regular Tsai Tb-Au-Si 1/1 AC and binary quasicrystals in order to establish an electronic phase diagram illustrating the boundary between long-ranged and short-ranged order in those systems.

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References (36)

  1. D. Levine and P. J. Steinhardt, Quasicrystals: A new class of ordered structures, Phys. Rev. Lett. 53, 2477 (1984).
  2. A. I. Goldman, Magnetism in icosahedral quasicrystals: Current status and open questions, Sci. Technol. Adv. Mater. 15, 044801 (2014).
  3. T. Fujiwara and Y. Ishii, Quasicrystals (Elsevier Science, Amsterdam, 2007), Vol. 3.
  4. G. Gebresenbut, T. Shiino, D. Eklöf, D. C. Joshi, F. Denoel, R. Mathieu, U. Häussermann, and C. Pay Gómez, Atomic-scale tuning of Tsai-type clusters in RE–Au–Si systems (RE = Gd, Tb, Ho), Inorg. Chem. 59, 9152 (2020).
  5. S. Suzuki, A. Ishikawa, T. Yamada, T. Sugimoto, A. Sakurai, and R. Tamura, Magnetism of Tsai-type quasicrystal approximants, Mater. Trans. 62, 298 (2021).
  6. F. Labib, K. Nawa, S. Suzuki, H. C. Wu, A. Ishikawa, K. Inagaki, T. Fujii, K. Kinjo, T. J. Sato, and R. Tamura, Unveiling exotic magnetic phase diagram of a non-Heisenberg quasicrystal approximant, Mater. Today Phys. 40, 101321 (2024).
  7. M. L. Fornasini, P. Manfrinetti, D. Mazzone, and S. K. Dhar, Crystal structure and magnetic properties of the compounds Yb(Zn,Al)6 and YbZn6, Z. Naturforsch. B 63, 237 (2008).
  8. T. Hiroto, T. J. Sato, H. Cao, T. Hawai, T. Yokoo, S. Itoh, and R. Tamura, Noncoplanar ferrimagnetism and local crystalline-electric-field anisotropy in the quasicrystal approximant Au70Si17Tb13, J. Phys.: Condens. Matter 32, 415802 (2020).
  9. T. Shiino, F. Denoel, G. H. Gebresenbut, C. P. Gómez, P. Nordblad, and R. Mathieu, Nonequilibrium dynamical behavior in noncoplanar magnets with chiral spin texture, Phys. Rev. B 105, L180409 (2022).
  10. H. Kawamura and T. Taniguchi, Spin glasses, in Handbook of Magnetic Materials, edited by K. Buschow (Elsevier, 2015), Vol. 24, pp. 1–137.
  11. G. H. Gebresenbut, T. Shiino, M. S. Andersson, N. Qureshi, O. Fabelo, P. Beran, D. Qvarngård, P. Henelius, A. Rydh, R. Mathieu, et al., Effect of pseudo-Tsai cluster incorporation on the magnetic structures of R-Au-Si(R=Tb,Ho) quasicrystal approximants, Phys. Rev. B 106, 184413 (2022).
  12. B. C. Chakoumakos, H. Cao, F. Ye, A. D. Stoica, M. Popovici, M. Sundaram, W. Zhou, J. S. Hicks, G. W. Lynn, and R. A. Riedel, Four-circle single-crystal neutron diffractometer at the High Flux Isotope Reactor, J. Appl. Crystallogr. 44, 655 (2011).
  13. 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).
  14. See Supplemental Material at http://link.aps.org/supplemental/10.1103/n3yq-b937 for details and results about magnetometry and nuclear and magnetic structure refinements.
  15. P. E. Jönsson, R. Mathieu, P. Nordblad, H. Yoshino, H. A. Katori, and A. Ito, Nonequilibrium dynamics of spin glasses: Examination of the ghost domain scenario, Phys. Rev. B 70, 174402 (2004).
  16. P. Nordblad, Competing interaction in magnets: The root of ordered disorder or only frustration? Phys. Scr. 88, 058301 (2013).
  17. K. Jonason and P. Nordblad, Sensitivity to temperature perturbations of the ageing states in a re-entrant ferromagnet, Eur. Phys. J. B 10, 23 (1999).
  18. R. Mathieu, P. Jönsson, D. N. H. Nam, and P. Nordblad, Memory and superposition in a spin glass, Phys. Rev. B 63, 092401 (2001).
  19. F. Labib, K. Nawa, Y. Nambu, H. Takakura, Y. Ikeda, K. Deguchi, M. Matsuura, A. Ishikawa, R. Kajimoto, K. Ikeuchi, et al., Universal whirling magnetic orders in non-Heisenberg Tsai-type quasicrystal approximants, arXiv:2503.01517.
  20. K. K. Thilakan, F. Denoel, Y.-C. Huang, O. Fabelo, R. Mathieu, C. P. Gómez, and M. Sahlberg, Single-crystal neutron diffraction study on the Ho13.6Au61.1Al25.3 quasicrystal approximant, J. Alloys Compd. 1002, 175263 (2024).
  21. K. Nawa, M. Avdeev, A. Ishikawa, H. Takakura, C.-W. Wang, D. Okuyama, R. Murasaki, R. Tamura, and T. J. Sato, Magnetic properties of the quasicrystal approximant Au65Ga21Tb14, Phys. Rev. Mater. 7, 054412 (2023).
  22. G. H. Gebresenbut, M. S. Andersson, P. Nordblad, M. Sahlberg, and C. Pay Gómez, Tailoring magnetic behavior in the Tb-Au-Si quasicrystal approximant system, Inorg. Chem. 55, 2001 (2016).
  23. G. M. Rotaru, B. Roessli, A. Amato, S. N. Gvasaliya, C. Mudry, S. G. Lushnikov, and T. A. Shaplygina, Spin-glass state and long-range magnetic order in Pb(Fe1/2Nb1/2)O3 seen via neutron scattering and muon spin rotation, Phys. Rev. B 79, 184430 (2009).
  24. J. A. Paixão, M. Ramos Silva, S. A. Sørensen, B. Lebech, G. H. Lander, P. J. Brown, S. Langridge, E. Talik, and A. P. Gonçalves, Neutron-scattering study of the magnetic structure of DyFe4Al8 and HoFe4Al8, Phys. Rev. B 61, 6176 (2000).
  25. M. Giot, A. Pautrat, G. André, D. Saurel, M. Hervieu, and J. Rodriguez-Carvajal, Magnetic states and spin-glass properties in Bi0.67Ca0.33MnO3: Macroscopic ac measurements and neutron scattering, Phys. Rev. B 77, 134445 (2008).
  26. S. Mitsuda, H. Yoshizawa, T. Watanabe, S. Itoh, Y. Endoh, and I. Mirebeau, Neutron depolarization studies on reentrant spin glass AuFe alloy, J. Phys. Soc. Jpn. 60, 1721 (1991).
  27. H. Kawamura, Chirality scenario of the spin-glass ordering, J. Phys. Soc. Jpn. 79, 011007 (2010).
  28. S. Watanabe, Topological magnetic textures and long-range orders in terbium-based quasicrystal and approximant, Proc. Natl. Acad. Sci. USA 118, e2112202118 (2021).
  29. T. J. Sato, A. Ishikawa, A. Sakurai, M. Hattori, M. Avdeev, and R. Tamura, Whirling spin order in the quasicrystal approximant Au72Al14Tb14, Phys. Rev. B 100, 054417 (2019).
  30. L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
  31. O. Beckman, E. Figueroa, K. Gramm, L. Lundgren, K. V. Rao, and H. S. Chen, Spin wave and scaling law analysis of amorphous (FexNi1−x)75P16B6Al3 by magnetization measurements, Phys. Scr. 25, 726 (1982).
  32. I. Mirebeau and N. Martin, Revisiting neutron studies of reentrant spin glasses: The role of small-angle scattering, J. Appl. Crystallogr. 55, 1173 (2022).
  33. B. V. B. Sarkissian, The appearance of critical behaviour at the onset of ferromagnetism in AuFe alloys, J. Phys. F: Met. Phys. 11, 2191 (1981).
  34. R. Padam, T. Sarkar, R. Mathieu, S. Thota, and D. Pal, Magnetic phase diagram of Co(Cr1−xAlx)2O4 (x=0.0–1.0), J. Appl. Phys. 122, 073908 (2017).
  35. D. C. Joshi, G. Gebresenbut, C. Pay Gomez, and R. Mathieu, Memory and rejuvenation in a quasicrystal, Europhys. Lett. 132, 27002 (2020).
  36. F. Denoel, D. C. Joshi, Y.-C. Huang, G. H. Gebresenbut, C. Pay Gómez, and R. Mathieu, Magnetic frustration and glassiness in an icosahedral i-Tb-Cd quasicrystal, Phys. Rev. B 109, 184425 (2024).

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