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Dynamical magnetism in the disordered cubic lattice material
Phys. Rev. B 114, 194423 – Published 23 October, 2026
DOI: https://doi.org/10.1103/jsvt-jc4l
Abstract
realizes a disordered simple-cubic spin- lattice in which ions randomly occupy one-third of the sites, placing the system just above the site-percolation threshold for magnetic order. Specific-heat, susceptibility, neutron spin-echo, and muon spin-rotation measurements reveal a broad thermodynamic crossover, short-range magnetic correlations, and persistent fast spin dynamics down to at least 0.1 K, with no evidence for static order or conventional spin-glass freezing within the experimental time windows. Monte Carlo simulations yield a broad distribution of orphan spins, finite clusters, and an infinite network. The weakly correlated spin fraction () inferred phenomenologically from magnetization is consistent with the calculated orphan-spin fraction (). Exact diagonalization of a diluted Heisenberg model captures the broad magnetic specific-heat anomaly and supports the coexistence of weakly and strongly correlated spin environments. These results support a picture in which spin- quantum fluctuations, together with dilution and proximity to the percolation threshold, can support a disorder-driven dynamical state with short-range correlations in three dimensions, distinct from both classical spin glasses and geometrically frustrated quantum spin liquids.
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References (43)
- C. Broholm, R. J. Cava, S. Kivelson, D. Nocera, M. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020).
- C. Balz, B. Lake, J. Reuther, H. Luetkens, R. Schönemann, T. Herrmannsdörfer, Y. Singh, A. T. M. Nazmul Islam, E. M. Wheeler, J. A. Rodriguez-Rivera, T. Guidi, G. G. Simeoni, C. Baines, and H. Ryll, Physical realization of a quantum spin liquid based on a complex frustration mechanism, Nat. Phys. 12, 942 (2016).
- Y. Shen, Y.-D. Li, H. Wo, Y. Li, S. Shen, B. Pan, Q. Wang, H. C. Walker, P. Steffens, M. Boehm, Y. Hao, D. L. Quintero-Castro, L. W. Harriger, M. D. Frontzek, L. Hao, S. Meng, Q. Zhang, G. Chen, and J. Zhao, Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate, Nature (London) 540, 559 (2016).
- S. Chillal, Y. Iqbal, H. O. Jeschke, J. A. Rodriguez-Rivera, R. Bewley, P. Manuel, D. Khalyavin, P. Steffens, R. Thomale, A. T. M. Nazmul Islam, J. Reuther, and B. Lake, Evidence for a three-dimensional quantum spin liquid in , Nat. Commun. 11, 2348 (2020).
- I. Živković, V. Favre, C. Salazar Mejia, H. O. Jeschke, A. Magrez, B. Dabholkar, V. Noculak, R. S. Freitas, M. Jeong, N. G. Hegde, L. Testa, P. Babkevich, Y. Su, P. Manuel, H. Luetkens, C. Baines, P. J. Baker, J. Wosnitza, O. Zaharko, Y. Iqbal, et al., Magnetic field induced quantum spin liquid in the two coupled trillium lattices of , Phys. Rev. Lett. 127, 157204 (2021).
- L. Savary and L. Balents, Disorder-induced quantum spin liquid in spin ice pyrochlores, Phys. Rev. Lett. 118, 087203 (2017).
- D. S. Fisher, Random antiferromagnetic quantum spin chains, Phys. Rev. B 50, 3799 (1994).
- L. Liu, W. Guo, and A. W. Sandvik, Quantum-critical scaling properties of the two-dimensional random-singlet state, Phys. Rev. B 102, 054443 (2020).
- U. Treiber and S. Kemmler-Sack, Über Ordnungs-Unordnungsphänomene bei Sauerstoff perowskiten vom Typ , J. Solid State Chem. 43, 51 (1982).
- K. Malarz, Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors, Phys. Rev. E 91, 043301 (2015).
- B. Sana, M. Barik, S. Lee, U. Jena, M. Baenitz, J. Sichelschmidt, S. Luther, H. Kühne, K. Sethupathi, M. S. Ramachandra Rao, K. Y. Choi, and P. Khuntia, Possible realization of a randomness-driven quantum disordered state in the antiferromagnet , Phys. Rev. B 110, 134412 (2024).
- S. M. Hossain, S. S. Rahaman, H. Gujrati, D. Bhoi, A. Matsuo, K. Kindo, M. Kumar, and M. Majumder, Evidence of random spin-singlet state in the three-dimensional quantum spin liquid candidate , Phys. Rev. B 110, L020406 (2024).
- P. Fouquet, G. Ehlers, B. Farago, C. Pappas, and F. Mezei, The wide-angle neutron spin echo spectrometer project WASP, J. Neutron Res. 15, 39 (2007).
- A. Amato, H. Luetkens, K. Sedlak, A. Stoykov, R. Scheuermann, M. Elender, A. Raselli, and D. Graf, The new versatile general purpose surface-muon instrument (GPS) based on silicon photomultipliers for measurements on a continuous-wave beam, Rev. Sci. Instrum. 88, 093301 (2017).
- D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 2018).
- M. Aizenman, On the number of incipient spanning clusters, Nucl. Phys. B 485, 551 (1997).
- 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).
- F. Lloret, M. Julve, J. Cano, R. Ruiz-García, and E. Pardo, Magnetic properties of six-coordinated high-spin cobalt (II) complexes: Theoretical background and its application, Inorg. Chim. Acta 361, 3432 (2008).
- H. Lueken, Magnetochemistry: An Introduction to Theory and Application (Springer-Verlag, Wiesbaden, 2013).
- J. A. M. Paddison, J. Ross Stewart, and A. L. Goodwin, SPINVERT: A program for refinement of paramagnetic diffuse scattering data, J. Phys.: Condens. Matter 25, 454220 (2013).
- R. M. Pickup, R. Cywinski, C. Pappas, B. Farago, and P. Fouquet, Generalized spin-glass relaxation, Phys. Rev. Lett. 102, 097202 (2009).
- G. Ehlers, Study of slow dynamic processes in magnetic systems by neutron spin-echo spectroscopy, J. Phys.: Condens. Matter 18, R231 (2006).
- F. Xu, Quantitative determination of quantum fluctuations in clean magnets I: Neutron spin echo, arXiv:2603.02431.
- A. Amato and E. Morenzoni, Introduction to Muon Spin Spectroscopy: Applications to Solid State and Material Sciences (Springer, Cham, Switzerland, 2024).
- A. Keren, Generalization of the Abragam relaxation function to a longitudinal field, Phys. Rev. B 50, 10039 (1994).
- S. R. Dunsiger, R. F. Kiefl, J. A. Chakhalian, J. E. Greedan, W. A. MacFarlane, R. I. Miller, G. D. Morris, A. N. Price, N. P. Raju, and J. E. Sonier, Magnetic field dependence of muon spin relaxation in geometrically frustrated , Phys. Rev. B 73, 172418 (2006).
- H. Bethe, On the theory of metals, Z. Phys. 71, 205 (1931).
- L. Hulthén, On the exchange problem in a crystal, Arkiv Mat. Astron. Fysik 26A, 1 (1938).
- E. Lieb and D. Mattis, Theory of ferromagnetism and the ordering of electronic energy levels, Phys. Rev. 125, 164 (1962).
- S. Eggert and I. Affleck, Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains, Phys. Rev. B 46, 10866 (1992).
- S.-W. Tsai and J. B. Marston, Density-matrix renormalization-group analysis of quantum critical points: Quantum spin chains, Phys. Rev. B 62, 5546 (2000).
- If the odd clusters are to behave as true orphan spins, this would lead to a higher density of free spins than found by magnetization. In practice, the theoretical value would be modified by additional interactions, such as second-nearest-neighbor couplings.
- Note that including a small antiferromagnetic does not necessarily break down the “fluctuating spins” picture discussed in the cluster analysis, as odd-size clusters will still have a spin which cannot be paired into a singlet.
- Note that for the disordered system, the exchange couplings are likely to be dependent on the local environment, i.e., be different for each lattice site.
- A. Fancelli, R. Flores-Calderón, O. Benton, B. Lake, R. Moessner, and J. Reuther, Fragile spin liquid in three dimensions, Phys. Rev. B 111, 134413 (2025).
- Y. J. Uemura, T. Yamazaki, D. R. Harshman, M. Senba, and E. J. Ansaldo, Muon-spin relaxation in AuFe and CuMn spin glasses, Phys. Rev. B 31, 546 (1985).
- S. Dash, A. Koley, and S. Kumar, Vacancy induced expansion of spin-liquid regime in the Heisenberg model, Phys. Rev. Lett. 136, 076502 (2026).
- D. A. Keen and A. L. Goodwin, The crystallography of correlated disorder, Nature (London) 521, 303 (2015).
- J. K. Jochum, C. Franz, T. Keller, and C. Pfleiderer, Extending MIEZE spectroscopy towards thermal wavelengths, J. Appl. Crystallogr. 55, 1424 (2022).
- F. Pratt, F. Lang, S. Blundell, W. Steinhardt, S. Haravifard, S. Mañas-Valero, E. Coronado, B. Huddart, and T. Lancaster, Studying spin diffusion and quantum entanglement with LF-, J. Phys.: Conf. Ser. 2462, 012038 (2023).
- D. Bruß, Characterizing entanglement, J. Math. Phys. 43, 4237 (2002).
- F. Xu, C. Aguilar-Maldonado, A. T. M. N. Islam, B. Lake, and C. Ritter, Crystal structure and magnetic correlations of a new quantum magnet; Institut Laue-Langevin (ILL): Grenoble, 2024, doi:10.5291/ILL-DATA.5-23-818; F. Xu, P. Fouquet, and B. Lake, Real time magnetic dynamics of a spin-1/2 equilateral triangular antiferromagnet: Part II; Institut Laue-Langevin (ILL): Grenoble, 2024, doi:10.5291/ILL-DATA.4-01-1852.
- C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Natl. Bur. Stand. 45, 255 (1950).