- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Two-state generalization of the strong collision model

Ola Kenji Forslund*

  • *Contact author: ola.forslund@physics.uu.se
PDF

Phys. Rev. B 112, 024309 – Published 17 July, 2025

DOI: https://doi.org/10.1103/wf5z-lj1c

Abstract

Muon spin relaxation is a powerful technique for probing static and dynamic local magnetic fields. The strong collision model, based on a Gaussian-Markovian process, is commonly used to account for dynamical effects. Yet, it remains limited in describing systems where the local field undergoes discrete state changes. To address this, I introduce a generalized two-state strong collision model that explicitly incorporates transitions between distinct local field environments during fluctuations. This extension allows for a more accurate representation of dynamical effects, particularly in systems where each collision alters the underlying static polarization function. Analytical and numerical solutions are presented, and the model's applicability is demonstrated and discussed across relevant physical systems—including low-dimensional magnets, systems with dynamic disorder, and ion and muon diffusion. These results offer an enhanced framework for interpreting data in complex materials and extend the method's reach to a broader class of dynamical phenomena in condensed matter physics.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (31)

  1. K. Nagamine, Introductory Muon Science (Cambridge University Press, Cambridge, UK, 2003).
  2. A. D. Hillier, S. J. Blundell, I. McKenzie, I. Umegaki, L. Shu, J. A. Wright, T. Prokscha, F. Bert, K. Shimomura, A. Berlie et al., Muon spin spectroscopy, Nat. Rev. Methods Primers 2, 4 (2022).
  3. S. J. Blundell, Muon-spin rotation studies of electronic properties of molecular conductors and superconductors, Chem. Rev. 104, 5717 (2004).
  4. D. C. Walker, Muon and Muonium Chemistry (Cambridge University Press, Cambridge, UK, 1983).
  5. E. Torikai, K. Nagamine, F. L. Pratt, I. Watanabe, Y. Ikedo, H. Urabe, and H. Grimm, Probing electron transfer in DNA – new life science with muons, Hyperfine Interact. 138, 509 (2001).
  6. J. Sugiyama, K. Mukai, Y. Ikedo, H. Nozaki, M. Månsson, and I. Watanabe, Li diffusion in LixCoO2 probed by muon-spin spectroscopy, Phys. Rev. Lett. 103, 147601 (2009).
  7. S. B. Sulaiman, N. Sahoo, S. Srinivas, F. Hagelberg, T. P. Das, E. Torikai, and K. Nagamine, Theory of location and associated hyperfine properties of the positive muon in La2CuO4, Hyperfine Interact. 84, 87 (1994).
  8. J. S. Möller, P. Bonfà, D. Ceresoli, F. Bernardini, S. J. Blundell, T. Lancaster, R. De Renzi, N. Marzari, I. Watanabe, S. Sulaiman, and M. I. Mohamed-Ibrahim, Playing quantum hide-and-seek with the muon: Localizing muon stopping sites, Phys. Scr. 88, 068510 (2013).
  9. T. D. Lee and C. N. Yang, Question of parity conservation in weak interactions, Phys. Rev. 104, 254 (1956).
  10. A. Le Yaouanc and P. D. De Reotier, Muon Spin Rotation, Relaxation, and Resonance: Applications to Condensed Matter, International Series of Monographs on Physics, Vol. 147 (Oxford University Press, Oxford, UK, 2011).
  11. A. Suter and B. M. Wojek, Musrfit: A free platform-independent framework for μSR data analysis, Phys. Procedia 30, 69 (2012).
  12. K. W. Kehr, G. Honig, and D. Richter, Stochastic theory of spin depolarization of muons diffusing in the presence of traps, Z. Phys. B 32, 49 (1978).
  13. K. Kojima, A. Keren, L. P. Le, G. M. Luke, B. Nachumi, W. D. Wu, Y. J. Uemura, K. Kiyono, S. Miyasaka, H. Takagi, and S. Uchida, Muon spin relaxation and magnetic susceptibility measurements in the Haldane system (Y2−xCax)Ba(Ni1−yMgy)O5, Phys. Rev. Lett. 74, 3471 (1995).
  14. M. R. Crook and R. Cywinski, Voigtian Kubo-Toyabe muon spin relaxation, J. Phys.: Condens. Matter 9, 1149 (1997).
  15. J. Lago, T. Lancaster, S. J. Blundell, S. T. Bramwell, F. L. Pratt, M. Shirai, and C. Baines, Magnetic ordering and dynamics in the XY pyrochlore antiferromagnet: A muon-spin relaxation study of Er2Ti2O7 and Er2Sn2O7, J. Phys.: Condens. Matter 17, 979 (2005).
  16. E. Karlsson, Solid State Phenomena: As Seen by Muons, Protons, and Excited Nuclei (Clarendon, Oxford, UK, 1995).
  17. R. Kubo and T. Toyabe, A stochastic model for low field resonance and relaxation, in Magnetic Resonance and Relaxation, Proceedings of the XIVth Colloque Ampere, Ljubljana (North-Holland, Amsterdam, 1967), pp. 810–823.
  18. I. McClelland, B. Johnston, P. J. Baker, M. Amores, E. J. Cussen, and S. A. Corr, Muon spectroscopy for investigating diffusion in energy storage materials, Annu. Rev. Mater. Res. 50, 371 (2020).
  19. D. R. Noakes and G. M. Kalvius, Anomalous zero-field muon spin relaxation in highly disordered magnets, Phys. Rev. B 56, 2352 (1997).
  20. N. Z. Ali, J. Sirker, J. Nuss, P. Horsch, and M. Jansen, Spin exchange dominated by charge fluctuations of the Wigner lattice in the chain cuprate Na5Cu3O6, Phys. Rev. B 84, 035113 (2011).
  21. P. A. Bhobe, A. Kumar, M. Taguchi, R. Eguchi, M. Matsunami, Y. Takata, A. K. Nandy, P. Mahadevan, D. D. Sarma, A. Neroni, E. Şaşıoğlu, M. Ležaić, M. Oura, Y. Senba, H. Ohashi, K. Ishizaka, M. Okawa, S. Shin, K. Tamasaku, Y. Kohmura et al., Electronic structure evolution across the Peierls metal-insulator transition in a correlated ferromagnet, Phys. Rev. X 5, 041004 (2015).
  22. R. Khasanov, D. Das, R. Gupta, C. Mielke, M. Elender, Q. Yin, Z. Tu, C. Gong, H. Lei, E. T. Ritz, R. M. Fernandes, T. Birol, Z. Guguchia, and H. Luetkens, Time-reversal symmetry broken by charge order in CsV3Sb5, Phys. Rev. Res. 4, 023244 (2022).
  23. O. K. Forslund, 1D to 3D magnetism in quantum materials: A study by muons, neutrons and x-rays, Ph.D. thesis, Kungliga Tekniska Högskolan, 2021.
  24. P. Dalmas de Réotier, A. Yaouanc, L. Keller, A. Cervellino, B. Roessli, C. Baines, A. Forget, C. Vaju, P. C. M. Gubbens, A. Amato, and P. J. C. King, Spin dynamics and magnetic order in magnetically frustrated Tb2Sn2O7, Phys. Rev. Lett. 96, 127202 (2006).
  25. M. Isobe, S. Koishi, S. Yamazaki, J.-i. Yamaura, H. Gotou, T. Yagi, and Y. Ueda, Substitution effect on metal-insulator transition of K2V8O16, J. Phys. Soc. Jpn. 78, 114713 (2009).
  26. D. R. Noakes, A correlation length measured by zero-field muon spin relaxation in disordered magnets, J. Phys.: Condens. Matter 11, 1589 (1999).
  27. A. Yaouanc, P. D. de Réotier, V. Glazkov, C. Marin, P. Bonville, J. A. Hodges, P. C. M. Gubbens, S. Sakarya, and C. Baines, Magnetic density of states at low energy in geometrically frustrated systems, Phys. Rev. Lett. 95, 047203 (2005).
  28. P. Bonville, J. A. Hodges, E. Bertin, J. P. Bouchaud, P. Dalmas de Réotier, L. P. Regnault, H. M. Rønnow, J. P. Sanchez, S. Sosin, and A. Yaouanc, Transitions and spin dynamics at very low temperature in the pyrochlores Yb2Ti2O7 and Gd2Sn2O7, Hyperfine Interact. 156–157, 103 (2004).
  29. M. Månsson and J. Sugiyama, Muon-spin relaxation study on Li-and Na-diffusion in solids, Phys. Scr. 88, 068509 (2013).
  30. R. J. Borg and G. J. Dienes, An Introduction to Solid State Diffusion (Elsevier, Amsterdam, 2012).
  31. J. Sugiyama, O. K. Forslund, E. Nocerino, N. Matsubara, K. Papadopoulos, Y. Sassa, S. P. Cottrell, A. D. Hillier, K. Ishida, M. Månsson, and J. H. Brewer, Lithium diffusion in LiFePO4 detected with μ±SR, Phys. Rev. Res. 2, 033161 (2020).

Outline

Information

Phys. Rev. B 112, 024309– Published 17 July, 2025
  • Received 28 April 2025
  • Revised 30 June 2025
  • Accepted 8 July 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation