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Interplay of electron-magnon scattering and spin-orbit induced electronic spin-flip scattering in a two-band Stoner model

Felix Dusabirane1,2,*, Kai Leckron1, Baerbel Rethfeld1, and Hans Christian Schneider1,†

  • *Contact author: f.dusabirane@ur.ac.rw
  • †Contact author: hc.schneider@rptu.de
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Phys. Rev. B 113, 104403 – Published 2 March, 2026

DOI: https://doi.org/10.1103/7vr4-57mk

Abstract

This paper presents a theoretical investigation of electron-magnon scattering processes in the ultrafast demagnetization in itinerant ferromagnets. In the framework of a ferromagnetic model system, we compute the spin-dependent dynamics of electrons in itinerant Bloch states by including electron-magnon and electron-electron scattering processes on an equal footing. While the former process flips the electronic spin accompanied by the creation or destruction of a magnon, the latter exchanges electronic angular momentum with the lattice due to the influence of spin-orbit coupling. We show that, for a realistic choice of the electron-magnon interaction and deposited pulse energy, the interplay of these two different scattering mechanisms leads to the creation of magnons and a transfer of angular momentum to the lattice that constitutes an essentially nonequilibrium microscopic scenario for the ultrafast demagnetization process in itinerant ferromagnets.

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References (70)

  1. E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, Ultrafast spin dynamics in ferromagnetic nickel, Phys. Rev. Lett. 76, 4250 (1996).
  2. M. Battiato, K. Carva, and P. M. Oppeneer, Superdiffusive spin transport as a mechanism of ultrafast demagnetization, Phys. Rev. Lett. 105, 027203 (2010).
  3. D. M. Nenno, B. Rethfeld, and H. C. Schneider, Particle-in-cell simulation of ultrafast hot-carrier transport in Fe/Au heterostructures, Phys. Rev. B 98, 224416 (2018).
  4. B. Koopmans, J. J. M. Ruigrok, F. Dalla Longa, and W. J. M. de Jonge, Unifying ultrafast magnetization dynamics, Phys. Rev. Lett. 95, 267207 (2005).
  5. B. Koopmans, G. Malinowski, F. Dalla Longa, D. Steiauf, M. Fähnle, T. Roth, M. Cinchetti, and M. Aeschlimann, Explaining the paradoxical diversity of ultrafast laser-induced demagnetization, Nat. Mater. 9, 259 (2010).
  6. J. Walowski, G. Müller, M. Djordjevic, M. Münzenberg, M. Kläui, C. A. F. Vaz, and J. A. C. Bland, Energy equilibration processes of electrons, magnons, and phonons at the femtosecond time scale, Phys. Rev. Lett. 101, 237401 (2008).
  7. W. Töws and G. M. Pastor, Many-body theory of ultrafast demagnetization and angular momentum transfer in ferromagnetic transition metals, Phys. Rev. Lett. 115, 217204 (2015).
  8. G. P. Zhang and W. Hübner, Laser-induced ultrafast demagnetization in ferromagnetic metals, Phys. Rev. Lett. 85, 3025 (2000).
  9. P. Elliott, N. Singh, K. Krieger, E. Gross, S. Sharma, and J. Dewhurst, The microscopic origin of spin-orbit mediated spin-flips, J. Magn. Magn. Mater. 502, 166473 (2020).
  10. J. K. Dewhurst, S. Shallcross, P. Elliott, S. Eisebitt, C. v. K. Schmising, and S. Sharma, Angular momentum redistribution in laser-induced demagnetization, Phys. Rev. B 104, 054438 (2021).
  11. T. Higuchi, C. Heide, K. Ullmann, H. B. Weber, and P. Hommelhoff, Light-field-driven currents in graphene, Nature (London) 550, 224 (2017).
  12. F. Siegrist, J. A. Gessner, M. Ossiander, C. Denker, Y.-P. Chang, M. C. Schröder, A. Guggenmos, Y. Cui, J. Walowski, U. Martens, J. K. Dewhurst, M. Münzenberg, S. Sharma, and M. Schultze, Light-wave dynamic control of magnetism, Nature (London) 571, 240 (2019).
  13. M. Stiehl, M. Weber, C. Seibel, J. Hoefer, S. T. Weber, D. M. Nenno, H. C. Schneider, B. Rethfeld, B. Stadtmüller, and M. Aeschlimann, Role of primary and secondary processes in the ultrafast spin dynamics of nickel, Appl. Phys. Lett. 120, 062410 (2022).
  14. M. S. Mrudul and P. M. Oppeneer, Ab initio investigation of laser-induced ultrafast demagnetization of L10 FePt: Intensity dependence and importance of electron coherence, Phys. Rev. B 109, 144418 (2024).
  15. S. Essert and H. C. Schneider, Electron-phonon scattering dynamics in ferromagnetic metals and their influence on ultrafast demagnetization processes, Phys. Rev. B 84, 224405 (2011).
  16. Y. Yafet, G factors and spin-lattice relaxation of conduction electrons, Solid State Physics (Elsevier, Amsterdam, 1963), Vol. 14, pp. 1–98.
  17. J. Fabian and S. Das Sarma, Spin relaxation of conduction electrons in polyvalent metals: Theory and a realistic calculation, Phys. Rev. Lett. 81, 5624 (1998).
  18. C. Grimaldi and P. Fulde, Theory of screening of the phonon-modulated spin-orbit interaction in metals, Phys. Rev. B 55, 15523 (1997).
  19. A. Baral, S. Vollmar, S. Kaltenborn, and H. C. Schneider, Re-examination of the Elliott–Yafet spin-relaxation mechanism, New J. Phys. 18, 023012 (2016).
  20. S. Vollmar, D. J. Hilton, and H. C. Schneider, Generalized Elliott-Yafet spin-relaxation time for arbitrary spin mixing, Phys. Rev. B 96, 075203 (2017).
  21. D. Steiauf and M. Fähnle, Elliott-Yafet mechanism and the discussion of femtosecond magnetization dynamics, Phys. Rev. B 79, 140401(R) (2009).
  22. K. Carva, M. Battiato, and P. M. Oppeneer, Ab initio investigation of the Elliott-Yafet electron-phonon mechanism in laser-induced ultrafast demagnetization, Phys. Rev. Lett. 107, 207201 (2011).
  23. M. Krauß, T. Roth, S. Alebrand, D. Steil, M. Cinchetti, M. Aeschlimann, and H. C. Schneider, Ultrafast demagnetization of ferromagnetic transition metals: The role of the Coulombinteraction, Phys. Rev. B 80, 180407(R) (2009).
  24. B. Y. Mueller, A. Baral, S. Vollmar, M. Cinchetti, M. Aeschlimann, H. C. Schneider, and B. Rethfeld, Feedback effect during ultrafast demagnetization dynamics in ferromagnets, Phys. Rev. Lett. 111, 167204 (2013).
  25. K. Leckron, S. Vollmar, and H. C. Schneider, Ultrafast spin-lattice relaxation in ferromagnets including spin-orbit fields, Phys. Rev. B 96, 140408(R) (2017).
  26. S. Vollmar, K. Leckron, and H. C. Schneider, Ultrafast demagnetization and its relation to microscopic momentum scattering dynamics in a Rashba ferromagnet, Phys. Rev. B 108, 094403 (2023).
  27. W. Weng, H. Huang, J. Briones, N. Teeny, B. Y. Mueller, M. Haag, T. Kuhn, and M. Fähnle, Unexpectedly marginal effect of electronic correlations on ultrafast demagnetization after femtosecond laser-pulse excitation, Phys. Rev. B 95, 224439 (2017).
  28. S. R. Tauchert, M. Volkov, D. Ehberger, D. Kazenwadel, M. Evers, H. Lange, A. Donges, A. Book, W. Kreuzpaintner, U. Nowak, and P. Baum, Polarized phonons carry angular momentum in ultrafast demagnetization, Nature (London) 602, 73 (2022).
  29. D. M. Juraschek, R. M. Geilhufe, H. Zhu, M. Basini, P. Baum, A. Baydin, S. Chaudhary, M. Fechner, B. Flebus, G. Grissonnanche, A. I. Kirilyuk, M. Lemeshko, S. F. Maehrlein, M. Mignolet, S. Murakami, Q. Niu, U. Nowak, C. P. Romao, H. Rostami, T. Satoh, et al., Chiral phonons, Nat. Phys. 21, 1532 (2025).
  30. J. J. Nakane and H. Kohno, Angular momentum of phonons and its application to single-spin relaxation, Phys. Rev. B 97, 174403 (2018).
  31. A. Rückriegel, S. Streib, G. E. W. Bauer, and R. A. Duine, Angular momentum conservation and phonon spin in magnetic insulators, Phys. Rev. B 101, 104402 (2020).
  32. M. Weißenhofer, P. Rieger, M. S. Mrudul, L. Mikadze, U. Nowak, and P. M. Oppeneer, Truly chiral phonons arising from chirality-selective magnon-phonon coupling Phys. Rev. Lett. 135, 216701 (2025).
  33. M. S. Mrudul, M. Weißenhofer, and P. M. Oppeneer, Generation of phonons with angular momentum during ultrafast demagnetization Phys. Rev. B 112, L180407 (2025).
  34. A. Baral and H. C. Schneider, Magnetic switching dynamics due to ultrafast exchange scattering: A model study, Phys. Rev. B 91, 100402(R) (2015).
  35. E. Carpene, E. Mancini, C. Dallera, M. Brenna, E. Puppin, and S. De Silvestri, Dynamics of electron-magnon interaction and ultrafast demagnetization in thin iron films, Phys. Rev. B 78, 174422 (2008).
  36. A. Manchon, Q. Li, L. Xu, and S. Zhang, Theory of laser-induced demagnetization at high temperatures, Phys. Rev. B 85, 064408 (2012).
  37. M. Haag, C. Illg, and M. Fähnle, Role of electron-magnon scatterings in ultrafast demagnetization, Phys. Rev. B 90, 014417 (2014).
  38. E. Turgut, D. Zusin, D. Legut, K. Carva, R. Knut, J. M. Shaw, C. Chen, Z. Tao, H. T. Nembach, T. J. Silva, et al., Stoner versus Heisenberg: Ultrafast exchange reduction and magnon generation during laser-induced demagnetization, Phys. Rev. B 94, 220408(R) (2016).
  39. S. Eich, M. Plötzing, M. Rollinger, S. Emmerich, R. Adam, C. Chen, H. C. Kapteyn, M. M. Murnane, L. Plucinski, D. Steil, B. Stadtmüller, M. Cinchetti, M. Aeschlimann, C. M. Schneider, and S. Mathias, Band structure evolution during the ultrafast ferromagnetic-paramagnetic phase transition in cobalt, Sci. Adv. 3, e1602094 (2017).
  40. C. Illg, M. Haag, and M. Fähnle, Ultrafast demagnetization after laser irradiation in transition metals: Ab initio calculations of the spin-flip electron-phonon scattering with reduced exchange splitting, Phys. Rev. B 88, 214404 (2013).
  41. M. Beens, R. A. Duine, and B. Koopmans, S-d model for local and nonlocal spin dynamics in laser-excited magnetic heterostructures, Phys. Rev. B 102, 054442 (2020).
  42. M. Beens, R. A. Duine, and B. Koopmans, Modeling ultrafast demagnetization and spin transport: The interplay of spin-polarized electrons and thermal magnons, Phys. Rev. B 105, 144420 (2022).
  43. M. Weißenhofer and P. M. Oppeneer, Ultrafast demagnetization through femtosecond generation of non‐thermal magnons, Adv. Phys. Res. 4, 2300103 (2024).
  44. M. Bonitz, D. Kremp, D. Scott, R. Binder, W.-D. Kraeft, and H. S. Köhler, Numerical analysis of non-Markovian effects in charge-carrier scattering: One-time versus two-time kinetic equations, J. Phys.: Condens. Matter 8, 6057 (1996).
  45. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2009).
  46. D. M. Edwards, The paramagnetic state of itinerant electron systems with local magnetic moments. I. Static properties, J. Phys. F: Met. Phys. 12, 1789 (1982).
  47. J. Hong and D. L. Mills, Theory of the spin dependence of the inelastic mean free path of electrons in ferromagnetic metals: A model study, Phys. Rev. B 59, 13840 (1999).
  48. V. P. Zhukov, E. V. Chulkov, and P. M. Echenique, GW + T theory of excited electron lifetimes in metals, Phys. Rev. B 72, 155109 (2005).
  49. A. B. Schmidt, M. Pickel, M. Donath, P. Buczek, A. Ernst, V. P. Zhukov, P. M. Echenique, L. M. Sandratskii, E. V. Chulkov, and M. Weinelt, Ultrafast magnon generation in an Fe film on Cu(100), Phys. Rev. Lett. 105, 197401 (2010).
  50. S. Paischer, G. Vignale, M. I. Katsnelson, A. Ernst, and P. A. Buczek, Nonlocal correlation effects due to virtual spin-flip processes in itinerant electron ferromagnets, Phys. Rev. B 107, 134410 (2023).
  51. J. A. Hertz and M. A. Klenin, Fluctuations in itinerant-electron paramagnets, Phys. Rev. B 10, 1084 (1974).
  52. L. C. Davis and S. H. Liu, Electron-magnon interaction in ferromagnetic transition metals, Phys. Rev. 163, 503 (1967).
  53. R. M. White and R. B. Woolsey, Magnon corrections to the effective mass of an electron in a magnetic semiconductor, Phys. Rev. 176, 908 (1968).
  54. R. B. Woolsey and R. M. White, Electron-magnon interaction in ferromagnetic semiconductors, Phys. Rev. B 1, 4474 (1970).
  55. S. Paischer, D. Eilmsteiner, M. I. Katsnelson, A. Ernst, and P. A. Buczek, Electronic correlations arising from anti-Stoner spin excitations: An ab initio study of itinerant ferro-and antiferromagnets, Phys. Rev. B 110, 165121 (2024).
  56. D. Y. Usachov, K. Ali, G. Poelchen, M. Mende, S. Schulz, M. Peters, K. Bokai, I. Y. Sklyadneva, V. Stolyarov, E. Chulkov, et al., Unveiling electron-phonon and electron-magnon interactions in the weak itinerant ferromagnet LaCo2P2, Adv. Phys. Res. 4, 2400137 (2025).
  57. F. Rossi and T. Kuhn, Theory of ultrafast phenomena in photoexcited semiconductors, Rev. Mod. Phys. 74, 895 (2002).
  58. M. Kira and S. W. Koch, Semiconductor Quantum Optics (Cambridge University Press, Cambridge, UK, 2012).
  59. M. Beens, J. P. Heremans, Y. Tserkovnyak, and R. A. Duine, Magnons versus electrons in thermal spin transport through metallic interfaces, J. Phys. D: Appl. Phys. 51, 394002 (2018).
  60. N. H. Long, P. Mavropoulos, S. Heers, B. Zimmermann, Y. Mokrousov, and S. Blügel, Spin-flip hot spots in ultrathin films of monovalent metals: Enhancement and anisotropy of the Elliott-Yafet parameter, Phys. Rev. B 88, 144408 (2013).
  61. K. Leckron and H. C. Schneider, Ferromagnetic model system with spin-orbit coupling: Dynamical gap and effective spin-flip scattering, J. Magn. Magn. Mater. 471, 482 (2019).
  62. B. Mueller, M. Haag, and M. Fähnle, Ab initio theory for ultrafast magnetization dynamics with a dynamic band structure, J. Magn. Magn. Mater. 414, 14 (2016).
  63. M. Sakoh and D. Edwards, Magnetic properties of iron and cobalt in a combined model of itinerant electrons and localized spins, Phys. Status Solidi B 70, 611 (1975).
  64. R. H. M. Groeneveld, R. Sprik, and A. Lagendijk, Effect of a nonthermal electron distribution on the electron-phonon energy relaxation process in noble metals, Phys. Rev. B 45, 5079 (1992).
  65. D. Mongin, P. Maioli, J. Burgin, P. Langot, E. Cottancin, S. D'addato, B. Canut, M. Treguer, A. Crut, F. Vallée, et al., Ultrafast electron-lattice thermalization in copper and other noble metal nanoparticles, J. Phys.: Condens. Matter 31, 084001 (2019).
  66. C. Voisin, N. Del Fatti, D. Christofilos, and F. Vallée, Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles, J. Phys. Chem. B 105, 2264 (2001).
  67. Y. Liu, L.-S. Xie, Z. Yuan, and K. Xia, Magnon-phonon relaxation in yttrium iron garnet from first principles, Phys. Rev. B 96, 174416 (2017).
  68. S. Paischer, D. Eilmsteiner, I. Maznichenko, N. Buczek, K. Zakeri, A. Ernst, and P. A. Buczek, Correlations, disorder, and multimagnon processes in terahertz spin dynamics of magnetic nanostructures: A first-principles investigation, Phys. Rev. B 109, L220405 (2024).
  69. B. Y. Mueller, T. Roth, M. Cinchetti, M. Aeschlimann, and B. Rethfeld, Driving force of ultrafast magnetization dynamics, New J. Phys. 13, 123010 (2011).
  70. M. C. T. D. Müller, S. Blügel, and C. Friedrich, Electron-magnon scattering in elementary ferromagnets from first principles: Lifetime broadening and band anomalies, Phys. Rev. B 100, 045130 (2019).

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Phys. Rev. B 113, 104403– Published 2 March, 2026
  • Received 16 October 2024
  • Accepted 5 February 2026
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