- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Nonlinear spin and orbital Rashba-Edelstein effects induced by a femtosecond laser pulse: Simulations for Au(001)

Oliver Busch, Franziska Ziolkowski, Börge Göbel*, Ingrid Mertig, and Jürgen Henk

  • *Contact author: boerge.goebel@physik.uni-halle.de
PDF

Phys. Rev. Research 7, 043023 – Published 6 October, 2025

DOI: https://doi.org/10.1103/mpz5-z4kk

Abstract

Rashba-type spin-orbit coupling gives rise to distinctive surface and interface phenomena, such as spin-momentum locking and spin splitting. In nonequilibrium settings, one of the key manifestations is the (Rashba-)Edelstein effect, where an electric current generates a net spin or orbital polarization perpendicular to the current direction. While the steady-state behavior of these effects is well studied, their dynamics on ultrafast timescales remain largely unexplored. In this work, we present a theoretical investigation of the ultrafast spin and orbital Edelstein effects on an Au(001) surface, triggered by excitation with a femtosecond laser pulse. These effects are intrinsic and inherently nonlinear. Using a real-space tight-binding model combined with time evolution governed by the von Neumann equation, we simulate the electron dynamics in response to the pulse. Our results reveal pronounced differences between the spin and orbital responses, offering detailed insights into their distinct temporal profiles and magnitudes. We further explore the associated charge, spin, and orbital currents, including the emergence of laser-induced spin and orbital Hall effects. Finally, we quantify the angular momentum transfer mediated by the light-matter interaction. These findings shed light on the intricate ultrafast dynamics driven by spin-orbit coupling and offer guidance for the design of next-generation spintronic and orbitronic devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. Y. A. Bychkov and É. I. Rashba, Properties of a 2D electron gas with lifted spectral degeneracy, JETP Lett. 39, 78 (1984).
  2. G. Bihlmayer, P. Noël, D. V. Vyalikh, E. V. Chulkov, and A. Manchon, Rashba-like physics in condensed matter, Nat. Rev. Phys. 4, 642 (2022).
  3. J. Henk, M. Hoesch, J. Osterwalder, A. Ernst, and P. Bruno, Spin–orbit coupling in the L-gap surface states of Au(111): Spin-resolved photoemission experiments and first-principles calculations, J. Phys.: Condens. Matter 16, 7581 (2004).
  4. C. R. Ast, J. Henk, A. Ernst, L. Moreschini, M. C. Falub, D. Pacilé, P. Bruno, K. Kern, and M. Grioni, Giant spin splitting through surface alloying, Phys. Rev. Lett. 98, 186807 (2007).
  5. A. G. Aronov and Y. B. Lyanda-Geller, Nuclear electric resonance and orientation of carrier spins by an electric field, JETP Lett. 50, 431 (1989).
  6. V. M. Edelstein, Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems, Solid State Commun. 73, 233 (1990).
  7. J.-I. Inoue, G. E. W. Bauer, and L. W. Molenkamp, Diffuse transport and spin accumulation in a Rashba two-dimensional electron gas, Phys. Rev. B 67, 033104 (2003).
  8. P. Gambardella and I. M. Miron, Current-induced spin–orbit torques, Philos. Trans. R. Soc. A. 369, 3175 (2011).
  9. A. Johansson, Theory of spin and orbital Edelstein effects, J. Phys.: Condens. Matter 36, 423002 (2024).
  10. S. Zhong, J. E. Moore, and I. Souza, Gyrotropic magnetic effect and the magnetic moment on the Fermi surface, Phys. Rev. Lett. 116, 077201 (2016).
  11. D. Go, J.-P. Hanke, P. M. Buhl, F. Freimuth, G. Bihlmayer, H.-W. Lee, Y. Mokrousov, and S. Blügel, Toward surface orbitronics: Giant orbital magnetism from the orbital Rashba effect at the surface of sp-metals, Sci. Rep. 7, 46742 (2017).
  12. T. Yoda, T. Yokoyama, and S. Murakami, Orbital Edelstein effect as a condensed-matter analog of solenoids, Nano Lett. 18, 916 (2018).
  13. L. Salemi, M. Berritta, A. K. Nandy, and P. M. Oppeneer, Orbitally dominated Rashba-Edelstein effect in noncentrosymmetric antiferromagnets, Nat. Commun. 10, 5381 (2019).
  14. A. Johansson, B. Göbel, J. Henk, M. Bibes, and I. Mertig, Spin and orbital Edelstein effects in a two-dimensional electron gas: Theory and application to SrTiO3 interfaces, Phys. Rev. Res. 3, 013275 (2021).
  15. B. Göbel, L. Schimpf, and I. Mertig, Chirality-induced orbital Edelstein effect in an analytically solvable model, Phys. Rev. Res. 7, 033180 (2025).
  16. O. Busch, F. Ziolkowski, B. Göbel, I. Mertig, and J. Henk, Ultrafast orbital Hall effect in metallic nanoribbons, Phys. Rev. Res. 6, 013208 (2024).
  17. C. A. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications (Oxford University Press, Great Clarendon Street, Oxford, UK, 2011).
  18. K. Krieger, J. K. Dewhurst, P. Elliott, S. Sharma, and E. K. U. Gross, Laser-induced demagnetization at ultrashort time scales: Predictions of TDDFT, J. Chem. Theory Comput. 11, 4870 (2015).
  19. J. K. Dewhurst, P. Elliott, S. Shallcross, E. K. U. Gross, and S. Sharma, Laser-induced intersite spin transfer, Nano Lett. 18, 1842 (2018).
  20. F. Töpler, J. Henk, and I. Mertig, Ultrafast spin dynamics in inhomogeneous systems: A density-matrix approach applied to Co/Cu interfaces, New J. Phys. 23, 033042 (2021).
  21. F. Ziolkowski, O. Busch, I. Mertig, and J. Henk, Ultrafast spin dynamics: Complementing theoretical analyses by quantum state measures, J. Phys.: Condens. Matter 35, 125501 (2023).
  22. O. Busch, F. Ziolkowski, I. Mertig, and J. Henk, Ultrafast dynamics of electrons excited by femtosecond laser pulses: Spin polarization and spin-polarized currents, Phys. Rev. B 108, 184401 (2023).
  23. O. Busch, F. Ziolkowski, I. Mertig, and J. Henk, Ultrafast dynamics of orbital angular momentum of electrons induced by femtosecond laser pulses: Generation and transfer across interfaces, Phys. Rev. B 108, 104408 (2023).
  24. T. Seki, Y. Hasegawa, S. Mitani, S. Takahashi, H. Imamura, S. Maekawa, J. Nitta, and K. Takanashi, Giant spin Hall effect in perpendicularly spin-polarized FePt/Au devices, Nat. Mater. 7, 125 (2008).
  25. M. Isasa, E. Villamor, L. E. Hueso, M. Gradhand, and F. Casanova, Temperature dependence of spin diffusion length and spin Hall angle in Au and Pt, Phys. Rev. B 91, 024402 (2015).
  26. L. K. Zou, S. H. Wang, Y. Zhang, J. R. Sun, J. W. Cai, and S. S. Kang, Large extrinsic spin Hall effect in Au-Cu alloys by extensive atomic disorder scattering, Phys. Rev. B 93, 014422 (2016).
  27. S. LaShell, B. A. McDougall, and E. Jensen, Spin splitting of an Au(111) surface state band observed with angle resolved photoelectron spectroscopy, Phys. Rev. Lett. 77, 3419 (1996).
  28. G. Nicolay, F. Reinert, S. Hüfner, and P. Blaha, Spin-orbit splitting of the L-gap surface state on Au(111) and Ag(111), Phys. Rev. B 65, 033407 (2001).
  29. M. Hoesch, M. Muntwiler, V. N. Petrov, M. Hengsberger, L. Patthey, M. Shi, M. Falub, T. Greber, and J. Osterwalder, Spin structure of the shockley surface state on Au(111), Phys. Rev. B 69, 241401 (2004).
  30. H. Cercellier, C. Didiot, Y. Fagot-Revurat, B. Kierren, L. Moreau, D. Malterre, and F. Reinert, Interplay between structural, chemical, and spectroscopic properties of Ag/Au(111) epitaxial ultrathin films: A way to tune the Rashba coupling, Phys. Rev. B 73, 195413 (2006).
  31. J. C. Slater and G. F. Koster, Simplified LCAO method for the periodic potential problem, Phys. Rev. 94, 1498 (1954).
  32. D. A. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids (Springer, Berlin, 2015).
  33. S. Konschuh, M. Gmitra, and J. Fabian, Tight-binding theory of the spin-orbit coupling in graphene, Phys. Rev. B 82, 245412 (2010).
  34. C. Barreteau, D. Spanjaard, and M.-C. Desjonquères, An efficient magnetic tight-binding method for transition metals and alloys, C. R. Phys. 17, 406 (2016).
  35. S. Savasta and R. Girlanda, The particle-photon interaction in systems described by model Hamiltonians in second quantization, Solid State Commun. 96, 517 (1995).
  36. J. Henk, T. Scheunemann, S. V. Halilov, and R. Feder, Magnetic dichroism and electron spin polarization in photoemission: Analytical results, J. Phys.: Condens. Matter 8, 47 (1996).
  37. A. Pezo, D. García Ovalle, and A. Manchon, Orbital Hall effect in crystals: Interatomic versus intra-atomic contributions, Phys. Rev. B 106, 104414 (2022).
  38. D. Go, D. Jo, C. Kim, and H.-W. Lee, Intrinsic spin and orbital Hall effects from orbital texture, Phys. Rev. Lett. 121, 086602 (2018).
  39. D. Go, D. Jo, H.-W. Lee, M. Kläui, and Y. Mokrousov, Orbitronics: Orbital currents in solids, Europhys. Lett. 135, 37001 (2021).
  40. G. D. Mahan, Many-Particle Physics (Springer, New York, 2000), 3rd ed.
  41. E. Tamura, W. Piepke, and R. Feder, New spin-polarization effect in photoemission from nonmagnetic surfaces, Phys. Rev. Lett. 59, 934 (1987).
  42. E. Tamura and R. Feder, Spin-polarized normal photoemission from non-magnetic (111)-surfaces by p-polarized light, Solid State Commun. 79, 989 (1991).
  43. E. Tamura and R. Feder, Spin polarization in normal photoemission by linearly polarized light from nonmagnetic (001) surfaces, Europhys. Lett. 16, 695 (1991).
  44. J. Henk and R. Feder, Spin polarization in normal photoemission by linearly polarized light from non-magnetic (110) surfaces, Europhys. Lett. 28, 609 (1994).
  45. M. Ünzelmann, H. Bentmann, P. Eck, T. Kißlinger, B. Geldiyev, J. Rieger, S. Moser, R. C. Vidal, K. Kißner, L. Hammer, M. A. Schneider, T. Fauster, G. Sangiovanni, D. Di Sante, and F. Reinert, Orbital-driven Rashba effect in a binary honeycomb monolayer AgTe, Phys. Rev. Lett. 124, 176401 (2020).
  46. T. Kobayashi, Y. Nakata, K. Yaji, T. Shishidou, D. Agterberg, S. Yoshizawa, F. Komori, S. Shin, M. Weinert, T. Uchihashi, and K. Sakamoto, Orbital angular momentum induced spin polarization of 2D metallic bands, Phys. Rev. Lett. 125, 176401 (2020).
  47. D. Xiao, Y. Yao, Z. Fang, and Q. Niu, Berry-phase effect in anomalous thermoelectric transport, Phys. Rev. Lett. 97, 026603 (2006).
  48. J. Shi, G. Vignale, D. Xiao, and Q. Niu, Quantum theory of orbital magnetization and its generalization to interacting systems, Phys. Rev. Lett. 99, 197202 (2007).
  49. X.-G. Ye, P.-F. Zhu, W.-Z. Xu, T.-Y. Zhao, and Z.-M. Liao, Nonlinear spin and orbital Edelstein effect in WTe2, Phys. Rev. B 110, L201407 (2024).
  50. R. Cross, Observations of a driven pendulum at low amplitudes, Eur. J. Phys. 42, 055001 (2021).
  51. G. Vignale and I. V. Tokatly, Theory of the nonlinear Rashba-Edelstein effect: The clean electron gas limit, Phys. Rev. B 93, 035310 (2016).
  52. H. Xu, J. Zhou, H. Wang, and J. Li, Light-induced static magnetization: Nonlinear Edelstein effect, Phys. Rev. B 103, 205417 (2021).
  53. Data are provided for the figures, https://doi.org/10.5281/zenodo.15357659.
  54. J. Premper, M. Trautmann, J. Henk, and P. Bruno, Spin-orbit splitting in an anisotropic two-dimensional electron gas, Phys. Rev. B 76, 073310 (2007).
  55. H. Chen, Q. Niu, and A. H. MacDonald, Anomalous Hall effect arising from noncollinear antiferromagnetism, Phys. Rev. Lett. 112, 017205 (2014).
  56. Y. Zhang, J. Železný, Y. Sun, J. van den Brink, and B. Yan, Spin Hall effect emerging from a noncollinear magnetic lattice without spin–orbit coupling, New J. Phys. 20, 073028 (2018).
  57. X. Zhou, J.-P. Hanke, W. Feng, F. Li, G.-Y. Guo, Y. Yao, S. Blügel, and Y. Mokrousov, Spin-order dependent anomalous Hall effect and magneto-optical effect in the noncollinear antiferromagnets Mn3XN with X=Ga, Zn, Ag, or Ni, Phys. Rev. B 99, 104428 (2019).
  58. O. Busch, B. Göbel, and I. Mertig, Microscopic origin of the anomalous Hall effect in noncollinear kagome magnets, Phys. Rev. Res. 2, 033112 (2020).
  59. O. Busch, B. Göbel, and I. Mertig, Spin Hall effect in noncollinear kagome antiferromagnets, Phys. Rev. B 104, 184423 (2021).
  60. D. Go, F. Freimuth, J.-P. Hanke, F. Xue, O. Gomonay, K.-J. Lee, S. Blügel, P. M. Haney, H.-W. Lee, and Y. Mokrousov, Theory of current-induced angular momentum transfer dynamics in spin-orbit coupled systems, Phys. Rev. Res. 2, 033401 (2020).

Outline

Information

Phys. Rev. Research 7, 043023– Published 6 October, 2025
  • Received 8 May 2025
  • Accepted 8 September 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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation