- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review B

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Impact of the impurity symmetry on orbital momentum relaxation and orbital Hall effect studied by the quantum Boltzmann equation 

V. V. Kabanov and A. V. Shumilin

PDF

Phys. Rev. B 110, 235161 – Published 30 December, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.235161

Abstract

We develop a quantum Boltzmann equation approach that incorporates microscopic impurity models into the theory of orbital transport, revealing how the impurity properties, including their symmetry, influence the relaxation of orbital momentum and the orbital Hall effect. Specifically, we demonstrate that when the impurity potential has axial symmetry, the relaxation is governed by the Dyakonov-Perel mechanism. In contrast, when this symmetry is broken, scattering can result in a rapid Elliott-Yafet relaxation of orbital momentum. The details of impurity potential also affect the intrinsic orbital Hall effect even when the impurity concentration is very small. Impurities that alter the orbital texture can also give rise to a skew-scattering contribution to the orbital Hall effect, although this does not necessarily dominate in materials that are nearly pristine because of the Dyakonov-Perel relaxation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. D. Go, D. Jo, H.-W. Lee, M. Kläui, and Y. Mokrousov, Orbitronics: Orbital currents in solids, Europhys. Lett. 135, 37001 (2021).
  2. T. G. Rappoport, First light on orbitronics as a viable alternative to electronics, Nature (London) 619, 38 (2023).
  3. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Orbitronics: The intrinsic orbital current in p-doped silicon, Phys. Rev. Lett. 95, 066601 (2005).
  4. N. Sato, F. Xue, R. M. White, C. Bi, and S. X. Wang, Two-terminal spin–orbit torque magnetoresistive random access memory, Nat. Electron. 1, 508 (2018).
  5. X. Han, X. Wang, C. Wan, G. Yu, and X. Lv, Spin-orbit torques: Materials, physics, and devices, Appl. Phys. Lett. 118, 120502 (2021).
  6. Y. Cao, G. Xing, H. Lin, N. Zhang, H. Zheng, and K. Wang, Prospect of spin-orbitronic devices and their applications, Science 23, 101614 (2020).
  7. G. Sala and P. Gambardella, Giant orbital Hall effect and orbital-to-spin conversion in 3d,5d, and 4f metallic heterostructures, Phys. Rev. Res. 4, 033037 (2022).
  8. Y.-G. Choi, D. Jo, K.-H. Ko, D. Go, K.-H. Kim, H. G. Park, C. Kim, B.-C. Min, G.-M. Choi, and H.-W. Lee, Observation of the orbital Hall effect in a light metal Ti, Nature (London) 619, 52 (2023).
  9. R. Fukunaga, S. Haku, H. Hayashi, and K. Ando, Orbital torque originating from orbital Hall effect in Zr, Phys. Rev. Res. 5, 023054 (2023).
  10. A. El Hamdi, J.-Y. Chauleau, M. Boselli, C. Thibault, C. Gorini, A. Smogunov, C. Barreteau, S. Gariglio, J.-M. Triscone, and M. Viret, Observation of the orbital inverse Rashba–Edelstein effect, Nat. Phys. 19, 1855 (2023).
  11. S. R. Park, C. H. Kim, J. Yu, J. H. Han, and C. Kim, Orbital-angular-momentum based origin of Rashba-type surface band splitting, Phys. Rev. Lett. 107, 156803 (2011).
  12. T. Adamantopoulos, M. Merte, D. Go, F. Freimuth, S. Blügel, and Y. Mokrousov, Orbital Rashba effect as a platform for robust orbital photocurrents, Phys. Rev. Lett. 132, 076901 (2024).
  13. Spintronics, edited by T. Dietl, D. D. Awschalom, M. Kaminska, and H. Ohno (Elsevier, Amsterdam, 2008).
  14. S. Lee, M.-G. Kang, D. Go, D. Kim, J.-H. Kang, T. Lee, G.-H. Lee, J. Kang, N. J. Lee, Y. Mokrousov et al., Efficient conversion of orbital Hall current to spin current for spin-orbit torque switching, Commun. Phys. 4, 234 (2021).
  15. J. Kim, D. Go, H. Tsai, D. Jo, K. Kondou, H.-W. Lee, and Y. C. Otani, Nontrivial torque generation by orbital angular momentum injection in ferromagnetic-metal/Cu/Al2O3 trilayers, Phys. Rev. B 103, L020407 (2021).
  16. H. Hayashi, D. Jo, D. Go, T. Gao, S. Haku, Y. Mokrousov, H.-W. Lee, and K. Ando, Observation of long-range orbital transport and giant orbital torque, Commun. Phys. 6, 32 (2023).
  17. F. Liu, B. Liang, J. Xu, C. Jia, and C. Jiang, Giant efficiency of long-range orbital torque in Co/Nb bilayers, Phys. Rev. B 107, 054404 (2023).
  18. M. Taniguchi, H. Hayashi, N. Soya, and K. Ando, Nonlocal orbital torques in magnetic multilayers, Appl. Phys. Express 16, 043001 (2023).
  19. 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).
  20. D. Jo, D. Go, and H.-W. Lee, Gigantic intrinsic orbital Hall effects in weakly spin-orbit coupled metals, Phys. Rev. B 98, 214405 (2018).
  21. G. Qu and G. Tatara, Intrinsic orbital and spin Hall effect in bismuth semimetal, Phys. Rev. B 107, 214421 (2023).
  22. J. T. Chalker, T. S. Pickles, and P. Shukla, Anderson localization in tight-binding models with flat bands, Phys. Rev. B 82, 104209 (2010).
  23. S. Ashhab, O. Voznyy, S. Hoogland, E. H. Sargent, and M. E. Madjet, Effect of disorder on transport properties in a tight-binding model for lead halide perovskites, Sci. Rep. 7, 8902 (2017).
  24. Spin Physics in Semiconductors, edited by M. I. Dyakonov (Springer, Cham, 2017).
  25. M. I. Dyakonov and A. V. Khaetskii, Relaxation of nonequilibrium carrier-density matrix in semiconductors with degenerate bands, Zh. Eksp. Teor. Fiz 86, 1843 (1984) [Sov. Phys. JETP 59, 1072 (1984)].
  26. M. M. Glazov and L. E. Golub, Quantum and classical multiple-scattering effects in the spin dynamics of cavity polaritons, Phys. Rev. B 77, 165341 (2008).
  27. V. P. Silin, Oscillations of a fermi-liquid in a magnetic field, Sov. Phys. JETP 6, 945 (1958).
  28. H. Smith and H. H. Jensen, Transport Phenomena (Oxford Science, Oxford, 1989).
  29. A. Khaetskii, Nonexistence of intrinsic spin currents, Phys. Rev. Lett. 96, 056602 (2006).
  30. A. Khaetskii, Intrinsic spin current for an arbitrary Hamiltonian and scattering potential, Phys. Rev. B 73, 115323 (2006).
  31. M. Trushin and J. Schliemann, Anisotropic current-induced spin accumulation in the two-dimensional electron gas with spin-orbit coupling, Phys. Rev. B 75, 155323 (2007).
  32. D. Culcer, E. M. Hankiewicz, G. Vignale, and R. Winkler, Side jumps in the spin Hall effect: Construction of the Boltzmann collision integral, Phys. Rev. B 81, 125332 (2010).
  33. C. Gorini, P. Schwab, R. Raimondi, and A. L. Shelankov, Non-Abelian gauge fields in the gradient expansion: Generalized Boltzmann and Eilenberger equations, Phys. Rev. B 82, 195316 (2010).
  34. V. P. Mineev, Low-temperature resistance in metals without inversion center, Phys. Rev. B 98, 165121 (2018).
  35. N. A. Sinitsyn, A. H. MacDonald, T. Jungwirth, V. K. Dugaev, and J. Sinova, Anomalous Hall effect in a two-dimensional Dirac band: The link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach, Phys. Rev. B 75, 045315 (2007).
  36. N. A. Sinitsyn, Semiclassical theories of the anomalous Hall effect, J. Phys.: Condens. Matter 20, 023201 (2008).
  37. M. M. Glazov and L. E. Golub, Valley Hall effect caused by the phonon and photon drag, Phys. Rev. B 102, 155302 (2020).
  38. T. Tanaka, H. Kontani, M. Naito, T. Naito, D. S. Hirashima, K. Yamada, and J. Inoue, Intrinsic spin Hall effect and orbital Hall effect in 4d and 5d transition metals, Phys. Rev. B 77, 165117 (2008).
  39. D. Giuliano, A. Nava, C. A. Perroni, M. Bibes, F. Trier, and M. Salluzzo, Spin-Hall current and nonlocal transport in ferromagnet-free multiband models for SrTiO3-based nanodevices in the presence of impurities, Phys. Rev. B 108, 075418 (2023).
  40. S. Han, H.-W. Lee, and K.-W. Kim, Orbital dynamics in centrosymmetric systems, Phys. Rev. Lett. 128, 176601 (2022).
  41. J. Sohn, J. M. Lee, and H.-W. Lee, Dyakonov-Perel-like orbital and spin relaxations in centrosymmetric systems, Phys. Rev. Lett. 132, 246301 (2024).
  42. S. Han, H.-W. Lee, and K.-W. Kim, Microscopic study of orbital textures, Curr. Appl. Phys. 50, 13 (2023).
  43. E. L. Ivchenko, Y. B. Lyanda-Geller, and G. E. Pikus, Current of thermalized spin-oriented photocarriers, Zh. Eksp. Teor. Fiz. 98, 989 (1990) [Sov. Phys. JETP. 71, 550 (1990)].
  44. V. P. Mineev, Low-temperature transport in metals without inversion centre, J. Exp. Theor. Phys. 129, 700 (2019).
  45. A. Ashrafi and D. L. Maslov, Chiral spin waves in Fermi liquids with spin-orbit coupling, Phys. Rev. Lett. 109, 227201 (2012).
  46. D. L. Maslov, A. Kumar, and S. Maiti, Collective spin modes in Fermi liquids with spin–orbit coupling, J. Exp. Theor. Phys. 135, 549 (2022).
  47. Z. M. Raines, D. L. Maslov, and L. I. Glazman, Spin-valley silin modes in graphene with substrate-induced spin-orbit coupling, Phys. Rev. B 105, L201201 (2022).
  48. M. Dyakonov and V. Perel, Current-induced spin orientation of electrons in semiconductors, Phys. Lett. A 35, 459 (1971).
  49. M. I. Dyakonov and V. I. Perel, Spin relaxation of conduction electrons in noncentrosymmetric semiconductors, Sov. Phys. Solid State, USSR 13, 3023 (1972).
  50. J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin Hall effects, Rev. Mod. Phys. 87, 1213 (2015).
  51. E. I. Rashba, Theory of electrical spin injection: Tunnel contacts as a solution of the conductivity mismatch problem, Phys. Rev. B 62, R16267 (2000).
  52. J. Borge and I. V. Tokatly, Boundary conditions for spin and charge diffusion in the presence of interfacial spin-orbit coupling, Phys. Rev. B 99, 241401(R) (2019).
  53. M. Rang and P. J. Kelly, Orbital relaxation length from first-principles scattering calculations, Phys. Rev. B 109, 214427 (2024).
  54. J.-I. Inoue, G. E. W. Bauer, and L. W. Molenkamp, Suppression of the persistent spin Hall current by defect scattering, Phys. Rev. B 70, 041303(R) (2004).
  55. O. Chalaev and D. Loss, Spin-Hall conductivity due to Rashba spin-orbit interaction in disordered systems, Phys. Rev. B 71, 245318 (2005).

Outline

Information

Phys. Rev. B 110, 235161– Published 30 December, 2024
  • Received 11 October 2024
  • Revised 13 December 2024
  • Accepted 13 December 2024
Crossmark - Check for updates button

©2024 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation