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
  • Editors' Suggestion
  • Open Access

Magnon-mediated electric current drag and nonlocal spin-Peltier effect in the ac regime

Oliver Franke, Duje Akrap, and Piet W. Brouwer

  • Dahlem Center for Complex Quantum Systems and Physics Department, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

Phys. Rev. B 113, 014419 – Published 14 January, 2026

DOI: https://doi.org/10.1103/zpts-44w3

Abstract

Electron-magnon coupling at the interface between a normal metal and a magnetically ordered insulator modifies the electrical conductivity of the normal metal, an effect known as spin-Hall magnetoresistance. It can also facilitate magnon-mediated electric current drag, the nonlocal electric current response of two normal metal layers separated by a magnetic insulator. Additionally, spin and heat transport are coupled both in the magnetic insulator and across the interfaces to normal metals. In this article, we present a theory of these spintronic and spin-caloritronic effects for time-dependent applied electric fields E(ω), with driving frequencies ω up to the terahertz regime. Our model describes how the dominant transport mechanism, coherent or incoherent magnons, evolves with the driving frequency ω.

View figure in article

Physics Subject Headings (PhySH)

See Also

Article Text

References (88)

  1. K. Uchida, J. Xiao, H. Adachi, J. Ohe, S. Takahashi, J. Ieda, T. Ota, Y. Kajiwara, H. Umezawa, H. Kawai, G. E. W. Bauer, S. Maekawa, and E. Saitoh, Spin Seebeck insulator, Nat. Mater. 9, 894 (2010).
  2. G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Spin caloritronics, Nat. Mater. 11, 391 (2012).
  3. M. I. Dyakonov and V. I. Perel, Possibility of orientating electron spins with current, JETP Lett. 13, 467 (1971).
  4. J. E. Hirsch, Spin Hall effect, Phys. Rev. Lett. 83, 1834 (1999).
  5. C. O. Avci, A. Quindeau, C.-F. Pai, M. Mann, L. Caretta, A. S. Tang, M. C. Onbasli, C. A. Ross, and G. S. D. Beach, Current-induced switching in a magnetic insulator, Nat. Mater. 16, 309 (2017).
  6. M. Yang, L. Sun, Y. Zeng, J. Cheng, K. He, X. Yang, Z. Wang, L. Yu, H. Niu, T. Ji, G. Chen, B. Miao, X. Wang, and H. Ding, Highly efficient field-free switching of perpendicular yttrium iron garnet with collinear spin current, Nat. Commun. 15, 3201 (2024).
  7. M. Weiler, M. Althammer, F. D. Czeschka, H. Huebl, M. S. Wagner, M. Opel, I.-M. Imort, G. Reiss, A. Thomas, R. Gross, and S. T. B. Goennenwein, Local charge and spin currents in magnetothermal landscapes, Phys. Rev. Lett. 108, 106602 (2012).
  8. S. Y. Huang, X. Fan, D. Qu, Y. P. Chen, W. G. Wang, J. Wu, T. Y. Chen, J. Q. Xiao, and C. L. Chien, Transport magnetic proximity effects in platinum, Phys. Rev. Lett. 109, 107204 (2012).
  9. H. Nakayama, M. Althammer, Y.-T. Chen, K. Uchida, Y. Kajiwara, D. Kikuchi, T. Ohtani, S. Geprägs, M. Opel, S. Takahashi, R. Gross, G. E. W. Bauer, S. T. B. Goennenwein, and E. Saitoh, Spin Hall magnetoresistance induced by a nonequilibrium proximity effect, Phys. Rev. Lett. 110, 206601 (2013).
  10. C. Hahn, G. de Loubens, O. Klein, M. Viret, V. V. Naletov, and J. Ben Youssef, Comparative measurements of inverse spin Hall effects and magnetoresistance in YIG/Pt and YIG/Ta, Phys. Rev. B 87, 174417 (2013).
  11. N. Vlietstra, J. Shan, V. Castel, J. Youssef, G. E. W. Bauer, G. E. W. Bauer, and V. Wees, Exchange magnetic field torques in YIG/Pt bilayers observed by the spin-Hall magnetoresistance, Appl. Phys. Lett. 103, 032401 (2013).
  12. M. Althammer, S. Meyer, H. Nakayama, M. Schreier, S. Altmannshofer, M. Weiler, H. Huebl, S. Geprägs, M. Opel, R. Gross, D. Meier, C. Klewe, T. Kuschel, J.-M. Schmalhorst, G. Reiss, L. Shen, A. Gupta, Y.-T. Chen, G. E. W. Bauer, E. Saitoh et al., Quantitative study of the spin Hall magnetoresistance in ferromagnetic insulator/normal metal hybrids, Phys. Rev. B 87, 224401 (2013).
  13. J. Lotze, H. Huebl, R. Gross, and S. T. B. Goennenwein, Spin Hall magnetoimpedance, Phys. Rev. B 90, 174419 (2014).
  14. J.-G. Choi, J. W. Lee, and B.-G. Park, Spin Hall magnetoresistance in heavy-metal/metallic-ferromagnet multilayer structures, Phys. Rev. B 96, 174412 (2017).
  15. Y.-T. Chen, S. Takahashi, H. Nakayama, M. Althammer, S. T. B. Goennenwein, E. Saitoh, and G. E. W. Bauer, Theory of spin Hall magnetoresistance, Phys. Rev. B 87, 144411 (2013).
  16. Y.-T. Chen, S. Takahashi, H. Nakayama, M. Althammer, S. T. B. Goennenwein, E. Saitoh, and G. E. W. Bauer, Theory of spin Hall magnetoresistance (SMR) and related phenomena, J. Phys.: Condens. Matter 28, 103004 (2016).
  17. X.-P. Zhang, F. S. Bergeret, and V. N. Golovach, Theory of spin Hall magnetoresistance from a microscopic perspective, Nano Lett. 19, 6330 (2019).
  18. S. S.-L. Zhang and S. Zhang, Magnon mediated electric current drag across a ferromagnetic insulator layer, Phys. Rev. Lett. 109, 096603 (2012).
  19. S. S.-L. Zhang and S. Zhang, Spin convertance at magnetic interfaces, Phys. Rev. B 86, 214424 (2012).
  20. Y. Kajiwara, K. Harii, S. Takahashi, J. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi, S. Maekawa, and E. Saitoh, Transmission of electrical signals by spin-wave interconversion in a magnetic insulator, Nature (London) 464, 262 (2010).
  21. L. J. Cornelissen, J. Liu, R. A. Duine, J. B. Youssef, and B. J. van Wees, Long-distance transport of magnon spin information in a magnetic insulator at room temperature, Nat. Phys. 11, 1022 (2015).
  22. S. T. B. Goennenwein, R. Schlitz, M. Pernpeintner, K. Ganzhorn, M. Althammer, R. Gross, and H. Huebl, Non-local magnetoresistance in YIG/Pt nanostructures, Appl. Phys. Lett. 107, 172405 (2015).
  23. R. Schlitz, S. Vélez, A. Kamra, C.-H. Lambert, M. Lammel, S. T. B. Goennenwein, and P. Gambardella, Control of nonlocal magnon spin transport via magnon drift currents, Phys. Rev. Lett. 126, 257201 (2021).
  24. J. Li, Y. Xu, M. Aldosary, C. Tang, Z. Lin, S. Zhang, R. Lake, and J. Shi, Observation of magnon-mediated current drag in Pt/yttrium iron garnet/Pt(Ta) trilayers, Nat. Commun. 7, 10858 (2016).
  25. H. Wu, C. H. Wan, X. Zhang, Z. H. Yuan, Q. T. Zhang, J. Y. Qin, H. X. Wei, X. F. Han, and S. Zhang, Observation of magnon-mediated electric current drag at room temperature, Phys. Rev. B 93, 060403(R) (2016).
  26. P. Muduli, R. Schlitz, T. Kosub, R. Hübner, A. Erbe, D. Makarov, and S. T. B. Goennenwein, Local and nonlocal spin Seebeck effect in lateral Pt–Cr2O3–Pt devices at low temperatures, APL Mater. 9, 021122 (2021).
  27. J. A. Fülöp, S. Tzortzakis, and T. Kampfrath, Laser-driven strong-field terahertz sources, Adv. Opt. Mater. 8, 1900681 (2020).
  28. J. Walowski and M. Münzenberg, Perspective: Ultrafast magnetism and THz spintronics, J. Appl. Phys. 120, 140901 (2016).
  29. O. Franke and P. W. Brouwer, following paper, Theory of nonlinear magnetoelectric transport effects in normal metal–magnetic insulator heterostructures, Phys. Rev. B 113, 014420 (2026).
  30. L. J. Cornelissen, K. J. H. Peters, G. E. W. Bauer, R. A. Duine, and B. J. van Wees, Magnon spin transport driven by the magnon chemical potential in a magnetic insulator, Phys. Rev. B 94, 014412 (2016).
  31. X.-G. Wang, Z.-W. Zhou, Y.-Z. Nie, Q.-L. Xia, and G.-H. Guo, Self-consistent study of local and nonlocal magnetoresistance in a YIG/Pt bilayer, Phys. Rev. B 97, 094401 (2018).
  32. D. A. Reiss, T. Kampfrath, and P. W. Brouwer, Theory of spin-Hall magnetoresistance in the ac terahertz regime, Phys. Rev. B 104, 024415 (2021).
  33. V. Sluka, Antiferromagnetic resonance excited by oscillating electric currents, Phys. Rev. B 96, 214412 (2017).
  34. O. Johansen, H. Skarsvåg, and A. Brataas, Spin-transfer antiferromagnetic resonance, Phys. Rev. B 97, 054423 (2018).
  35. R. Schmidt and P. W. Brouwer, Theory of the low-temperature longitudinal spin Seebeck effect, Phys. Rev. B 103, 014412 (2021).
  36. A. J. Schellekens, K. C. Kuiper, R. R. J. C. de Wit, and B. Koopmans, Ultrafast spin-transfer torque driven by femtosecond pulsed-laser excitation, Nat. Commun. 5, 4333 (2014).
  37. I. Razdolski, A. Alekhin, N. Ilin, J. P. Meyburg, V. Roddatis, D. Diesing, U. Bovensiepen, and A. Melnikov, Nanoscale interface confinement of ultrafast spin transfer torque driving non-uniform spin dynamics, Nat. Commun. 8, 15007 (2017).
  38. J. Kimling, G.-M. Choi, J. T. Brangham, T. Matalla-Wagner, T. Huebner, T. Kuschel, F. Yang, and D. G. Cahill, Picosecond spin Seebeck effect, Phys. Rev. Lett. 118, 057201 (2017).
  39. T. S. Seifert, S. Jaiswal, J. Barker, S. T. Weber, I. Razdolski, J. Cramer, O. Gueckstock, S. F. Maehrlein, L. Nadvornik, S. Watanabe, C. Ciccarelli, A. Melnikov, G. Jakob, M. Münzenberg, S. T. B. Goennenwein, G. Woltersdorf, B. Rethfeld, P. W. Brouwer, M. Wolf, M. Kläui et al., Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy, Nat. Commun. 9, 2899 (2018).
  40. T. Kampfrath, M. Battiato, P. Maldonado, G. Eilers, J. Nötzold, S. Mährlein, V. Zbarsky, F. Freimuth, Y. Mokrousov, S. Blügel, M. Wolf, I. Radu, P. M. Oppeneer, and M. Münzenberg, Terahertz spin current pulses controlled by magnetic heterostructures, Nat. Nanotechnol. 8, 256 (2013).
  41. T. S. Seifert, N. M. Tran, O. Gueckstock, S. M. Rouzegar, L. Nadvornik, S. Jaiswal, G. Jakob, V. V. Temnov, M. Münzenberg, M. Wolf, M. Kläui, and T. Kampfrath, Terahertz spectroscopy for all-optical spintronic characterization of the spin-Hall-effect metals Pt, W and Cu80Ir20, J. Phys. D: Appl. Phys. 51, 364003 (2018).
  42. O. Franke, Numerical evaluation of ac magnetoelectric transport in normal-metal – magnetic-insulator heterostructures, Zenodo (2025), doi: 10.5281/zenodo.15849570.
  43. M. I. Dyakonov and V. I. Perel, Current-induced spin orientation of electrons in semiconductors, Phys. Lett. A 35, 459 (1971).
  44. S. Takahashi, H. Imamura, and S. Maekawa, Spin injection and spin transport in hybrid nanostructures, in Concepts in Spin Electronics, edited by S. Maekawa (Oxford University Press, Oxford, 2006), pp. 343–370.
  45. R. S. Nair, E. Barati, K. Gupta, Z. Yuan, and P. J. Kelly, Spin-flip diffusion length in 5d transition metal elements: A first-principles benchmark, Phys. Rev. Lett. 126, 196601 (2021).
  46. A. Vedyaev, N. Ryzhanova, N. Strelkov, A. Lobachev, and B. Dieny, Spin accumulation dynamics in spin valves in the terahertz regime, Phys. Rev. B 101, 014401 (2020).
  47. L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B 54, 9353 (1996).
  48. J. C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater. 159, L1 (1996).
  49. Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Enhanced Gilbert damping in thin ferromagnetic films, Phys. Rev. Lett. 88, 117601 (2002).
  50. A. Brataas, Y. V. Nazarov, and G. E. W. Bauer, Finite-element theory of transport in ferromagnet-normal metal systems, Phys. Rev. Lett. 84, 2481 (2000).
  51. J. Xiao, G. E. W. Bauer, K.-c. Uchida, E. Saitoh, and S. Maekawa, Theory of magnon-driven spin Seebeck effect, Phys. Rev. B 81, 214418 (2010).
  52. S. A. Bender and Y. Tserkovnyak, Interfacial spin and heat transfer between metals and magnetic insulators, Phys. Rev. B 91, 140402(R) (2015).
  53. Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Spin pumping and magnetization dynamics in metallic multilayers, Phys. Rev. B 66, 224403 (2002).
  54. D. A. Reiss and P. W. Brouwer, Finite-frequency spin conductance of the interface between a ferro- or ferrimagnetic insulator and a normal metal, Phys. Rev. B 106, 144423 (2022).
  55. J. Flipse, F. K. Dejene, D. Wagenaar, G. E. W. Bauer, J. Ben Youssef, and B. J. van Wees, Observation of the spin Peltier effect for magnetic insulators, Phys. Rev. Lett. 113, 027601 (2014).
  56. L. J. Cornelissen, J. Shan, and B. J. van Wees, Temperature dependence of the magnon spin diffusion length and magnon spin conductivity in the magnetic insulator yttrium iron garnet, Phys. Rev. B 94, 180402(R) (2016).
  57. H. Jiao and G. E. W. Bauer, Spin backflow and ac voltage generation by spin pumping and the inverse spin Hall effect, Phys. Rev. Lett. 110, 217602 (2013).
  58. D. Wei, M. Obstbaum, M. Ribow, C. H. Back, and G. Woltersdorf, Spin Hall voltages from a.c. and d.c. spin currents, Nat. Commun. 5, 3768 (2014).
  59. Z. Qiu, K. Ando, K. Uchida, Y. Kajiwara, R. Takahashi, H. Nakayama, T. An, Y. Fujikawa, and E. Saitoh, Spin mixing conductance at a well-controlled platinum/yttrium iron garnet interface, Appl. Phys. Lett. 103, 092404 (2013).
  60. M. Weiler, M. Althammer, M. Schreier, J. Lotze, M. Pernpeintner, S. Meyer, H. Huebl, R. Gross, A. Kamra, J. Xiao, Y.-T. Chen, H. Jiao, G. E. W. Bauer, and S. T. B. Goennenwein, Experimental test of the spin mixing interface conductivity concept, Phys. Rev. Lett. 111, 176601 (2013).
  61. V. Cherepanov, I. Kolokolov, and V. L'vov, The saga of YIG: Spectra, thermodynamics, interaction and relaxation of magnons in a complex magnet, Phys. Rep. 229, 81 (1993).
  62. Z. Shi, Q. Xi, J. Li, Y. Li, M. Aldosary, Y. Xu, J. Zhou, S.-M. Zhou, and J. Shi, Role of magnon-magnon scattering in magnon polaron spin Seebeck effect, Phys. Rev. Lett. 127, 277203 (2021).
  63. C. W. Corti, Thermophysical data on platinum: Resistivity and conductivity values recommended, Platin. Met. Rev. 28, 164 (1984).
  64. Z. Lin, L. V. Zhigilei, and V. Celli, Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium, Phys. Rev. B 77, 075133 (2008).
  65. CRC Handbook of Chemistry and Physics, 103rd ed., edited by J. R. Rumble, T. J. Bruno, and M. J. Doa (CRC Press, Boca Raton, FL, 2022).
  66. S. E. Sullivan, H. Lee, A. Weathers, and L. Shi, Frequency-dependent phonon-mediated unidirectional magnetoresistance in a metal on an insulator with highly nonequilibrium magnons, Phys. Rev. B 107, L140412 (2023).
  67. W. P. Sterk, D. Peerlings, and R. A. Duine, Magnon contribution to unidirectional spin Hall magnetoresistance in ferromagnetic-insulator/heavy-metal bilayers, Phys. Rev. B 99, 064438 (2019).
  68. S. R. Boona and J. P. Heremans, Magnon thermal mean free path in yttrium iron garnet, Phys. Rev. B 90, 064421 (2014).
  69. A. A. Tulapurkar and Y. Suzuki, Boltzmann approach to dissipation produced by a spin-polarized current, Phys. Rev. B 83, 012401 (2011).
  70. T. Taniguchi, Joule heating in spin Hall geometry, Appl. Phys. Express 9, 073005 (2016).
  71. S. Daimon, R. Iguchi, T. Hioki, E. Saitoh, and K.-I. Uchida, Thermal imaging of spin Peltier effect, Nat. Commun. 7, 13754 (2016).
  72. A. Sola, V. Basso, M. Kuepferling, C. Dubs, and M. Pasquale, Experimental proof of the reciprocal relation between spin Peltier and spin Seebeck effects in a bulk YIG/Pt bilayer, Sci. Rep. 9, 2047 (2019).
  73. K. Uchida, R. Iguchi, S. Daimon, R. Ramos, A. Anadón, I. Lucas, P. A. Algarabel, L. Morellón, M. H. Aguirre, M. R. Ibarra, and E. Saitoh, Enhancement of the spin Peltier effect in multilayers, Phys. Rev. B 95, 184437 (2017).
  74. G. Liu, X.-G. Wang, Z. Z. Luan, L. F. Zhou, S. Y. Xia, B. Yang, Y. Z. Tian, G.-H. Guo, J. Du, and D. Wu, Magnonic unidirectional spin Hall magnetoresistance in a heavy-metal-ferromagnetic-insulator bilayer, Phys. Rev. Lett. 127, 207206 (2021).
  75. B. N. Narozhny and A. Levchenko, Coulomb drag, Rev. Mod. Phys. 88, 025003 (2016).
  76. C. O. Avci, K. Garello, A. Ghosh, M. Gabureac, S. F. Alvarado, and P. Gambardella, Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers, Nat. Phys. 11, 570 (2015).
  77. C. O. Avci, J. Mendil, G. S. D. Beach, and P. Gambardella, Origins of the unidirectional spin Hall magnetoresistance in metallic bilayers, Phys. Rev. Lett. 121, 087207 (2018).
  78. A. A. Tulapurkar, Y. Suzuki, A. Fukushima, H. Kubota, H. Maehara, K. Tsunekawa, D. D. Djayaprawira, N. Watanabe, and S. Yuasa, Spin-torque diode effect in magnetic tunnel junctions, Nature (London) 438, 339 (2005).
  79. J. C. Sankey, P. M. Braganca, A. G. F. Garcia, I. N. Krivorotov, R. A. Buhrman, and D. C. Ralph, Spin-transfer-driven ferromagnetic resonance of individual nanomagnets, Phys. Rev. Lett. 96, 227601 (2006).
  80. L. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, Spin-torque ferromagnetic resonance induced by the spin Hall effect, Phys. Rev. Lett. 106, 036601 (2011).
  81. K. Kondou, H. Sukegawa, S. Mitani, K. Tsukagoshi, and S. Kasai, Evaluation of spin Hall angle and spin diffusion length by using spin current-induced ferromagnetic resonance, Appl. Phys. Express 5, 073002 (2012).
  82. A. Ganguly, K. Kondou, H. Sukegawa, S. Mitani, S. Kasai, Y. Niimi, Y. Otani, and A. Barman, Thickness dependence of spin torque ferromagnetic resonance in Co75Fe25/Pt bilayer films, Appl. Phys. Lett. 104, 072405 (2014).
  83. M. Schreier, T. Chiba, A. Niedermayr, J. Lotze, H. Huebl, S. Geprägs, S. Takahashi, G. E. W. Bauer, R. Gross, and S. T. B. Goennenwein, Current-induced spin torque resonance of a magnetic insulator, Phys. Rev. B 92, 144411 (2015).
  84. J. Sklenar, W. Zhang, M. B. Jungfleisch, W. Jiang, H. Chang, J. E. Pearson, M. Wu, J. B. Ketterson, and A. Hoffmann, Driving and detecting ferromagnetic resonance in insulators with the spin Hall effect, Phys. Rev. B 92, 174406 (2015).
  85. S. M. Rezende and J. C. López Ortiz, Thermal properties of magnons in yttrium iron garnet at elevated magnetic fields, Phys. Rev. B 91, 104416 (2015).
  86. N. D. Mermin, Lindhard dielectric function in the relaxation-time approximation, Phys. Rev. B 1, 2362 (1970).
  87. N. P. Padture and P. G. Klemens, Low thermal conductivity in garnets, J. Am. Ceram. Soc. 80, 1018 (1997).
  88. M. Schreier, A. Kamra, M. Weiler, J. Xiao, G. E. W. Bauer, R. Gross, and S. T. B. Goennenwein, Magnon, phonon, and electron temperature profiles and the spin Seebeck effect in magnetic insulator/normal metal hybrid structures, Phys. Rev. B 88, 094410 (2013).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation