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Magnon-mediated electric current drag and nonlocal spin-Peltier effect in the ac regime
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 , with driving frequencies up to the terahertz regime. Our model describes how the dominant transport mechanism, coherent or incoherent magnons, evolves with the driving frequency .
Physics Subject Headings (PhySH)
See Also
Theory of nonlinear magnetoelectric transport effects in normal metal–magnetic insulator heterostructures
Article Text
References (88)
- 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).
- G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Spin caloritronics, Nat. Mater. 11, 391 (2012).
- M. I. Dyakonov and V. I. Perel, Possibility of orientating electron spins with current, JETP Lett. 13, 467 (1971).
- J. E. Hirsch, Spin Hall effect, Phys. Rev. Lett. 83, 1834 (1999).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- J. Lotze, H. Huebl, R. Gross, and S. T. B. Goennenwein, Spin Hall magnetoimpedance, Phys. Rev. B 90, 174419 (2014).
- 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).
- 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).
- 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).
- X.-P. Zhang, F. S. Bergeret, and V. N. Golovach, Theory of spin Hall magnetoresistance from a microscopic perspective, Nano Lett. 19, 6330 (2019).
- S. S.-L. Zhang and S. Zhang, Magnon mediated electric current drag across a ferromagnetic insulator layer, Phys. Rev. Lett. 109, 096603 (2012).
- S. S.-L. Zhang and S. Zhang, Spin convertance at magnetic interfaces, Phys. Rev. B 86, 214424 (2012).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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––Pt devices at low temperatures, APL Mater. 9, 021122 (2021).
- J. A. Fülöp, S. Tzortzakis, and T. Kampfrath, Laser-driven strong-field terahertz sources, Adv. Opt. Mater. 8, 1900681 (2020).
- J. Walowski and M. Münzenberg, Perspective: Ultrafast magnetism and THz spintronics, J. Appl. Phys. 120, 140901 (2016).
- 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).
- 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).
- 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).
- 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).
- V. Sluka, Antiferromagnetic resonance excited by oscillating electric currents, Phys. Rev. B 96, 214412 (2017).
- O. Johansen, H. Skarsvåg, and A. Brataas, Spin-transfer antiferromagnetic resonance, Phys. Rev. B 97, 054423 (2018).
- R. Schmidt and P. W. Brouwer, Theory of the low-temperature longitudinal spin Seebeck effect, Phys. Rev. B 103, 014412 (2021).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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 , J. Phys. D: Appl. Phys. 51, 364003 (2018).
- O. Franke, Numerical evaluation of ac magnetoelectric transport in normal-metal – magnetic-insulator heterostructures, Zenodo (2025), doi: 10.5281/zenodo.15849570.
- M. I. Dyakonov and V. I. Perel, Current-induced spin orientation of electrons in semiconductors, Phys. Lett. A 35, 459 (1971).
- 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.
- 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).
- 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).
- L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B 54, 9353 (1996).
- J. C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater. 159, L1 (1996).
- Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Enhanced Gilbert damping in thin ferromagnetic films, Phys. Rev. Lett. 88, 117601 (2002).
- 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).
- 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).
- S. A. Bender and Y. Tserkovnyak, Interfacial spin and heat transfer between metals and magnetic insulators, Phys. Rev. B 91, 140402(R) (2015).
- Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, Spin pumping and magnetization dynamics in metallic multilayers, Phys. Rev. B 66, 224403 (2002).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- C. W. Corti, Thermophysical data on platinum: Resistivity and conductivity values recommended, Platin. Met. Rev. 28, 164 (1984).
- 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).
- 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).
- 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).
- 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).
- S. R. Boona and J. P. Heremans, Magnon thermal mean free path in yttrium iron garnet, Phys. Rev. B 90, 064421 (2014).
- A. A. Tulapurkar and Y. Suzuki, Boltzmann approach to dissipation produced by a spin-polarized current, Phys. Rev. B 83, 012401 (2011).
- T. Taniguchi, Joule heating in spin Hall geometry, Appl. Phys. Express 9, 073005 (2016).
- S. Daimon, R. Iguchi, T. Hioki, E. Saitoh, and K.-I. Uchida, Thermal imaging of spin Peltier effect, Nat. Commun. 7, 13754 (2016).
- 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).
- 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).
- 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).
- B. N. Narozhny and A. Levchenko, Coulomb drag, Rev. Mod. Phys. 88, 025003 (2016).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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).
- 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 /Pt bilayer films, Appl. Phys. Lett. 104, 072405 (2014).
- 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).
- 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).
- 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).
- N. D. Mermin, Lindhard dielectric function in the relaxation-time approximation, Phys. Rev. B 1, 2362 (1970).
- N. P. Padture and P. G. Klemens, Low thermal conductivity in garnets, J. Am. Ceram. Soc. 80, 1018 (1997).
- 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).