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Negative temperature coefficient of Gilbert damping in magnetic bilayers

Lulu Cao1,2,3,4, Yuting Gong5, Xianyang Lu3,4, Yongbing Xu3,4,5, Ya Zhai1,*, Jing Wu2,†, Roy W. Chantrell2, and Richard F. L. Evans2,‡

  • 1Key Laboratory of Quantum Materials and Devices of Ministry of Education, School of Physics, Southeast University, Nanjing 211189, China
  • 2School of Physics, Engineering and Technology, University of York, York YO10 5DD, United Kingdom
  • 3National Key Laboratory of Spintronics, Nanjing University, Suzhou 215163, China
  • 4School of Integrated Circuits, Nanjing University, Suzhou 215163, China
  • 5Jiangsu Provincial Key Laboratory of Advanced Photonic and Electronic Materials, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China

  • *Contact author: yazhai@seu.edu.cn
  • †Contact author: jing.wu@york.ac.uk
  • ‡Contact author: richard.evans@york.ac.uk
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Phys. Rev. B 113, L220409 – Published 22 June, 2026

DOI: https://doi.org/10.1103/qc2z-thq5

Abstract

The Gilbert damping of magnetic materials is an important magnetic parameter that determines the switching speed and energy dissipation of spintronic devices. In simple metals, the intrinsic Gilbert damping increases with temperature and diverges near the Curie temperature as a result of spin fluctuations. Here we present atomistic simulations and experimental measurements showing surprising and opposite behavior in Py/Nd bilayers, where the Gilbert damping decreases with increasing temperature. The effect arises because of the enhanced damping at the interface as a result of spin pumping, where elevated temperatures cause a dynamic separation of the interfacial and bulk magnetization during relaxation. Furthermore, the temperature dependence of the damping can be controlled by varying the thickness of the Nd capping layer. Our findings present a spintronic effect that can be used to modify the dynamic properties of nanoscale materials and devices for enhanced energy efficiency or with improved switching dynamics.

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References (35)

  1. M. C. Hickey and J. S. Moodera, Origin of intrinsic Gilbert damping, Phys. Rev. Lett. 102, 137601 (2009).
  2. M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, Ultra-low magnetic damping of a metallic ferromagnet, Nat. Phys. 12, 839 (2016).
  3. Z. Lu, I. P. Miranda, S. Streib, Q. Xu, R. Cheenikundil, M. Pereiro, E. Sjöqvist, O. Eriksson, A. Bergman, D. Thonig, and A. Delin, Chemical disorder effects on Gilbert damping of FeCo alloys, Phys. Rev. B 110, 174428 (2024).
  4. Y. Zhao, Q. Song, S.-H. Yang, T. Su, W. Yuan, S. S. P. Parkin, J. Shi, and W. Han, Experimental investigation of temperature-dependent Gilbert damping in permalloy thin films, Sci. Rep. 6, 22890 (2016).
  5. Y. Tserkovnyak, A. Brataas, and Gerrit E. W. Bauer, Spin pumping and magnetization dynamics in metallic multilayers, Phys. Rev. B 66, 224403 (2002).
  6. Y. Tserkovnyak, A. Brataas, and Gerrit E. W. Bauer, Enhanced Gilbert damping in thin ferromagnetic films, Phys. Rev. Lett. 88, 117601 (2002).
  7. O. Šipr, S. Mankovsky, and H. Ebert, Spin wave stiffness and exchange stiffness of doped permalloy via ab initio calculations, Phys. Rev. B 100, 024435 (2019).
  8. Y. Liu, Z. Yuan, R. J. H. Wesselink, A. A. Starikov, and P. J. Kelly, Interface enhancement of Gilbert damping from first principles, Phys. Rev. Lett. 113, 207202 (2014).
  9. D. Richardson, S. Katz, J. Wang, Y. K. Takahashi, K. Srinivasan, A. Kalitsov, K. Hono, A. Ajan, and M. Wu, Near-Tc ferromagnetic resonance and damping in FePt-based heat-assisted magnetic recording media, Phys. Rev. Appl. 10, 054046 (2018).
  10. M. Strungaru, S. Ruta, Richard F. L. Evans, and R. W. Chantrell, Model of magnetic damping and anisotropy at elevated temperatures: Application to granular FePt films, Phys. Rev. Appl. 14, 014077 (2020).
  11. A. Whitney, C. Liu, T. S. Santos, R. V. Chopdekar, M. Carey, G. Street, V. Kalappattil, K. Leistikow, and M. Wu, Damping in free layers of spin-transfer-torque magnetic memory at elevated temperatures, Phys. Rev. Appl. 20, 034006 (2023).
  12. L. Thomas et al., STT-MRAM devices with low damping and moment optimized for LLC applications at Ox nodes, in 2018 IEEE International Electron Devices Meeting (IEDM) (IEEE, New York, 2018), pp. 27.3.1–27.3.4.
  13. L. Cao, S. Ruta, R. Khamtawi, P. Chureemart, Y. Zhai, R. F. L. Evans, and R. W. Chantrell, Simulation study of the Gilbert damping in Ni80Fe20/Nd bilayers: Comparison with experiments, J. Phys.: Condens. Matter 36, 305901 (2024).
  14. E. Barati and M. Cinal, Quantum mechanism of nonlocal Gilbert damping in magnetic trilayers, Phys. Rev. B 91, 214435 (2015).
  15. R. F. L. Evans, W. J. Fan, P. Chureemart, T. A. Ostler, M. O. A. Ellis, and R. W. Chantrell, Atomistic spin model simulations of magnetic nanomaterials, J. Phys.: Condens. Matter 26, 103202 (2014).
  16. D. Hinzke, U. Atxitia, K. Carva, P. Nieves, O. Chubykalo-Fesenko, P. M. Oppeneer, and U. Nowak, Multiscale modeling of ultrafast element-specific magnetization dynamics of ferromagnetic alloys, Phys. Rev. B 92, 054412 (2015).
  17. See Supplemental Material at http://link.aps.org/supplemental/10.1103/qc2z-thq5 for additional model details, parameters, and figures.
  18. S. Sampan-a-pai, J. Chureemart, R. W. Chantrell, R. Chepulskyy, S. Wang, D. Apalkov, R. F. L. Evans, and P. Chureemart, Temperature and thickness dependence of statistical fluctuations of the Gilbert damping in bilayers, Phys. Rev. Appl. 11, 044001 (2019).
  19. H. Callen and E. Callen, The present status of the temperature dependence of magnetocrystalline anisotropy, and the l(l+1)/2 power law, J. Phys. Chem. Solids 27, 1271 (1966).
  20. C. Zener, Classical theory of the temperature dependence of magnetic anisotropy energy, Phys. Rev. 96, 1335 (1954).
  21. R. M. Moon, J. W. Cable, and W. C. Koehler, Magnetic structure of neodymium, J. Appl. Phys. 35, 1041 (1964).
  22. Y. P. Irkhin, Electron structure of the 4f shells and magnetism of rare-earth metals, Sov. Phys. Usp. 31, 163 (1988).
  23. M. O. A. Ellis, R. F. L. Evans, T. A. Ostler, J. Barker, U. Atxitia, O. Chubykalo-Fesenko, and R. W. Chantrell, The Landau-Lifshitz equation in atomistic models, Low Temp. Phys. 41, 705 (2015).
  24. A. Lyberatos, D. Berkov, and R. Chantrell, A method for the numerical simulation of the thermal magnetization fluctuations in micromagnetics, J. Phys.: Condens. Matter 5, 8911 (1993).
  25. J. Foros, G. Woltersdorf, B. Heinrich, and A. Brataas, Scattering of spin current injected in Pd(001), J. Appl. Phys. 97, 10A714 (2005).
  26. L. Cao, Z. Huang, Y. Gong, Q. Guo, M. Jalali, J. Du, Y. Xu, Q. Chen, X. Lu, and Y. Zhai, Magnetic field modulated ultrafast spin dynamics at Ni80Fe20/Neodymium interface, Opt. Express 31, 21731 (2023).
  27. 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).
  28. P. B. Allen, Empirical electron-phonon λ values from resistivity of cubic metallic elements, Phys. Rev. B 36, 2920 (1987).
  29. E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, Ultrafast spin dynamics in ferromagnetic nickel, Phys. Rev. Lett. 76, 4250 (1996).
  30. Y. Gong, X. Lu, J. Su, Z. Chen, L. Yang, Y. Yan, Y. Li, X. Ruan, J. Du, J. Cai, J. Wu, L. He, R. Zhang, H. Meng, B. Liu, and Y. Xu, Tuning interfacial spin pump in Ta/CoFeB/MgO films by ultrafast laser pulse, Appl. Phys. Lett. 119, 092404 (2021).
  31. L. Bo, X. Ruan, Z. Wu, H. Tu, J. Du, J. Wu, X. Lu, L. He, and Y. Xu, Transient enhancement of magnetization damping in CoFeB film via pulsed laser excitation, Appl. Phys. Lett. 109, 042401 (2016).
  32. X. Tao, Q. Liu, B. Miao, R. Yu, Z. Feng, L. Sun, B. You, J. Du, K. Chen, S. Zhang, L. Zhang, Z. Yuan, D. Wu, and H. Ding, Self-consistent determination of spin Hall angle and spin diffusion length in Pt and Pd: The role of the interface spin loss, Sci. Adv. 4, eaat1670 (2018).
  33. N. T. Binh, S. Ruta, O. Hovorka, Richard F. L. Evans, and R. W. Chantrell, Influence of finite-size effects on the Curie temperature of L10−FePt, Phys. Rev. B 106, 054421 (2022).
  34. vampire software package v9, 2025, https://vampire.york.ac.uk/.
  35. The data supporting this research is openly available from the research data repository of the University of York at https://doi.org/10.15124/254bf8a1-42c7-4ea0-ba57-aa35ff9e5928.

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Phys. Rev. B 113, L220409– Published 22 June, 2026
  • Received 7 July 2025
  • Revised 16 January 2026
  • Accepted 30 April 2026
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