Abstract
The understanding of how spins move and can be manipulated at pico- and femtosecond timescales has implications for ultrafast and energy-efficient data-processing and storage applications. However, the possibility of realizing commercial technologies based on ultrafast spin dynamics has been hampered by our limited knowledge of the physics behind processes on this timescale. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast timescales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report direct experimental evidence of intrinsic inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetization at a frequency of ~0.5 THz. This allows us to reveal that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.
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Data availability
Data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
References
Beaurepaire, E., Merle, J.-C., Daunois, A. & Bigot, J.-Y. Ultrafast spin dynamics in ferromagnetic nickel. Phys. Rev. Lett. 76, 4250–4253 (1996).
Koopmans, B., Van Kampen, M., Kohlhepp, J. T. & De Jonge, W. J. M. Ultrafast magneto-optics in nickel: magnetism or optics?. Phys. Rev. Lett. 85, 844–847 (2000).
Koopmans, B., Van Kampen, M. & De Jonge, W. J. M. Experimental access to femtosecond spin dynamics. J. Phys. Condens. Matter 15, S723–S736 (2003).
Koopmans, B., Ruigrok, J. J. M., Dalla Longa, F. & De Jonge, W. J. M. Unifying ultrafast magnetization dynamics. Phys. Rev. Lett. 95, 267207 (2005).
Stamm, C. et al. Femtosecond modification of electron localization and transfer of angular momentum in nickel. Nat. Mater. 6, 740–743 (2007).
Longa, F. D., Kohlhepp, J. T., De Jonge, W. J. M. & Koopmans, B. Influence of photon angular momentum on ultrafast demagnetization in nickel. Phys. Rev. B 75, 224431 (2007).
Carpene, E. et al. Dynamics of electron–magnon interaction and ultrafast demagnetization in thin iron films. Phys. Rev. B 78, 174422 (2008).
Koopmans, B. et al. Explaining the paradoxical diversity of ultrafast laser-induced demagnetization. Nat. Mater. 9, 259–265 (2010).
Boeglin, C. et al. Distinguishing the ultrafast dynamics of spin and orbital moments in solids. Nature 465, 458–461 (2010).
Kirilyuk, A., Kimel, A. V. & Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 82, 2731–2784 (2010).
Battiato, M., Carva, K. & Oppeneer, P. M. Superdiffusive spin transport as a mechanism of ultrafast demagnetization. Phys. Rev. Lett. 105, 027203 (2010).
Schmidt, A. B. et al. Ultrafast magnon generation in an Fe film on Cu(100). Phys. Rev. Lett. 105, 197401 (2010).
Radu, I. et al. Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins. Nature 472, 205–208 (2011).
Stefan, M. et al. Probing the timescale of the exchange interaction in a ferromagnetic alloy. Proc. Natl Acad. Sci. USA 109, 4792–4797 (2012).
Carva, K., Battiato, M., Legut, D. & Oppeneer, P. M. Ab initio theory of electron–phonon mediated ultrafast spin relaxation of laser-excited hot electrons in transition-metal ferromagnets. Phys. Rev. B 87, 184425 (2013).
Lambert, C.-H. et al. All-optical control of ferromagnetic thin films and nanostructures. Science 345, 1337–1340 (2014).
Henighan, T. et al. Generation mechanism of terahertz coherent acoustic phonons in Fe. Phys. Rev. B 93, 220301 (2016).
Eich, S. et al. Band structure evolution during the ultrafast ferromagnetic–paramagnetic phase transition in cobalt. Sci. Adv. 3, e1602094 (2017).
Dornes, C. et al. The ultrafast Einstein–de Haas effect. Nature 565, 209–212 (2019).
Iacocca, E. et al. Spin-current-mediated rapid magnon localisation and coalescence after ultrafast optical pumping of ferrimagnetic alloys. Nat. Commun. 10, 1756 (2019).
Stanciu, C. D. et al. Subpicosecond magnetization reversal across ferrimagnetic compensation points. Phys. Rev. Lett. 99, 217204 (2007).
Ciornei, M.-C., Rubí, J. M. & Wegrowe, J.-E. Magnetization dynamics in the inertial regime: nutation predicted at short time scales. Phys. Rev. B 83, 020410 (2011).
Böttcher, D., Ernst, A. & Henk, J. Atomistic magnetization dynamics in nanostructures based on first principles calculations: application to Co nanoislands on Cu(111). J. Phys. Condens. Matter 23, 296003 (2011).
Wegrowe, J.-E. & Ciornei, M.-C. Magnetization dynamics, gyromagnetic relation and inertial effects. Am. J. Phys. 80, 607–611 (2012).
Olive, E., Lansac, Y. & Wegrowe, J.-E. Beyond ferromagnetic resonance: the inertial regime of the magnetization. Appl. Phys. Lett. 100, 192407 (2012).
Bhattacharjee, S., Nordström, L. & Fransson, J. Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles. Phys. Rev. Lett. 108, 057204 (2012).
Olive, E., Lansac, Y., Meyer, M., Hayoun, M. & Wegrowe, J.-E. Deviation from the Landau–Lifshitz–Gilbert equation in the inertial regime of the magnetization. J. Appl. Phys. 117, 213904 (2015).
Thonig, D., Eriksson, O. & Pereiro, M. Magnetic moment of inertia within the torque–torque correlation model. Sci. Rep. 7, 931 (2017).
Mondal, R., Berritta, M. & Oppeneer, P. M. Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms. J. Phys. Condens. Matter 30, 265801 (2018).
Kikuchi, T. & Tatara, G. Spin dynamics with inertia in metallic ferromagnets. Phys. Rev. B 92, 184410 (2015).
Fähnle, M. Comparison of theories of fast and ultrafast magnetization dynamics. J. Magn. Magn. Mater. 469, 28–29 (2019).
Bastardis, R., Vernay, F. & Kachkachi, H. Magnetization nutation induced by surface effects in nanomagnets. Phys. Rev. B 98, 165444 (2018).
Gilbert, T. L. A phenomenological theory of damping in ferromagnetic materials. IEEE Trans. Magn. 40, 3443–3449 (2004).
Böttcher, D. & Henk, J. Significance of nutation in magnetization dynamics of nanostructures. Phys. Rev. B 86, 020404 (2012).
Zhu, J.-X., Nussinov, Z., Shnirman, A. & Balatsky, A. V. Novel spin dynamics in a Josephson junction. Phys. Rev. Lett. 92, 107001 (2004).
Kimel, A. V. et al. Inertia-driven spin switching in antiferromagnets. Nat. Phys. 5, 727–731 (2009).
Fähnle, M., Steiauf, D. & Illg, C. Generalized Gilbert equation including inertial damping: derivation from an extended breathing Fermi surface model. Phys. Rev. B 84, 172403 (2011).
Hoffmann, M. C. & Fülöp, J. A. Intense ultrashort terahertz pulses: generation and applications. J. Phys. D 44, 083001 (2011).
Kampfrath, T., Tanaka, K. & Nelson, K. A. Resonant and nonresonant control over matter and light by intense terahertz transients. Nat. Photon. 7, 680–690 (2013).
Vicario, C. et al. Off-resonant magnetization dynamics phase-locked to an intense phase-stable terahertz transient. Nat. Photon. 7, 720–723 (2013).
Bonetti, S. et al. THz-driven ultrafast spin-lattice scattering in amorphous metallic ferromagnets. Phys. Rev. Lett. 117, 087205 (2016).
Hafez, H. A. et al. Extremely efficient terahertz high-harmonic generation in graphene by hot Dirac fermions. Nature 561, 507–511 (2018).
Noe, G. T. et al. Coherent terahertz excitation of magnons to 30 T. In 2018 Conference on Lasers and Electro-Optics (CLEO) 1–2 (IEEE, 2018).
Polley, D. et al. THz-driven demagnetization with perpendicular magnetic anisotropy: towards ultrafast ballistic switching. J. Phys. D 51, 084001 (2018).
Kovalev, S. et al. Probing ultra-fast processes with high dynamic range at 4th-generation light sources: arrival time and intensity binning at unprecedented repetition rates. Struct. Dyn. 4, 024301 (2017).
Kovalev, S. et al. Selective THz control of magnetic order: new opportunities from superradiant undulator sources. J. Phys. D 51, 114007 (2018).
Hudl, M. et al. Nonlinear magnetization dynamics driven by strong terahertz fields. Phys. Rev. Lett. 123, 197204 (2019).
Li, Y., Barra, A.-L., Auffret, S., Ebels, U. & Bailey, W. E. Inertial terms to magnetization dynamics in ferromagnetic thin films. Phys. Rev. B 92, 140413 (2015).
Razdolski, I. et al. Nanoscale interface confinement of ultrafast spin transfer torque driving non-uniform spin dynamics. Nat. Commun. 8, 15007 (2017).
Green, B. et al. High-field high-repetition-rate sources for the coherent THz control of matter. Sci. Rep. 6, 22256 (2016).
Acknowledgements
We thank J. Lindner (HZDR, Dresden) for helpful discussions and Z. Wang and S. Germansky for experimental support. The research leading to this result has been partly supported by the project CALIPSOplus under grant agreement no. 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. Parts of this research were carried out at ELBE at Helmholtz-Zentrum Dresden-Rossendorf e.V., a member of the Helmholtz Association. We thank U. Lehnert and J. Teichert for assistance and the ELBE team for operating the TELBE facility. S.K., B.G. and M.G. acknowledge support from the European Cluster of Advanced Laser Light Sources (EUCALL) project, which has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement no. 654220. N.A., I.I., M.G. and S.K. acknowledge support from the European Commission’s Horizon 2020 research and innovation programme, under grant agreement no. DLV-737038(TRANSPIRE). K.N., D.P., N.Z.H. and S.B. acknowledge support from the European Research Council, Starting Grant 715452 MAGNETIC-SPEED-LIMIT.
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S.B. designed the experiment. S.B. and M.G. coordinated the project. K.N., N.A., S.K., D.P., N.Z.H., B.G., J.-C.D., I.I., M.C., M.B., M.G. and S.B. performed the measurements at TELBE. K.N., N.A. and S.B. performed the data analysis. K.N., V.S., M.d’A. and C.S. performed the inertial LLG simulations. S.S.P.K.A., O.H., A.S. and K.L. fabricated and characterized the samples. K.N. and S.B. coordinated the work on the paper, with contributions from N.A., S.K., S.S.P.K.A., A.S., K.L., O.H., J.-E.W. and M.G. and discussions with all authors.
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Neeraj, K., Awari, N., Kovalev, S. et al. Inertial spin dynamics in ferromagnets. Nat. Phys. 17, 245–250 (2021). https://doi.org/10.1038/s41567-020-01040-y
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DOI: https://doi.org/10.1038/s41567-020-01040-y
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