Abstract
As a fundamental parameter in magnetism, the phenomenological Gilbert damping constant α determines the performance of many spintronic devices. For most magnetic materials, α is treated as an isotropic parameter entering the Landau–Lifshitz–Gilbert equation. However, could the Gilbert damping be anisotropic? Although several theoretical approaches have suggested that anisotropic α could appear in single-crystalline bulk systems, experimental evidence of its existence is scarce. Here, we report the emergence of anisotropic magnetic damping by exploring a quasi-two-dimensional single-crystalline ferromagnetic metal/semiconductor interface—that is, a Fe/GaAs(001) heterojunction. The observed anisotropic damping shows twofold C2v symmetry, which is expected from the interplay of interfacial Rashba and Dresselhaus spin–orbit interaction, and is manifested by the anisotropic density of states at the Fe/GaAs (001) interface. This discovery of anisotropic damping will enrich the understanding of magnetization relaxation mechanisms and can provide a route towards the search for anisotropic damping at other ferromagnetic metal/semiconductor interfaces.
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References
Kamberský, V. On ferromagnetic resonance damping in metals. Czech. J. Phys. B 26, 1366–1383 (1976).
Thonig, D. & Henk, J. Gilbert damping tensor within the breathing Fermi surface model: anisotropy and non-locality. New. J. Phys. 16, 013032 (2014).
Gilmore, K., Idzerda, Y. U. & Stiles, M. D. Identification of the dominant precession-damping mechanism in Fe, Co, and Ni by first-principles calculations. Phys. Rev. Lett. 99, 027204 (2007).
Brataas, A., Tserkovnyak, Y. & Bauer, G. E. W. Scattering theory of Gilbert damping. Phys. Rev. Lett. 101, 037207 (2008).
Liu, Y., Starikov, A. A., Yuan, Z. & Kelly, P. J. First-principles calculations of magnetization relaxation in pure Fe, Co, and Ni with frozen thermal lattice disorder. Phys. Rev. B 84, 014412 (2011).
Mankovsky, S., Ködderitzsch, D., Woltersdorf, G. & Ebert, H. First-principles calculation of the Gilbert damping parameter via the linear response formalism with application to magnetic transition metals and alloys. Phys. Rev. B 87, 014430 (2013).
Turek, I. et al. Nonlocal torque operators in ab initio theory of the Gilbert damping in random ferromagnetic alloys. Phys. Rev. B 92, 214407 (2015).
Garate, I. & MacDonald, A. Gilbert damping in conducting ferromagnets. II. Model tests of the torque-correction formula. Phys. Rev. B 79, 064404 (2009).
Mizukami, S. et al. Long-lived ultrafast spin precession in manganese alloys films with a large perpendicular magnetic anisotropy. Phys. Rev. Lett. 106, 117201 (2011).
Schoen, M. A. W. et al. Ultra-low magnetic damping of a metallic ferromagnet. Nat. Phys. 12, 839–842 (2016).
Oogane, M. et al. Gilbert magnetic damping constant of epitaxially grown Co-based Heusler alloy thin films. Appl. Phys. Lett. 96, 252501 (2010).
Oogane, M. et al. Magnetic damping in ferromagnetic thin films. Jpn. J. Appl. Phys. 45, 3889–3891 (2006).
He, P. et al. Quadratic scaling of intrinsic Gilbert damping with spin-orbital coupling in L10 FePdPt films: experiments and ab initio calculations. Phys. Rev. Lett. 110, 077203 (2013).
Bhagat, S. M. & Lubitz, P. Temperature variation of ferromagnetic relaxation in the 3d transition metals. Phys. Rev. B 10, 179–185 (1974).
Safonov, V. L. Tensor form of magnetic damping. J. Appl. Phys. 91, 8653–8655 (2002).
Steiauf, D. & Fähnle, M. Damping of spin dynamics in nanostructures: An ab initio study. Phys. Rev. B 72, 064450 (2005).
Seib, J., Steiauf, D. & Fähnle, M. Linewidth of ferromagnetic resonance for systems with anisotropic damping. Phys. Rev. B 79, 092418 (2009).
Gilmore, K. & Stiles, M. D. Anisotropic damping of the magnetization dynamics in Ni, Co, and Fe. Phys. Rev. B 81, 174414 (2010).
Meckenstock, R. et al. Anisotropic Gilbert damping in epitaxial Fe films on InAs (001). J. Mag. Mag. Mater. 272–276, 1203–1204 (2004).
Zhai, Y. et al. A study on ferromagnetic resonance linewidth of single crystalline ultrathin Fe film grown on GaAs substrate. J. Appl. Phys. 101, 09D120 (2007).
Yilgin, R. et al. Anisotropic intrinsic damping constant of epitaxial Co2MnSi Heusler alloy films. Jpn. J. Appl. Phys. 46, L205–L208 2007).
Kasatani, Y. & Nozaki, Y. Crystallographic anisotropy of the intrinsic Gilbert damping for single-crystalline Fe film. J. Magn. Soc. Jpn. 39, 221–226 (2015).
Zhu, H. J. et al. Room-temperature spin injection from Fe to GaAs. Phys. Rev. Lett. 87, 016601 (2001).
Chen, L. et al. Robust spin-orbit torque and spin-galvanic effect at the Fe/GaAs (001) interface at room temperature. Nat. Commun. 7, 13802 (2016).
Gmitra, M. et al. Magnetic control of spin-orbit fields: A first-principles study of Fe/GaAs junctions. Phys. Rev. Lett. 111, 036603 (2013).
Hupfauer, T. et al. Emergence of spin-orbit fields in magnetotransport of quasi-two-dimensional iron on gallium arsenide. Nat. Commun. 6, 7374 (2015).
Buchner, M. et al. Anisotropic polar magneto-optic Kerr effect of ultrathin Fe/GaAs (001) layers due to interfacial spin-orbit interaction. Phys. Rev. Lett. 117, 157202 (2016).
Fang, D. et al. Spin-orbit-driven ferromagnetic resonance. Nat. Nanotech. 6, 413–417 (2011).
Arials, R. & Mills, D. L. Extrinsic contributions to the ferromagnetic resonance response of ultrathin film. Phys., Rev. B 60, 7395–7409 (1999).
McMichael, R. D. et al. Localized ferromagnetic resonance in inhomogeneous thin films. Phys. Rev. Lett. 90, 227601 (2003).
Zakeri, Kh. et al. Spin dynamics in ferromagnets: Gilbert damping and two-magnon scattering. Phys., Rev. B 76, 104416 (2007).
Mizukami, S. et al. The study on ferromagnetic resonance linewidth for NM/80NiFe/NM (NM=Cu, Ta, Pd and Pt) films. Jpn. J. Appl. Phys. 40, 580–585 (2001).
Skrotskii, G. V. & Kurbatov, L. V. Theory of the anisotropy of the width of ferromagnetic resonance absorption line. Sov. Phys. JETP 35, 148–151 (1959).
Suhl, H. Ferromagnetic resonance in Nickel ferrite between one and two kilomegacycles. Phys. Rev. 97, 555–557 (1955).
Tserkovnyak, Y. et al. Spin pumping and magnetization dynamics in metallic multilayers. Phys. Rev. B 66, 224403 (2002).
Pai, C. F. et al. Dependence of efficiency of spin Hall torque on the transparency of Pt/ferromagnetic layer interfaces. Phys. Rev. B 92, 064426 (2015).
Wastlbauer, G. & Bland, J. A. C. Structural and magnetic properties of ultrathin epitaxial Fe films on GaAs (001) and related semiconductor substrates. Adv. Phys. 54, 137–219 (2005).
Gordon, R. A. & Crozier, E. D. In-plane structure anisotropy of ultra-thin Fe films on GaAs (001)- 4×6: X-ray absorption fine structure spectroscopy measurements. Phys. Rev. B 74, 165405 (2006).
Moser, J. et al. Tunneling anisotropic magnetoresistance and spin-orbit coupling in Fe/GaAs/Au tunnel junctions. Phys. Rev. Lett. 99, 056601 (2007).
Ebert, H. et al. Calculating condensed matter properties using the KKR-Green’s function method—recent developments and applications. Rep. Prog. Phys. 74, 096501 (2011).
Acknowledgements
The authors thank M. Gmitra and J. Fabian for fruitful discussions. L. Chen is grateful for support from the Alexander von Humboldt Foundation. This work is support by the German Science Foundation (DFG) via SFB 689 and SFB 1277.
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L.C., C.H.B. and D.W. planned the study. L.C. fabricated the devices, and collected and analysed the data. M.A.W.S. carried out the full-film FMR measurements and L.C. analysed the data. H.S.K. performed the magnetization measurements. M.K., D.S. and D.B. grew the samples. S.W., S.M. and H.E. carried out the first-principle calculations. L.C. wrote the manuscript with input from S.W., S.M., H.E., C.H.B. and D.W. All authors discussed the results.
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Chen, L., Mankovsky, S., Wimmer, S. et al. Emergence of anisotropic Gilbert damping in ultrathin Fe layers on GaAs(001). Nature Phys 14, 490–494 (2018). https://doi.org/10.1038/s41567-018-0053-8
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DOI: https://doi.org/10.1038/s41567-018-0053-8
