Temperature Dependence of Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides

Authors

  • B. Heinz Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern, Graduate School Materials Science in Mainz
  • Q. Wang Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern, Nanomagnetism and Magnonics, Faculty of Physics, University of Vienna
  • R. Verba Institute of Magnetism
  • V.I. Vasyuchka Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern
  • M. Kewenig Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern
  • P. Pirro Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern
  • M. Schneider Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern
  • T. Meyer Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern, THATec Innovation GmbH
  • B. Lägel Nano Structuring Center, Technische Universit¨at Kaiserslautern
  • C. Dubs INNOVENT e.V., Technologieentwicklung
  • T. Brächer Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern
  • O.V. Dobrovolskiy Nanomagnetism and Magnonics, Faculty of Physics, University of Vienna
  • A.V. Chumak Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universit¨at Kaiserslautern, Nanomagnetism and Magnonics, Faculty of Physics, University of Vienna

DOI:

https://doi.org/10.15407/ujpe65.12.1094

Keywords:

spin waves, yttrium iron garnet, Brillouin light scattering spectroscopy, low temperatures

Abstract

The field of magnonics attracts significant attention due to the possibility of utilizing information coded into the spin-wave phase or amplitude to perform computation operations on the nanoscale. Recently, spin waves were investigated in Yttrium Iron Garnet (YIG) waveguides with widths down to 50 nm and aspect ratios of thickness to width approaching unity. A critical width was found, below which the exchange interaction suppresses the dipolar pinning phenomenon, and the system becomes unpinned. Here, we continue these investigations and analyze the pinning phenomenon and spin-wave dispersion as functions of temperature, thickness, and material parameters. Higher order modes, the influence of a finite wavevector along the waveguide, and the impact of the pinning phenomenon on the spin-wave lifetime are discussed, as well as the influence of a trapezoidal cross-section and edge roughness of the waveguide. The presented results are of particular interest for potential applications in magnonic devices and the incipient field of quantum magnonics at cryogenic temperatures.

References

A.V. Chumak, V.I. Vasyuchka, A.A. Serga, B. Hillebrands. Magnon spintronics. Nat. Phys. 11, 453 (2015). https://doi.org/10.1038/nphys3347

V.V. Kruglyak, S.O. Demokritov, D. Grundler. Magnonics. J. Phys. D 43, 264001 (2010). https://doi.org/10.1088/0022-3727/43/26/264001

C.S. Davies, A. Francis, A.V. Sadovnikov, S.V. Chertopalov, M.T. Bryan, S.V. Grishin, D.A. Allwood, Y.P. Sharaevskii, S.A. Nikitov, V. V. Kruglyak. Towards graded-index magnonics: Steering spin waves in magnonic networks. Phys. Rev. B 92, 020408 (2015). https://doi.org/10.1103/PhysRevB.92.020408

A. Khitun, M. Bao, K.L. Wang. Magnonic logic circuits. J. Phys. D: Appl. Phys. 43, 264005 (2010). https://doi.org/10.1088/0022-3727/43/26/264005

M. Schneider, T. Br¨acher, D. Breitbach, V. Lauer, P. Pirro, D.A. Bozhko, H.Y. Musiienko-Shmarova, B. Heinz, Q. Wang, T. Meyer, F. Heussner, S. Keller, E.T. Papaioannou, B. L¨agel, T. L¨ober, C. Dubs, A.N. Slavin, V.S. Tiberkevich, A.A. Serga, B. Hillebrands, A.V. Chumak. Bose-Einstein condensation of quasiparticles by rapid cooling. Nat. Nanotechnol. 15, 457 (2020). https://doi.org/10.1038/s41565-020-0671-z

M. Krawczyk, D. Grundler. Review and prospects of magnonic crystals and devices with reprogrammable band structure. J. Phys.: Condens. Matt. 26, 123202 (2014). https://doi.org/10.1088/0953-8984/26/12/123202

S. Wintz, V. Tiberkevich, M. Weigand, J. Raabe, J. Lindner, A. Erbe, A. Slavin, J. Fassbender. Magnetic vortex cores as tunable spin-wave emitters. Nat. Nanotechnol. 11, 948 EP (2016). https://doi.org/10.1038/nnano.2016.117

T. Br¨acher, P. Pirro. An analog magnon adder for all-magnonic neurons. J. Appl. Phys. 124, 152119 (2018). https://doi.org/10.1063/1.5042417

Q. Wang, P. Pirro, R. Verba, A. Slavin, B. Hillebrands, A.V. Chumak. Reconfigurable nanoscale spin-wave directional coupler. Sci. Adv. 4, e1701517 (2018). https://doi.org/10.1126/sciadv.1701517

O. Zografos, B. Soree, A. Vaysset, S. Cosemans, L. Amaru, P. Gaillardon, G. De Micheli, R. Lauwereins, S. Sayan, P. Raghavan, I.P. Radu, A. Thean. Design and bench-marking of hybrid cmos-spin wave device circuits compared to 10nm CMOS. In: Work-in-Progress session, 52nd Design Automation Conference (DAC), 7-11 June 2015, San Francisco, CA, USA (2015), pp. 686-689.

S. Manipatruni, D.E. Nikonov, I.A. Young. Beyond CMOS computing with spin and polarization. Nature Physics 14, 338 (2018). https://doi.org/10.1038/s41567-018-0101-4

A. Chumak. Fundamentals of magnon-based computing. arXiv 1901.08934 (2019).

Q. Wang, M. Kewenig, M. Schneider, R. Verba, B. Heinz, M. Geilen, M. Mohseni, B. L¨agel, F. Ciubotaru, C. Adelmann, C. Dubs, S.D. Cotofana, T. Br¨acher, P. Pirro, A.V. Chumak. A magnonic directional coupler for integrated magnonic half-adders. Nat. Electron. (2020). https://doi.org/10.1038/s41928-020-00485-6

B.A. Ivanov, C.E. Zaspel. Magnon modes for thin circular vortex-state magnetic dots. Appl. Phys. Lett. 81, 1261 (2002). https://doi.org/10.1063/1.1499515

G.T. Rado, J.R. Weertman. Spin-wave resonance in a ferromagnetic metal. J. Phys. Chem. Sol. 11, 315 (1959). https://doi.org/10.1016/0022-3697(59)90233-1

R.W. Damon, J.R. Eshbach. Magnetostatic modes of a ferromagnet slab. J. Phys. Chem. Sol. 19, 308 (1961). https://doi.org/10.1016/0022-3697(61)90041-5

K.Y. Guslienko, S.O. Demokritov, B. Hillebrands, A.N. Slavin. Effective dipolar boundary conditions for dynamic magnetization in thin magnetic stripes. Phys. Rev. B 66, 132402 (2002). https://doi.org/10.1103/PhysRevB.66.132402

K.Y. Guslienko, A.N. Slavin. Boundary conditions for magnetization in magnetic nanoelements. Phys. Rev. B 72, 014463 (2005). https://doi.org/10.1103/PhysRevB.72.014463

K.Y. Guslienko, A.N. Slavin. Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes. J. Magn. Magnet. Mater. 323, 2418 (2011). https://doi.org/10.1016/j.jmmm.2011.05.020

R.E. Arias. Spin-wave modes of ferromagnetic films. Phys. Rev. B 94, 134408 (2016). https://doi.org/10.1103/PhysRevB.94.134408

B. Heinz, T. Br¨acher, M. Schneider, Q. Wang, B. L¨agel, A.M. Friedel, D. Breitbach, S. Steinert, T. Meyer, M. Kewenig, C. Dubs, P. Pirro, A.V. Chumak, Propagation of spin-wave packets in individual nanosized yttrium iron garnet magnonic conduits. Nano Lett. 20, 4220 (2020). https://doi.org/10.1021/acs.nanolett.0c00657

T. Br¨acher, O. Boulle, G. Gaudin, P. Pirro. Creation of unidirectional spin-wave emitters by utilizing interfacial Dzyaloshinskii-Moriya interaction. Phys. Rev. B 95, 064429 (2017). https://doi.org/10.1103/PhysRevB.95.064429

V.E. Demidov, S.O. Demokritov. Magnonic waveguides studied by microfocus Brillouin light scattering. IEEE Trans. Magnet. 51, 1 (2015). https://doi.org/10.1109/TMAG.2014.2388196

F. Ciubotaru, T. Devolder, M. Manfrini, C. Adelmann, I.P. Radu. All electrical propagating spin wave spectroscopy with broadband wavevector capability. Appl. Phys. Lett. 109, 012403 (2016). https://doi.org/10.1063/1.4955030

P. Pirro, T. Br¨acher, A. V. Chumak, B. L¨agel, C. Dubs, O. Surzhenko, P. G¨arnert, B. Leven, B. Hillebrands. Spin-wave excitation and propagation in microstructured waveguides of yttrium iron garnet/Pt bilayers. Appl. Phys. Lett. 104, 012402 (2014). https://doi.org/10.1063/1.4861343

M. Mruczkiewicz, P. Graczyk, P. Lupo, A. Adeyeye, G. Gubbiotti, M. Krawczyk. Spin-wave nonreciprocity and magnonic band structure in a thin permalloy film induced by dynamical coupling with an array of Ni stripes. Phys. Rev. B 96, 104411 (2017). https://doi.org/10.1103/PhysRevB.96.104411

A. Haldar, A.O. Adeyeye. Deterministic control of magnetization dynamics in reconfigurable nanomagnetic networks for logic applications. ACS Nano 10, 1690 (2016). https://doi.org/10.1021/acsnano.5b07849

R. Verba, V. Tiberkevich, E. Bankowski, T. Meitzler, G. Melkov, A. Slavin. Conditions for the spin wave nonreciprocity in an array of dipolarly coupled magnetic nanopillars. Appl. Phys. Lett. 103, 082407 (2013). https://doi.org/10.1063/1.4819435

T. Br¨acher, P. Pirro, B. Hillebrands. Parallel pumping for magnon spintronics: Amplification and manipulation of magnon spin currents on the micron-scale. Phys. Rep. 699, 1 (2017). https://doi.org/10.1016/j.physrep.2017.07.003

G.S. Abo, Y. Hong, J. Park, J. Lee, W. Lee, B. Choi. Definition of magnetic exchange length. IEEE Trans. Magnet. 49, 4937 (2013). https://doi.org/10.1109/TMAG.2013.2258028

Q. Wang, B. Heinz, R. Verba, M. Kewenig, P. Pirro, M. Schneider, M. Thomas, B. L¨agel, C. Dubs, T. Br¨acher, A.V. Chumak. Spin pinning and spin-wave dispersion in nanoscopic ferromagnetic waveguides. Phys. Rev. Lett. 122, 247202 (2019). https://doi.org/10.1103/PhysRevLett.122.247202

Y. Tabuchi, S. Ishino, A. Noguchi, T. Ishikawa, R. Yamazaki, K. Usami, Y. Nakamura. Coherent coupling between a ferromagnetic magnon and a superconducting qubit. Science 349, 405 (2015). https://doi.org/10.1126/science.aaa3693

O.V. Dobrovolskiy, R. Sachser, T. Br¨acher, T. B¨ottcher, V.V. Kruglyak, R.V. Vovk, V.A. Shklovskij, M. Huth, B. Hillebrands, A.V. Chumak. Magnon-fluxon interaction in a ferromagnet/superconductor heterostructure. Nat. Phys. 15, 477 (2019). https://doi.org/10.1038/s41567-019-0428-5

I. Golovchanskiy, N. Abramov, M. Pfirrmann, T. Piskor, J. Voss, D. Baranov, R. Hovhannisyan, V. Stolyarov, C. Dubs, A. Golubov, V. Ryazanov, A. Ustinov, M. Weides. Interplay of magnetization dynamics with a microwave waveguide at cryogenic temperatures. Phys. Rev. Appl. 11, 044076 (2019). https://doi.org/10.1103/PhysRevApplied.11.044076

O.V. Prokopenko, D.A. Bozhko, V.S. Tyberkevych, A.V. Chumak, V.I. Vasyuchka, A.A. Serga, O. Dzyapko, R.V. Verba, A.V. Talalaevskij, D.V. Slobodianiuk, Y.V. Kobljanskyj, V.A.Moiseienko, S.V. Sholom, V.Y.Malyshev. Recent trends in microwave magnetism and superconductivity. Ukr. J. Phys. 64, 888 (2019). https://doi.org/10.15407/ujpe64.10.888

L. Mihalceanu, D.A. Bozhko, V.I. Vasyuchka, A.A. Serga, B. Hillebrands, A. Pomyalov, V.S. L'vov, V.S. Tyberkevych. Magnon Bose-Einstein condensates and supercurrents over a wide temperature range. Ukr. J. Phys. 64, 927 (2019). https://doi.org/10.15407/ujpe64.10.927

S. Kosen, A.F. van Loo, D.A. Bozhko, L. Mihalceanu, A.D. Karenowska. Microwave magnon damping in YIG films at millikelvin temperatures. APL. Mater. 7, 101120 (2019). https://doi.org/10.1063/1.5115266

C. Dubs, O. Surzhenko, R. Thomas, J. Osten, T. Schneider, K. lenz, J. Grenzer, R. H¨ubner, E. Wendler. Low damping and microstructural perfection of sub-40nm-thin yttrium iron garnet films grown by liquid phase epitaxy. Phys. Rev. Materials 4, 024416 (2020). https://doi.org/10.1103/PhysRevMaterials.4.024416

I.S. Maksymov, M. Kostylev. Broadband stripline ferromagnetic resonance spectroscopy of ferromagnetic films, multilayers and nanostructures. Phys. E: Lowdimensional Systems and Nanostructures 69, 253 (2015). https://doi.org/10.1016/j.physe.2014.12.027

A. Vansteenkiste, J. Leliaert, M. Dvornik, M. Helsen, F. Garcia-Sanchez, B. Van Waeyenberge. The design and verification of mumax3. AIP Advances 4, 107133 (2014). https://doi.org/10.1063/1.4899186

I.S. Maksymov, M. Kostylev. Broadband stripline ferromagnetic resonance spectroscopy of ferromagnetic films, multilayers and nanostructures. Physica E 69, 253 (2015). https://doi.org/10.1016/j.physe.2014.12.027

R. Verba, G. Melkov, V. Tiberkevich, A. Slavin. Collective spin-wave excitations in a two-dimensional array of coupled magnetic nanodots. Phys. Rev. B 85, 014427 (2012). https://doi.org/10.1103/PhysRevB.85.014427

R. Verba. Spin waves in arrays of magnetic nanodots with magnetodipolar coupling. Ukr. J. Phys. 58, 758 (2013). https://doi.org/10.15407/ujpe58.08.0758

A. Gurevich, G. Melkov. Magnetization Oscillations and Waves (CRC Press, 1996).

V.V. Kruglyak, O.Y. Gorobets, Y.I. Gorobets, A.N. Kuchko. Magnetization boundary conditions at a ferromagnetic interface of finite thickness. J. Phys.: Cond. Matt. 26, 406001 (2014). https://doi.org/10.1088/0953-8984/26/40/406001

T. Sebastian, K. Schultheiss, B. Obry, B. Hillebrands, H. Schultheiss. Micro-focused Brillouin light scattering: imaging spin waves at the nanoscale. Front. Phys. 3, 35 (2015).

M.B. Jungfleisch, W. Zhang, W. Jiang, H. Chang, J. Sklenar, S.M. Wu, J.E. Pearson, A. Bhattacharya, J.B. Ketterson, M. Wu, A. Hoffmann. Spin waves in micro-structured yttrium iron garnet nanometer-thick films. J. Appl. Phys. 117, 17D128 (2015). https://doi.org/10.1063/1.4916027

B.A. Kalinikos, A.N. Slavin. Theory of dipoleexchange spin wave spectrum for ferromagnetic films with mixed exchange boundary conditions. J. Phys. C 19, 7013 (1986). https://doi.org/10.1088/0022-3719/19/35/014

P. Hansen, P. R¨oschmann, W. Tolksdorf. Saturation magnetization of gallium-substituted yttrium iron garnet. J. Appl. Phys. 45, 2728 (1974). https://doi.org/10.1063/1.1663657

R.C. LeCraw, L.R.Walker. Temperature dependence of the spin-wave spectrum of yttrium iron garnet. J. Appl. Phys. 32, S167 (1961). https://doi.org/10.1063/1.2000390

A.V. Sadovnikov, E.N. Beginin, S.E. Sheshukova, D.V. Romanenko, Y.P. Sharaevskii, S.A. Nikitov. Directional multimode coupler for planar magnonics: Sidecoupled magnetic stripes. Appl. Phys. Lett. 107, 202405 (2015). https://doi.org/10.1063/1.4936207

A.V. Sadovnikov, A.A. Grachev, S.E. Sheshukova, Y.P. Sharaevskii, A.A. Serdobintsev, D.M. Mitin, S.A. Nikitov. Magnon straintronics: Reconfigurable spinwave routing in strain-controlled bilateral magnetic stripes. Phys. Rev. Lett. 120, 257203 (2018). https://doi.org/10.1103/PhysRevLett.120.257203

A.V. Sadovnikov, S.A. Odintsov, E.N. Beginin, S.E. Sheshukova, Y.P. Sharaevskii, S.A. Nikitov. Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes. Phys. Rev. B 96, 144428 (2017). https://doi.org/10.1103/PhysRevB.96.144428

D.D. Stancil. Phenomenological propagation loss theory for magnetostatic waves in thin ferrite films. J. Appl. Phys. 59, 218 (1986). https://doi.org/10.1063/1.336867

D.D. Stancil, A. Prabhakar. Spin Waves. Theory and Applications (Springer, 2009). https://doi.org/10.1007/978-0-387-77865-5_10

R. Verba, V. Tiberkevich, A. Slavin. Damping of linear spin-wave modes in magnetic nanostructures: Local, non-local, and coordinate-dependent damping. Phys. Rev. B 98, 104408 (2018). https://doi.org/10.1103/PhysRevB.98.104408

Downloads

Published

2020-12-18

How to Cite

Heinz, B., Wang, Q., Verba, R., Vasyuchka, V., Kewenig, M., Pirro, P., Schneider, M., Meyer, T., Lägel, B., Dubs, C., Brächer, T., Dobrovolskiy, O., & Chumak, A. (2020). Temperature Dependence of Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides. Ukrainian Journal of Physics, 65(12), 1094. https://doi.org/10.15407/ujpe65.12.1094

Issue

Vol. 65 No. 12 (2020)

Section

Physics of magnetic phenomena and physics of ferroics

License

Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine

The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:

1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.

2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.

3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.

4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.

5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.

6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.

Crossref
Scopus
Google Scholar
Europe PMC