Walker Breakdown with a Twist: Dynamics of Multilayer Domain Walls and Skyrmions Driven by Spin-Orbit Torque

Lemesh, Ivan; Beach, Geoffrey S. D.

doi:10.1103/physrevapplied.12.044031

Walker Breakdown with a Twist: Dynamics of Multilayer Domain Walls and Skyrmions Driven by Spin-Orbit Torque

Journal Article · Tue Oct 15 00:00:00 EDT 2019 · Physical Review Applied

DOI:https://doi.org/10.1103/physrevapplied.12.044031· OSTI ID:1802330

^[1]; Beach, Geoffrey S. D. ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); OSTI
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Current-induced dynamics of twisted domain walls and skyrmions in ferromagnetic perpendicularly magnetized multilayers is studied through three-dimensional micromagnetic simulations and analytical modeling. In this work, it is shown that such systems generally exhibit a Walker-breakdown-like phenomenon in the presence of a current-induced dampinglike spin-orbit torque. Above a critical current threshold, corresponding to typical velocities of the order of tens of m/s, domain walls in some layers start to precess with frequencies in the gigahertz regime, which leads to oscillatory motion and a significant drop in mobility. This phenomenon originates from complex stray field interactions and occurs for a wide range of multilayer materials and structures that include at least three ferromagnetic layers and finite Dzyaloshinskii-Moriya interaction. An analytical model is developed to describe the precessional dynamics in multilayers with surface-volume stray field interactions, yielding qualitative agreement with micromagnetic simulations.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: Defense Advanced Research Projects Agency (DARPA); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012371

OSTI ID:: 1802330

Journal Information:: Physical Review Applied, Journal Name: Physical Review Applied Journal Issue: 4 Vol. 12; ISSN 2331-7019

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (85)

Current-Induced Skyrmion Generation through Morphological Thermal Transitions in Chiral Ferromagnetic Heterostructures Lemesh, Ivan; Litzius, Kai; Böttcher, Marie Advanced Materials, Vol. 30, Issue 49 https://doi.org/10.1002/adma.201805461	journal	October 2018
Domain wall depinning governed by the spin Hall effect Haazen, P. P. J.; Murè, E.; Franken, J. H. Nature Materials, Vol. 12, Issue 4 https://doi.org/10.1038/nmat3553	journal	February 2013
Future perspectives for spintronic devices Hirohata, Atsufumi; Takanashi, Koki Journal of Physics D: Applied Physics, Vol. 47, Issue 19 https://doi.org/10.1088/0022-3727/47/19/193001	journal	April 2014
Universal absence of Walker breakdown and linear current-velocity relation via spin-orbit torques in coupled and single domain wall motion Risinggård, Vetle; Linder, Jacob Physical Review B, Vol. 95, Issue 13 https://doi.org/10.1103/physrevb.95.134423	journal	April 2017
Accurate model of the stripe domain phase of perpendicularly magnetized multilayers Lemesh, Ivan; Büttner, Felix; Beach, Geoffrey S. D. Physical Review B, Vol. 95, Issue 17 https://doi.org/10.1103/physrevb.95.174423	journal	May 2017
Twisted domain walls and skyrmions in perpendicularly magnetized multilayers Lemesh, Ivan; Beach, Geoffrey S. D. Physical Review B, Vol. 98, Issue 10 https://doi.org/10.1103/physrevb.98.104402	journal	September 2018
Asymmetric Ferromagnetic Resonance, Universal Walker Breakdown, and Counterflow Domain Wall Motion in the Presence of Multiple Spin-Orbit Torques Linder, Jacob; Alidoust, Mohammad arXiv https://doi.org/10.48550/arxiv.1306.4680	text	January 2013
Tailoring magnetic energies to form dipole skyrmions and skyrmion lattices Montoya, S. A.; Couture, S.; Chess, J. J. arXiv https://doi.org/10.48550/arxiv.1608.01368	text	January 2016
Micromagnetic understanding of current-driven domain wall motion in patterned nanowires Thiaville, A.; Nakatani, Y.; Miltat, J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0407628	text	January 2004
Bloch wall dynamics in ultrathin ferromagnetic films Tarasenko, S. V.; Stankiewicz, A.; Tarasenko, V. V. Journal of Magnetism and Magnetic Materials, Vol. 189, Issue 1 https://doi.org/10.1016/S0304-8853(98)00230-3	journal	October 1998
Room-Temperature Current-Induced Generation and Motion of sub-100 nm Skyrmions Legrand, William; Maccariello, Davide; Reyren, Nicolas Nano Letters, Vol. 17, Issue 4 https://doi.org/10.1021/acs.nanolett.7b00649	journal	March 2017
Nanoscale magnetic skyrmions in metallic films and multilayers: a new twist for spintronics Wiesendanger, Roland Nature Reviews Materials, Vol. 1, Issue 7 https://doi.org/10.1038/natrevmats.2016.44	journal	June 2016
Real-space observation of a two-dimensional skyrmion crystal Yu, X. Z.; Onose, Y.; Kanazawa, N. Nature, Vol. 465, Issue 7300 https://doi.org/10.1038/nature09124	journal	June 2010
Spin-orbit torque-driven skyrmion dynamics revealed by time-resolved X-ray microscopy Woo, Seonghoon; Song, Kyung Mee; Han, Hee-Sung Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15573	journal	May 2017
Current-induced skyrmion generation and dynamics in symmetric bilayers Hrabec, A.; Sampaio, J.; Belmeguenai, M. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15765	journal	June 2017
Dynamics of field-driven domain-wall propagation in ferromagnetic nanowires Beach, Geoffrey S. D.; Nistor, Corneliu; Knutson, Carl Nature Materials, Vol. 4, Issue 10 https://doi.org/10.1038/nmat1477	journal	September 2005
Observation of the intrinsic pinning of a magnetic domain wall in a ferromagnetic nanowire Koyama, T.; Chiba, D.; Ueda, K. Nature Materials, Vol. 10, Issue 3 https://doi.org/10.1038/nmat2961	journal	February 2011
Current-driven dynamics of chiral ferromagnetic domain walls Emori, Satoru; Bauer, Uwe; Ahn, Sung-Min Nature Materials, Vol. 12, Issue 7 https://doi.org/10.1038/nmat3675	journal	June 2013
Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets Woo, Seonghoon; Litzius, Kai; Krüger, Benjamin Nature Materials, Vol. 15, Issue 5 https://doi.org/10.1038/nmat4593	journal	February 2016
Chiral spin torque at magnetic domain walls Ryu, Kwang-Su; Thomas, Luc; Yang, See-Hun Nature Nanotechnology, Vol. 8, Issue 7 https://doi.org/10.1038/nnano.2013.102	journal	June 2013
Nucleation, stability and current-induced motion of isolated magnetic skyrmions in nanostructures Sampaio, J.; Cros, V.; Rohart, S. Nature Nanotechnology, Vol. 8, Issue 11 https://doi.org/10.1038/nnano.2013.210	journal	October 2013
Topological properties and dynamics of magnetic skyrmions Nagaosa, Naoto; Tokura, Yoshinori Nature Nanotechnology, Vol. 8, Issue 12 https://doi.org/10.1038/nnano.2013.243	journal	December 2013
Skyrmions on the track Fert, Albert; Cros, Vincent; Sampaio, João Nature Nanotechnology, Vol. 8, Issue 3 https://doi.org/10.1038/nnano.2013.29	journal	March 2013
Domain-wall velocities of up to 750 m s−1 driven by exchange-coupling torque in synthetic antiferromagnets Yang, See-Hun; Ryu, Kwang-Su; Parkin, Stuart Nature Nanotechnology, Vol. 10, Issue 3 https://doi.org/10.1038/nnano.2014.324	journal	February 2015
Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature Moreau-Luchaire, C.; Moutafis, C.; Reyren, N. Nature Nanotechnology, Vol. 11, Issue 5 https://doi.org/10.1038/nnano.2015.313	journal	January 2016
Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures Boulle, Olivier; Vogel, Jan; Yang, Hongxin Nature Nanotechnology, Vol. 11, Issue 5 https://doi.org/10.1038/nnano.2015.315	journal	January 2016
Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques Büttner, Felix; Lemesh, Ivan; Schneider, Michael Nature Nanotechnology, Vol. 12, Issue 11 https://doi.org/10.1038/nnano.2017.178	journal	October 2017
Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions Heinze, Stefan; von Bergmann, Kirsten; Menzel, Matthias Nature Physics, Vol. 7, Issue 9 https://doi.org/10.1038/nphys2045	journal	July 2011
Dynamics and inertia of skyrmionic spin structures Büttner, Felix; Moutafis, C.; Schneider, M. Nature Physics, Vol. 11, Issue 3 https://doi.org/10.1038/nphys3234	journal	February 2015
Skyrmion Hall effect revealed by direct time-resolved X-ray microscopy Litzius, Kai; Lemesh, Ivan; Krüger, Benjamin Nature Physics, Vol. 13, Issue 2 https://doi.org/10.1038/nphys4000	journal	December 2016
Magnetostatic twists in room-temperature skyrmions explored by nitrogen-vacancy center spin texture reconstruction Dovzhenko, Y.; Casola, F.; Schlotter, S. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-05158-9	journal	July 2018
Deriving the skyrmion Hall angle from skyrmion lattice dynamics Brearton, R.; Turnbull, L. A.; Verezhak, J. A. T. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-22857-y	journal	May 2021
Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet Caretta, Lucas; Mann, Maxwell; Büttner, Felix Nature Nanotechnology, Vol. 13, Issue 12 https://doi.org/10.1038/s41565-018-0255-3	journal	September 2018
Thermal skyrmion diffusion used in a reshuffler device Zázvorka, Jakub; Jakobs, Florian; Heinze, Daniel Nature Nanotechnology, Vol. 14, Issue 7 https://doi.org/10.1038/s41565-019-0436-8	journal	April 2019
Chiral exchange drag and chirality oscillations in synthetic antiferromagnets Yang, See-Hun; Garg, Chirag; Parkin, Stuart S. P. Nature Physics, Vol. 15, Issue 6 https://doi.org/10.1038/s41567-019-0438-3	journal	March 2019
Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications Büttner, Felix; Lemesh, Ivan; Beach, Geoffrey S. D. Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-22242-8	journal	March 2018
A strategy for the design of skyrmion racetrack memories Tomasello, R.; Martinez, E.; Zivieri, R. Scientific Reports, Vol. 4, Issue 1 https://doi.org/10.1038/srep06784	journal	October 2014
Topological, non-topological and instanton droplets driven by spin-transfer torque in materials with perpendicular magnetic anisotropy and Dzyaloshinskii–Moriya Interaction Carpentieri, Mario; Tomasello, Riccardo; Zivieri, Roberto Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep16184	journal	November 2015
The motion of 180° domain walls in uniform dc magnetic fields Schryer, N. L.; Walker, L. R. Journal of Applied Physics, Vol. 45, Issue 12 https://doi.org/10.1063/1.1663252	journal	December 1974
Low‐field magnetoresistance and domain drag in ferromagnets Berger, L. Journal of Applied Physics, Vol. 49, Issue 3 https://doi.org/10.1063/1.324716	journal	March 1978
Current induced domain wall dynamics in the presence of a transverse magnetic field in out-of-plane magnetized materials Boulle, O.; Buda-Prejbeanu, L. D.; Miron, M. Journal of Applied Physics, Vol. 112, Issue 5 https://doi.org/10.1063/1.4747907	journal	September 2012
Determining the Gilbert damping in perpendicularly magnetized Pt/Co/AlO _x films Schellekens, A. J.; Deen, L.; Wang, D. Applied Physics Letters, Vol. 102, Issue 8 https://doi.org/10.1063/1.4794538	journal	February 2013
The design and verification of MuMax3 Vansteenkiste, Arne; Leliaert, Jonathan; Dvornik, Mykola AIP Advances, Vol. 4, Issue 10 https://doi.org/10.1063/1.4899186	journal	October 2014
Potential implementation of reservoir computing models based on magnetic skyrmions Bourianoff, George; Pinna, Daniele; Sitte, Matthias AIP Advances, Vol. 8, Issue 5 https://doi.org/10.1063/1.5006918	journal	May 2018
A skyrmion-based spin-torque nano-oscillator Garcia-Sanchez, F.; Sampaio, J.; Reyren, N. New Journal of Physics, Vol. 18, Issue 7 https://doi.org/10.1088/1367-2630/18/7/075011	journal	July 2016
Modeling the Shape of Axisymmetric Skyrmions in Magnetic Multilayers Legrand, William; Ronceray, Nathan; Reyren, Nicolas Physical Review Applied, Vol. 10, Issue 6 https://doi.org/10.1103/PhysRevApplied.10.064042	journal	December 2018
Magnetic Skyrmion as a Nonlinear Resistive Element: A Potential Building Block for Reservoir Computing Prychynenko, Diana; Sitte, Matthias; Litzius, Kai Physical Review Applied, Vol. 9, Issue 1 https://doi.org/10.1103/PhysRevApplied.9.014034	journal	January 2018
Skyrmion Gas Manipulation for Probabilistic Computing Pinna, D.; Abreu Araujo, F.; Kim, J. -V. Physical Review Applied, Vol. 9, Issue 6 https://doi.org/10.1103/PhysRevApplied.9.064018	journal	June 2018
Interfacial effects on magnetic relaxation in Co/Pt multilayers Yuan, S. J.; Sun, L.; Sang, H. Physical Review B, Vol. 68, Issue 13 https://doi.org/10.1103/PhysRevB.68.134443	journal	October 2003
Implications of the B20 crystal structure for the magnetoelectronic structure of MnSi Jeong, T.; Pickett, W. E. Physical Review B, Vol. 70, Issue 7 https://doi.org/10.1103/PhysRevB.70.075114	journal	August 2004
Asymmetric ferromagnetic resonance, universal Walker breakdown, and counterflow domain wall motion in the presence of multiple spin-orbit torques Linder, Jacob; Alidoust, Mohammad Physical Review B, Vol. 88, Issue 6 https://doi.org/10.1103/PhysRevB.88.064420	journal	August 2013
Accurate calculation of the transverse anisotropy of a magnetic domain wall in perpendicularly magnetized multilayers Büttner, Felix; Krüger, Benjamin; Eisebitt, Stefan Physical Review B, Vol. 92, Issue 5 https://doi.org/10.1103/PhysRevB.92.054408	journal	August 2015
Tailoring magnetic energies to form dipole skyrmions and skyrmion lattices Montoya, S. A.; Couture, S.; Chess, J. J. Physical Review B, Vol. 95, Issue 2 https://doi.org/10.1103/PhysRevB.95.024415	journal	January 2017
Universal absence of Walker breakdown and linear current-velocity relation via spin-orbit torques in coupled and single domain wall motion Risinggård, Vetle; Linder, Jacob Physical Review B, Vol. 95, Issue 13 https://doi.org/10.1103/PhysRevB.95.134423	journal	April 2017
Accurate model of the stripe domain phase of perpendicularly magnetized multilayers Lemesh, Ivan; Büttner, Felix; Beach, Geoffrey S. D. Physical Review B, Vol. 95, Issue 17 https://doi.org/10.1103/PhysRevB.95.174423	journal	May 2017
Twisted domain walls and skyrmions in perpendicularly magnetized multilayers Lemesh, Ivan; Beach, Geoffrey S. D. Physical Review B, Vol. 98, Issue 10 https://doi.org/10.1103/PhysRevB.98.104402	journal	September 2018
Spin-orbit torque induced dipole skyrmion motion at room temperature Montoya, Sergio A.; Tolley, Robert; Gilbert, Ian Physical Review B, Vol. 98, Issue 10 https://doi.org/10.1103/PhysRevB.98.104432	journal	September 2018
Domain Wall Tilting in the Presence of the Dzyaloshinskii-Moriya Interaction in Out-of-Plane Magnetized Magnetic Nanotracks Boulle, O.; Rohart, S.; Buda-Prejbeanu, L. D. Physical Review Letters, Vol. 111, Issue 21 https://doi.org/10.1103/PhysRevLett.111.217203	journal	November 2013
Steady-State Motion of Magnetic Domains Thiele, A. A. Physical Review Letters, Vol. 30, Issue 6 https://doi.org/10.1103/PhysRevLett.30.230	journal	February 1973
Roles of Nonequilibrium Conduction Electrons on the Magnetization Dynamics of Ferromagnets Zhang, S.; Li, Z. Physical Review Letters, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevLett.93.127204	journal	September 2004
Creep and Flow Regimes of Magnetic Domain-Wall Motion in Ultrathin Pt / Co / Pt Films with Perpendicular Anisotropy Metaxas, P. J.; Jamet, J. P.; Mougin, A. Physical Review Letters, Vol. 99, Issue 21 https://doi.org/10.1103/PhysRevLett.99.217208	journal	November 2007
Hybrid chiral domain walls and skyrmions in magnetic multilayers Legrand, William; Chauleau, Jean-Yves; Maccariello, Davide Science Advances, Vol. 4, Issue 7 https://doi.org/10.1126/sciadv.aat0415	journal	July 2018
Real-Space Observation of Helical Spin Order Uchida, Masaya; Onose, Yoshinori; Matsui, Yoshio Science, Vol. 311, Issue 5759 https://doi.org/10.1126/science.1120639	journal	January 2006
Magnetic Domain-Wall Racetrack Memory Parkin, S. S. P.; Hayashi, M.; Thomas, L. Science, Vol. 320, Issue 5873, p. 190-194 https://doi.org/10.1126/science.1145799	journal	April 2008
Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum Liu, L.; Pai, C. -F.; Li, Y. Science, Vol. 336, Issue 6081 https://doi.org/10.1126/science.1218197	journal	May 2012
Blowing magnetic skyrmion bubbles Jiang, W.; Upadhyaya, P.; Zhang, W. Science, Vol. 349, Issue 6245 https://doi.org/10.1126/science.aaa1442	journal	June 2015
Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films Thiaville, André; Rohart, Stanislas; Jué, Émilie EPL (Europhysics Letters), Vol. 100, Issue 5 https://doi.org/10.1209/0295-5075/100/57002	journal	December 2012
Domain wall mobility, stability and Walker breakdown in magnetic nanowires Mougin, A.; Cormier, M.; Adam, J. P. Europhysics Letters (EPL), Vol. 78, Issue 5 https://doi.org/10.1209/0295-5075/78/57007	journal	May 2007
Micromagnetic understanding of current-driven domain wall motion in patterned nanowires Thiaville, A.; Nakatani, Y.; Miltat, J. Europhysics Letters (EPL), Vol. 69, Issue 6 https://doi.org/10.1209/epl/i2004-10452-6	journal	March 2005
Thermal skyrmion diffusion used in a reshuffler device Zázvorka, Jakub; Jakobs, Florian; Heinze, Daniel Nature Publishing Group https://doi.org/10.25358/openscience-466	text	January 2019
Current induced domain wall dynamics in the presence of a transverse magnetic field in out-of-plane magnetized materials Boulle, O.; Buda-Prejbeanu, L. D.; Miron, M. arXiv https://doi.org/10.48550/arxiv.1207.4970	text	January 2012
Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films Thiaville, Andre; Rohart, Stanislas; Jue, Emilie arXiv https://doi.org/10.48550/arxiv.1211.5970	text	January 2012
Current-driven dynamics of chiral ferromagnetic domain walls Emori, Satoru; Bauer, Uwe; Ahn, Sung-Min arXiv https://doi.org/10.48550/arxiv.1302.2257	text	January 2013
Topological, non topological and instanton droplets driven by spin-transfer torque in materials with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya Interaction Carpentieri, Mario; Tomasello, Riccardo; Zivieri, Roberto arXiv https://doi.org/10.48550/arxiv.1503.05161	preprint	January 2015
A skyrmion-based spin-torque nano-oscillator Garcia-Sanchez, F.; Sampaio, J.; Reyren, N. arXiv https://doi.org/10.48550/arxiv.1602.00118	text	January 2016
Universal Absence of Walker Breakdown and Linear Current-Velocity Relation via Spin-Orbit Torques in Coupled and Single Domain Wall Motion Risinggård, Vetle; Linder, Jacob arXiv https://doi.org/10.48550/arxiv.1701.00786	text	January 2017
Skyrmion Gas Manipulation for Probabilistic Computing Pinna, Daniele; Araujo, Flavio Abreu; Kim, Joo-Von arXiv https://doi.org/10.48550/arxiv.1701.07750	text	January 2017
Room-temperature current-induced generation and motion of sub-100nm skyrmions Legrand, William; Maccariello, Davide; Reyren, Nicolas arXiv https://doi.org/10.48550/arxiv.1702.04616	text	January 2017
Spin-orbit torque-driven skyrmion dynamics revealed by time-resolved X-ray microscopy Woo, Seonghoon; Song, Kyung Mee; Han, Hee-Sung arXiv https://doi.org/10.48550/arxiv.1705.09019	text	January 2017
Potential implementation of Reservoir Computing models based on magnetic skyrmions Bourianoff, George; Pinna, Daniele; Sitte, Matthias arXiv https://doi.org/10.48550/arxiv.1709.08911	text	January 2017
Hybrid chiral domain walls and skyrmions in magnetic multilayers Legrand, William; Chauleau, Jean-Yves; Maccariello, Davide arXiv https://doi.org/10.48550/arxiv.1712.05978	text	January 2017
Twisted domain walls and skyrmions in perpendicularly magnetized multilayers Lemesh, Ivan; Beach, Geoffrey S. D. arXiv https://doi.org/10.48550/arxiv.1809.01247	text	January 2018
Implications of the B20 Crystal Structure for the Magneto-electronic Structure of MnSi Jeong, T.; Pickett, W. E. arXiv https://doi.org/10.48550/arxiv.cond-mat/0403442	text	January 2004
Domain wall mobility, stability and Walker breakdown in magnetic nanowires Mougin, A.; Cormier, M.; Adam, J. P. arXiv https://doi.org/10.48550/arxiv.cond-mat/0702492	text	January 2007
Creep and flow regimes of magnetic domain wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy Metaxas, P. J.; Jamet, J. P.; Mougin, A. arXiv https://doi.org/10.48550/arxiv.cond-mat/0702654	text	January 2007

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