Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations
Abstract
We derive the skyrmion dynamics in response to a weak external drive, taking all the magnon modes into account. A skyrmion has rotational symmetry, and the magnon modes can be characterized by an angular momentum. For a weak distortion of a skyrmion, only the magnon modes with an angular momentum | m | = 1 govern the dynamics of skyrmion topological center. We also determine that the skyrmion inertia comes by way of the magnon modes in the continuum spectrum. For a skyrmion driven by a magnetic field gradient or by a spin transfer torque generated by a current, the dynamical response is practically instantaneous. This justifies the rigid skyrmion approximation used in Thiele's collective coordinate approach. For a skyrmion driven by a spin Hall torque, the torque couples to the skyrmion motion through the magnons in the continuum and damping; therefore the skyrmion dynamics shows sizable inertia in this case. The trajectory of a skyrmion is an ellipse for an ac drive of spin Hall torque.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1394985
- Alternate Identifier(s):
- OSTI ID: 1368611
- Report Number(s):
- LA-UR-17-26376
Journal ID: ISSN 2469-9950; PRBMDO; TRN: US1702841
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 1; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Material Science
Citation Formats
Lin, Shi-Zeng. Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations. United States: N. p., 2017.
Web. doi:10.1103/PhysRevB.96.014407.
Lin, Shi-Zeng. Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations. United States. https://doi.org/10.1103/PhysRevB.96.014407
Lin, Shi-Zeng. Thu .
"Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations". United States. https://doi.org/10.1103/PhysRevB.96.014407. https://www.osti.gov/servlets/purl/1394985.
@article{osti_1394985,
title = {Dynamics and inertia of a skyrmion in chiral magnets and interfaces: A linear response approach based on magnon excitations},
author = {Lin, Shi-Zeng},
abstractNote = {We derive the skyrmion dynamics in response to a weak external drive, taking all the magnon modes into account. A skyrmion has rotational symmetry, and the magnon modes can be characterized by an angular momentum. For a weak distortion of a skyrmion, only the magnon modes with an angular momentum | m | = 1 govern the dynamics of skyrmion topological center. We also determine that the skyrmion inertia comes by way of the magnon modes in the continuum spectrum. For a skyrmion driven by a magnetic field gradient or by a spin transfer torque generated by a current, the dynamical response is practically instantaneous. This justifies the rigid skyrmion approximation used in Thiele's collective coordinate approach. For a skyrmion driven by a spin Hall torque, the torque couples to the skyrmion motion through the magnons in the continuum and damping; therefore the skyrmion dynamics shows sizable inertia in this case. The trajectory of a skyrmion is an ellipse for an ac drive of spin Hall torque.},
doi = {10.1103/PhysRevB.96.014407},
journal = {Physical Review B},
number = 1,
volume = 96,
place = {United States},
year = {Thu Jul 06 00:00:00 EDT 2017},
month = {Thu Jul 06 00:00:00 EDT 2017}
}
Web of Science
Works referenced in this record:
Spin Transfer Torques in MnSi at Ultralow Current Densities
journal, December 2010
- Jonietz, F.; Muhlbauer, S.; Pfleiderer, C.
- Science, Vol. 330, Issue 6011
Spin-Torque Switching with the Giant Spin Hall Effect of Tantalum
journal, May 2012
- Liu, L.; Pai, C. -F.; Li, Y.
- Science, Vol. 336, Issue 6081
A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics
journal, January 1958
- Dzyaloshinsky, I.
- Journal of Physics and Chemistry of Solids, Vol. 4, Issue 4
Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep
journal, June 2013
- Lin, Shi-Zeng; Reichhardt, Charles; Batista, Cristian D.
- Physical Review B, Vol. 87, Issue 21
Driven Skyrmions and Dynamical Transitions in Chiral Magnets
journal, May 2013
- Lin, Shi-Zeng; Reichhardt, Charles; Batista, Cristian D.
- Physical Review Letters, Vol. 110, Issue 20
Skyrmions on the track
journal, March 2013
- Fert, Albert; Cros, Vincent; Sampaio, João
- Nature Nanotechnology, Vol. 8, Issue 3
Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy
journal, May 2016
- Hayami, Satoru; Lin, Shi-Zeng; Batista, Cristian D.
- Physical Review B, Vol. 93, Issue 18
Thermodynamically stable magnetic vortex states in magnetic crystals
journal, December 1994
- Bogdanov, A.; Hubert, A.
- Journal of Magnetism and Magnetic Materials, Vol. 138, Issue 3
Dynamics and inertia of skyrmionic spin structures
journal, February 2015
- Büttner, Felix; Moutafis, C.; Schneider, M.
- Nature Physics, Vol. 11, Issue 3
Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet
journal, September 2015
- Leonov, A. O.; Mostovoy, M.
- Nature Communications, Vol. 6, Issue 1
Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions
journal, February 2016
- Lin, Shi-Zeng; Hayami, Satoru
- Physical Review B, Vol. 93, Issue 6
Dynamics of an Insulating Skyrmion under a Temperature Gradient
journal, August 2013
- Kong, Lingyao; Zang, Jiadong
- Physical Review Letters, Vol. 111, Issue 6
Steady-State Motion of Magnetic Domains
journal, February 1973
- Thiele, A. A.
- Physical Review Letters, Vol. 30, Issue 6
Spin Hall torque magnetometry of Dzyaloshinskii domain walls
journal, November 2014
- Emori, Satoru; Martinez, Eduardo; Lee, Kyung-Jin
- Physical Review B, Vol. 90, Issue 18
Topological properties and dynamics of magnetic skyrmions
journal, December 2013
- Nagaosa, Naoto; Tokura, Yoshinori
- Nature Nanotechnology, Vol. 8, Issue 12
Current-driven excitation of magnetic multilayers
journal, June 1996
- Slonczewski, J. C.
- Journal of Magnetism and Magnetic Materials, Vol. 159, Issue 1-2
Blowing magnetic skyrmion bubbles
journal, June 2015
- Jiang, W.; Upadhyaya, P.; Zhang, W.
- Science, Vol. 349, Issue 6245
Electric-Field-Induced Skyrmion Distortion and Giant Lattice Rotation in the Magnetoelectric Insulator
journal, September 2014
- White, J. S.; Prša, K.; Huang, P.
- Physical Review Letters, Vol. 113, Issue 10
Real-space observation of a two-dimensional skyrmion crystal
journal, June 2010
- Yu, X. Z.; Onose, Y.; Kanazawa, N.
- Nature, Vol. 465, Issue 7300
Magnetic bubblecade memory based on chiral domain walls
journal, March 2015
- Moon, Kyoung-Woong; Kim, Duck-Ho; Yoo, Sang-Cheol
- Scientific Reports, Vol. 5, Issue 1
Current-driven dynamics of chiral ferromagnetic domain walls
journal, June 2013
- Emori, Satoru; Bauer, Uwe; Ahn, Sung-Min
- Nature Materials, Vol. 12, Issue 7
Current-induced rotational torques in the skyrmion lattice phase of chiral magnets
journal, August 2011
- Everschor, Karin; Garst, Markus; Duine, R. A.
- Physical Review B, Vol. 84, Issue 6
Skyrmion Lattice in a Chiral Magnet
journal, February 2009
- Muhlbauer, S.; Binz, B.; Jonietz, F.
- Science, Vol. 323, Issue 5916
Microscopic approach to current-driven domain wall dynamics
journal, November 2008
- Tatara, Gen; Kohno, Hiroshi; Shibata, Junya
- Physics Reports, Vol. 468, Issue 6
Chiral spin torque at magnetic domain walls
journal, June 2013
- Ryu, Kwang-Su; Thomas, Luc; Yang, See-Hun
- Nature Nanotechnology, Vol. 8, Issue 7
New Mechanism of Anisotropic Superexchange Interaction
journal, March 1960
- Moriya, Tôru
- Physical Review Letters, Vol. 4, Issue 5
Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films
journal, December 2012
- Thiaville, André; Rohart, Stanislas; Jué, Émilie
- EPL (Europhysics Letters), Vol. 100, Issue 5
Universal current-velocity relation of skyrmion motion in chiral magnets
journal, February 2013
- Iwasaki, Junichi; Mochizuki, Masahito; Nagaosa, Naoto
- Nature Communications, Vol. 4, Issue 1
Inertia and Chiral Edge Modes of a Skyrmion Magnetic Bubble
journal, November 2012
- Makhfudz, Imam; Krüger, Benjamin; Tchernyshyov, Oleg
- Physical Review Letters, Vol. 109, Issue 21
Skyrmion flow near room temperature in an ultralow current density
journal, January 2012
- Yu, X. Z.; Kanazawa, N.; Zhang, W. Z.
- Nature Communications, Vol. 3, Issue 1
Roles of Nonequilibrium Conduction Electrons on the Magnetization Dynamics of Ferromagnets
journal, September 2004
- Zhang, S.; Li, Z.
- Physical Review Letters, Vol. 93, Issue 12
Inertia, diffusion, and dynamics of a driven skyrmion
journal, November 2014
- Schütte, Christoph; Iwasaki, Junichi; Rosch, Achim
- Physical Review B, Vol. 90, Issue 17
Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions
journal, July 2011
- Heinze, Stefan; von Bergmann, Kirsten; Menzel, Matthias
- Nature Physics, Vol. 7, Issue 9
Rotating skyrmion lattices by spin torques and field or temperature gradients
journal, August 2012
- Everschor, Karin; Garst, Markus; Binz, Benedikt
- Physical Review B, Vol. 86, Issue 5
Electric field control of the skyrmion lattice in Cu 2 OSeO 3
journal, October 2012
- White, J. S.; Levatić, I.; Omrani, A. A.
- Journal of Physics: Condensed Matter, Vol. 24, Issue 43
Writing and Deleting Single Magnetic Skyrmions
journal, August 2013
- Romming, N.; Hanneken, C.; Menzel, M.
- Science, Vol. 341, Issue 6146
Collective-variable approach to the dynamics of nonlinear magnetic excitations with application to vortices
journal, November 1994
- Völkel, A. R.; Wysin, G. M.; Mertens, F. G.
- Physical Review B, Vol. 50, Issue 17
Multiple- States and the Skyrmion Lattice of the Triangular-Lattice Heisenberg Antiferromagnet under Magnetic Fields
journal, January 2012
- Okubo, Tsuyoshi; Chung, Sungki; Kawamura, Hikaru
- Physical Review Letters, Vol. 108, Issue 1
A non-linear field theory
journal, February 1961
- Skyrme, T. H. R.
- Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 260, Issue 1300, p. 127-138
Magnon-skyrmion scattering in chiral magnets
journal, September 2014
- Schütte, Christoph; Garst, Markus
- Physical Review B, Vol. 90, Issue 9
Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect
journal, January 2014
- Mochizuki, M.; Yu, X. Z.; Seki, S.
- Nature Materials, Vol. 13, Issue 3
Skyrmion in a real magnetic film
journal, October 1998
- Abanov, Ar.; Pokrovsky, V. L.
- Physical Review B, Vol. 58, Issue 14
A unified field theory of mesons and baryons
journal, March 1962
- Skyrme, T. H. R.
- Nuclear Physics, Vol. 31
Anisotropic Superexchange Interaction and Weak Ferromagnetism
journal, October 1960
- Moriya, Tôru
- Physical Review, Vol. 120, Issue 1
ac Current Generation in Chiral Magnetic Insulators and Skyrmion Motion induced by the Spin Seebeck Effect
journal, May 2014
- Lin, Shi-Zeng; Batista, Cristian D.; Reichhardt, Charles
- Physical Review Letters, Vol. 112, Issue 18
Internal modes of a skyrmion in the ferromagnetic state of chiral magnets
journal, January 2014
- Lin, Shi-Zeng; Batista, Cristian D.; Saxena, Avadh
- Physical Review B, Vol. 89, Issue 2
Emergent electrodynamics of skyrmions in a chiral magnet
journal, February 2012
- Schulz, T.; Ritz, R.; Bauer, A.
- Nature Physics, Vol. 8, Issue 4
Skyrmion motion driven by oscillating magnetic field
journal, February 2016
- Moon, Kyoung-Woong; Kim, Duck-Ho; Je, Soong-Geun
- Scientific Reports, Vol. 6, Issue 1
Works referencing / citing this record:
Spin torque nano-oscillators based on antiferromagnetic skyrmions
journal, January 2019
- Shen, Laichuan; Xia, Jing; Zhao, Guoping
- Applied Physics Letters, Vol. 114, Issue 4
Current-Induced Dynamics of the Antiferromagnetic Skyrmion and Skyrmionium
journal, December 2019
- Shen, Laichuan; Li, Xiaoguang; Zhao, Yuelei
- Physical Review Applied, Vol. 12, Issue 6
Breathing mode of a skyrmion on a lattice
journal, January 2020
- Garanin, Dmitry A.; Jaafar, Reem; Chudnovsky, Eugene M.
- Physical Review B, Vol. 101, Issue 1
Spin torque nano-oscillators based on antiferromagnetic skyrmions
text, January 2018
- Shen, Laichuan; Xia, Jing; Zhao, Guoping
- arXiv
Breathing Mode of a Skyrmion on a Lattice
text, January 2019
- Garanin, Dmitry A.; Jaafar, Reem; Chudnovsky, Eugene M.
- arXiv