Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions

Lin, Shi-Zeng; Hayami, Satoru

doi:10.1103/PhysRevB.93.064430

Title: Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions

Journal Article · Mon Feb 01 00:00:00 EST 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.93.064430· OSTI ID:1249058

Lin, Shi-Zeng ^[1]; Hayami, Satoru ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Magnetic skyrmions have attracted considerable attention recently for their huge potential in spintronic applications. Generally skyrmions are big compared to the atomic lattice constant, which allows for the Ginzburg-Landau type description in the continuum limit. This description successfully captures the main experimental observations on skyrmions in B20 compound without inversion symmetry. Skyrmions can also exist in inversion-symmetric magnets with competing interactions. Here, we derive a general Ginzburg-Landau theory for skyrmions in these magnets valid in the long-wavelength limit. We study the unusual static and dynamical properties of skyrmions based on the derived Ginzburg-Landau theory. We show that an easy axis spin anisotropy is sufficient to stabilize a skyrmion lattice. Interestingly, the skyrmion in inversion-symmetric magnets has a new internal degree of freedom associated with the rotation of helicity, i.e., the “spin” of the skyrmion as a particle, in addition to the usual translational motion of skyrmions (orbital motion). The orbital and spin degree of freedoms of an individual skyrmion can couple to each other, and give rise to unusual behavior that is absent for the skyrmions stabilized by the Dzyaloshinskii-Moriya interaction. Finally, the derived Ginzburg-Landau theory provides a convenient and general framework to discuss skyrmion physics and will facilitate the search for skyrmions in inversion-symmetric magnets.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1249058

Alternate ID(s):: OSTI ID: 1239458

Report Number(s):: LA-UR-15-29577; PRBMDO

Journal Information:: Physical Review B, Vol. 93, Issue 6; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 174 works

Citation information provided by
Web of Science

References (65)

Thermodynamically stable magnetic vortex states in magnetic crystals Bogdanov, A.; Hubert, A. Journal of Magnetism and Magnetic Materials, Vol. 138, Issue 3 https://doi.org/10.1016/0304-8853(94)90046-9	journal	December 1994
Skyrmion Lattice in a Chiral Magnet Muhlbauer, S.; Binz, B.; Jonietz, F. Science, Vol. 323, Issue 5916 https://doi.org/10.1126/science.1166767	journal	February 2009
Robust Formation of Skyrmions and Topological Hall Effect Anomaly in Epitaxial Thin Films of MnSi Li, Yufan; Kanazawa, N.; Yu, X. Z. Physical Review Letters, Vol. 110, Issue 11 https://doi.org/10.1103/PhysRevLett.110.117202	journal	March 2013
Topological Hall Effect in the $A$ Phase of MnSi Neubauer, A.; Pfleiderer, C.; Binz, B. Physical Review Letters, Vol. 102, Issue 18 https://doi.org/10.1103/PhysRevLett.102.186602	journal	May 2009
Observation of Skyrmions in a Multiferroic Material Seki, S.; Yu, X. Z.; Ishiwata, S. Science, Vol. 336, Issue 6078 https://doi.org/10.1126/science.1214143	journal	April 2012
Magnetoelectric nature of skyrmions in a chiral magnetic insulator Cu $_{2}$ OSeO $_{3}$ Seki, S.; Ishiwata, S.; Tokura, Y. Physical Review B, Vol. 86, Issue 6 https://doi.org/10.1103/PhysRevB.86.060403	journal	August 2012
Spin Transfer Torques in MnSi at Ultralow Current Densities Jonietz, F.; Muhlbauer, S.; Pfleiderer, C. Science, Vol. 330, Issue 6011 https://doi.org/10.1126/science.1195709	journal	December 2010
Skyrmion flow near room temperature in an ultralow current density Yu, X. Z.; Kanazawa, N.; Zhang, W. Z. Nature Communications, Vol. 3, Issue 1 https://doi.org/10.1038/ncomms1990	journal	January 2012
Emergent electrodynamics of skyrmions in a chiral magnet Schulz, T.; Ritz, R.; Bauer, A. Nature Physics, Vol. 8, Issue 4 https://doi.org/10.1038/nphys2231	journal	February 2012
Dynamics of an Insulating Skyrmion under a Temperature Gradient Kong, Lingyao; Zang, Jiadong Physical Review Letters, Vol. 111, Issue 6 https://doi.org/10.1103/PhysRevLett.111.067203	journal	August 2013
ac Current Generation in Chiral Magnetic Insulators and Skyrmion Motion induced by the Spin Seebeck Effect Lin, Shi-Zeng; Batista, Cristian D.; Reichhardt, Charles Physical Review Letters, Vol. 112, Issue 18 https://doi.org/10.1103/PhysRevLett.112.187203	journal	May 2014
Thermally driven ratchet motion of a skyrmion microcrystal and topological magnon Hall effect Mochizuki, M.; Yu, X. Z.; Seki, S. Nature Materials, Vol. 13, Issue 3 https://doi.org/10.1038/nmat3862	journal	January 2014
Large anisotropic deformation of skyrmions in strained crystal Shibata, K.; Iwasaki, J.; Kanazawa, N. Nature Nanotechnology, Vol. 10, Issue 7 https://doi.org/10.1038/nnano.2015.113	journal	June 2015
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
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
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
Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe Yu, X. Z.; Kanazawa, N.; Onose, Y. Nature Materials, Vol. 10, Issue 2 https://doi.org/10.1038/nmat2916	journal	December 2010
Long-Wavelength Helimagnetic Order and Skyrmion Lattice Phase in ${Cu}_{2} {OSeO}_{3}$ Adams, T.; Chacon, A.; Wagner, M. Physical Review Letters, Vol. 108, Issue 23 https://doi.org/10.1103/PhysRevLett.108.237204	journal	June 2012
Theory of helical magnetic structures and phase transitions in MnSi and FeGe Bak, P.; Jensen, M. H. Journal of Physics C: Solid State Physics, Vol. 13, Issue 31 https://doi.org/10.1088/0022-3719/13/31/002	journal	November 1980
Spin-Wave Modes and Their Intense Excitation Effects in Skyrmion Crystals Mochizuki, Masahito Physical Review Letters, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevLett.108.017601	journal	January 2012
Observation of Magnetic Excitations of Skyrmion Crystal in a Helimagnetic Insulator ${Cu}_{2} {OSeO}_{3}$ Onose, Y.; Okamura, Y.; Seki, S. Physical Review Letters, Vol. 109, Issue 3 https://doi.org/10.1103/PhysRevLett.109.037603	journal	July 2012
Magnetoelectric resonances and predicted microwave diode effect of the skyrmion crystal in a multiferroic chiral-lattice magnet Mochizuki, Masahito; Seki, Shinichiro Physical Review B, Vol. 87, Issue 13 https://doi.org/10.1103/PhysRevB.87.134403	journal	April 2013
Microwave magnetoelectric effect via skyrmion resonance modes in a helimagnetic multiferroic Okamura, Y.; Kagawa, F.; Mochizuki, M. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3391	journal	August 2013
Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets Schwarze, T.; Waizner, J.; Garst, M. Nature Materials, Vol. 14, Issue 5 https://doi.org/10.1038/nmat4223	journal	March 2015
Microwave-induced dynamic switching of magnetic skyrmion cores in nanodots Zhang, Bin; Wang, Weiwei; Beg, Marijan Applied Physics Letters, Vol. 106, Issue 10 https://doi.org/10.1063/1.4914496	journal	March 2015
A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics Dzyaloshinsky, I. Journal of Physics and Chemistry of Solids, Vol. 4, Issue 4 https://doi.org/10.1016/0022-3697(58)90076-3	journal	January 1958
Anisotropic Superexchange Interaction and Weak Ferromagnetism Moriya, Tôru Physical Review, Vol. 120, Issue 1 https://doi.org/10.1103/PhysRev.120.91	journal	October 1960
New Mechanism of Anisotropic Superexchange Interaction Moriya, Tôru Physical Review Letters, Vol. 4, Issue 5 https://doi.org/10.1103/PhysRevLett.4.228	journal	March 1960
Comments on Nonlinear Wave Equations as Models for Elementary Particles Derrick, G. H. Journal of Mathematical Physics, Vol. 5, Issue 9 https://doi.org/10.1063/1.1704233	journal	September 1964
Magnetic stripes and skyrmions with helicity reversals Yu, X.; Mostovoy, M.; Tokunaga, Y. Proceedings of the National Academy of Sciences, Vol. 109, Issue 23 https://doi.org/10.1073/pnas.1118496109	journal	May 2012
Skyrmion in a real magnetic film Abanov, Ar.; Pokrovsky, V. L. Physical Review B, Vol. 58, Issue 14 https://doi.org/10.1103/PhysRevB.58.R8889	journal	October 1998
From bubble to Skyrmion: Dynamic transformation mediated by a strong magnetic tip Kirakosyan, A. S.; Pokrovsky, V. L. Journal of Magnetism and Magnetic Materials, Vol. 305, Issue 2 https://doi.org/10.1016/j.jmmm.2006.01.113	journal	October 2006
Multiple- $q$ States and the Skyrmion Lattice of the Triangular-Lattice Heisenberg Antiferromagnet under Magnetic Fields Okubo, Tsuyoshi; Chung, Sungki; Kawamura, Hikaru Physical Review Letters, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevLett.108.017206	journal	January 2012
Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet Leonov, A. O.; Mostovoy, M. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9275	journal	September 2015
Stabilization of skyrmion textures by uniaxial distortions in noncentrosymmetric cubic helimagnets Butenko, A. B.; Leonov, A. A.; Rößler, U. K. Physical Review B, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevB.82.052403	journal	August 2010
Extended elliptic skyrmion gratings in epitaxial MnSi thin films Wilson, M. N.; Karhu, E. A.; Quigley, A. S. Physical Review B, Vol. 86, Issue 14 https://doi.org/10.1103/PhysRevB.86.144420	journal	October 2012
Extended Skyrmion Phase in Epitaxial $FeGe (111)$ Thin Films Huang, S. X.; Chien, C. L. Physical Review Letters, Vol. 108, Issue 26 https://doi.org/10.1103/PhysRevLett.108.267201	journal	June 2012
Topology of cosmic domains and strings Kibble, T. W. B. Journal of Physics A: Mathematical and General, Vol. 9, Issue 8 https://doi.org/10.1088/0305-4470/9/8/029	journal	August 1976
Cosmological experiments in superfluid helium? Zurek, W. H. Nature, Vol. 317, Issue 6037 https://doi.org/10.1038/317505a0	journal	October 1985
Modification of the Landau-Lifshitz equation in the presence of a spin-polarized current in colossal- and giant-magnetoresistive materials Bazaliy, Ya. B.; Jones, B. A.; Zhang, Shou-Cheng Physical Review B, Vol. 57, Issue 6 https://doi.org/10.1103/PhysRevB.57.R3213	journal	February 1998
Domain-Wall Dynamics and Spin-Wave Excitations with Spin-Transfer Torques Li, Z.; Zhang, S. Physical Review Letters, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevLett.92.207203	journal	May 2004
Microscopic approach to current-driven domain wall dynamics Tatara, Gen; Kohno, Hiroshi; Shibata, Junya Physics Reports, Vol. 468, Issue 6 https://doi.org/10.1016/j.physrep.2008.07.003	journal	November 2008
Numerical technique for integration of the Landau–Lifshitz equation Serpico, C.; Mayergoyz, I. D.; Bertotti, G. Journal of Applied Physics, Vol. 89, Issue 11 https://doi.org/10.1063/1.1358818	journal	June 2001
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
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
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
Spin Hall torque magnetometry of Dzyaloshinskii domain walls Emori, Satoru; Martinez, Eduardo; Lee, Kyung-Jin Physical Review B, Vol. 90, Issue 18 https://doi.org/10.1103/PhysRevB.90.184427	journal	November 2014
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
Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep Lin, Shi-Zeng; Reichhardt, Charles; Batista, Cristian D. Physical Review B, Vol. 87, Issue 21 https://doi.org/10.1103/PhysRevB.87.214419	journal	June 2013
Universal current-velocity relation of skyrmion motion in chiral magnets Iwasaki, Junichi; Mochizuki, Masahito; Nagaosa, Naoto Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2442	journal	February 2013
Spin dynamics in the geometrically frustrated multiferroic ${CuCrO}_{2}$ Poienar, M.; Damay, F.; Martin, C. Physical Review B, Vol. 81, Issue 10 https://doi.org/10.1103/PhysRevB.81.104411	journal	March 2010
The toroidal moment in condensed-matter physics and its relation to the magnetoelectric effect Spaldin, Nicola A.; Fiebig, Manfred; Mostovoy, Maxim Journal of Physics: Condensed Matter, Vol. 20, Issue 43 https://doi.org/10.1088/0953-8984/20/43/434203	journal	October 2008
Microscopic approach to current-driven domain wall dynamics Tatara, Gen; Kohno, Hiroshi; Shibata, Junya arXiv https://doi.org/10.48550/arxiv.0807.2894	text	January 2008
Skyrmion Lattice in a Chiral Magnet Mühlbauer, S.; Binz, B.; Jonietz, F. arXiv https://doi.org/10.48550/arxiv.0902.1968	text	January 2009
Stabilization of Skyrmion textures by uniaxial distortions in noncentrosymmetric cubic helimagnets Butenko, A. B.; Leonov, A. A.; Rößler, U. K. arXiv https://doi.org/10.48550/arxiv.0904.4842	text	January 2009
Spin dynamics in the geometrically frustrated multiferroic CuCrO2 Poienar, M.; Damay, F.; Martin, C. arXiv https://doi.org/10.48550/arxiv.0912.1962	text	January 2009
Spin Transfer Torques in MnSi at Ultra-low Current Densities Jonietz, F.; Mühlbauer, S.; Pfleiderer, C. arXiv https://doi.org/10.48550/arxiv.1012.3496	text	January 2010
Spin-Wave Modes and Their Intense Excitation Effects in Skyrmion Crystals Mochizuki, Masahito arXiv https://doi.org/10.48550/arxiv.1111.5667	text	January 2011
Extended elliptic skyrmion gratings in epitaxial MnSi thin films Wilson, M. N.; Karhu, E. A.; Quigley, A. S. arXiv https://doi.org/10.48550/arxiv.1210.1440	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
Magnetoelectric Resonances and Predicted Microwave Diode Effect of Skyrmion Crystal in Multiferroic Chiral-Lattice Magnet Mochizuki, Masahito; Seki, Shinichiro arXiv https://doi.org/10.48550/arxiv.1303.4491	text	January 2013
AC current generation in chiral magnetic insulators and skyrmion motion induced by the spin Seebeck effect Lin, Shi-Zeng; Batista, Cristian D.; Reichhardt, Charles arXiv https://doi.org/10.48550/arxiv.1308.2634	text	January 2013
Microwave-induced dynamic switching of magnetic skyrmion cores in nanodots Zhang, Bin; Wang, Weiwei; Beg, Marijan arXiv https://doi.org/10.48550/arxiv.1503.02869	text	January 2015
From Bubble to Skyrmion: Dynamic Transformation Mediated by a Strong Magnetic Tip Kirakosyan, A. S.; Pokrovsky, V. L. arXiv https://doi.org/10.48550/arxiv.cond-mat/0305487	text	January 2003
Skyrmion in a real magnetic film Abanov, Ar.; Pokrovsky, V. L. arXiv https://doi.org/10.48550/arxiv.cond-mat/9801114	text	January 1998

Cited By (44)

Steering Magnetic Skyrmions with Currents: A Nonequilibrium Green's Functions Approach Viñas Boström, Emil; Verdozzi, Claudio physica status solidi (b), Vol. 256, Issue 7 https://doi.org/10.1002/pssb.201800590	journal	February 2019
Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition Zhang, Xichao; Xia, Jing; Zhou, Yan Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/s41467-017-01785-w	journal	November 2017
Isolated zero field sub-10 nm skyrmions in ultrathin Co films Meyer, Sebastian; Perini, Marco; von Malottki, Stephan Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-11831-4	journal	August 2019
Skyrmion phase and competing magnetic orders on a breathing kagomé lattice Hirschberger, Max; Nakajima, Taro; Gao, Shang Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-13675-4	journal	December 2019
Creation and Annihilation of Skyrmions in the Frustrated Magnets with Competing Exchange Interactions Hu, Yong; Chi, Xiaodan; Li, Xuesi Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-017-16348-8	journal	November 2017
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
Trochoidal motion and pair generation in skyrmion and antiskyrmion dynamics under spin–orbit torques Ritzmann, Ulrike; von Malottki, Stephan; Kim, Joo-Von Nature Electronics, Vol. 1, Issue 8 https://doi.org/10.1038/s41928-018-0114-0	journal	August 2018
Writing skyrmions with a magnetic dipole Garanin, Dmitry A.; Capic, Daniel; Zhang, Senfu Journal of Applied Physics, Vol. 124, Issue 11 https://doi.org/10.1063/1.5044273	journal	September 2018
Frustration and chiral orderings in correlated electron systems Batista, Cristian D.; Lin, Shi-Zeng; Hayami, Satoru Reports on Progress in Physics, Vol. 79, Issue 8 https://doi.org/10.1088/0034-4885/79/8/084504	journal	July 2016
Magnetic field gradient driven dynamics of isolated skyrmions and antiskyrmions in frustrated magnets Liang, J. J.; Yu, J. H.; Chen, J. New Journal of Physics, Vol. 20, Issue 5 https://doi.org/10.1088/1367-2630/aac24c	journal	May 2018
B – T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo Böttcher, M.; Heinze, S.; Egorov, S. New Journal of Physics, Vol. 20, Issue 10 https://doi.org/10.1088/1367-2630/aae282	journal	October 2018
Current-Driven Dynamics of Frustrated Skyrmions in a Synthetic Antiferromagnetic Bilayer Xia, Jing; Zhang, Xichao; Ezawa, Motohiko Physical Review Applied, Vol. 11, Issue 4 https://doi.org/10.1103/physrevapplied.11.044046	journal	April 2019
Stabilty of biskyrmions in centrosymmetric magnetic films Capic, Daniel; Garanin, Dmitry A.; Chudnovsky, Eugene M. Physical Review B, Vol. 100, Issue 1 https://doi.org/10.1103/physrevb.100.014432	journal	July 2019
Tunable skyrmion-skyrmion binding on the surface of a topological insulator Tiwari, Kunal L.; Lavoie, J.; Pereg-Barnea, T. Physical Review B, Vol. 100, Issue 12 https://doi.org/10.1103/physrevb.100.125414	journal	September 2019
From skyrmions to $Z_{2}$ vortices in distorted chiral antiferromagnets Osorio, S. A.; Sturla, M. B.; Rosales, H. D. Physical Review B, Vol. 100, Issue 22 https://doi.org/10.1103/physrevb.100.220404	journal	December 2019
Field-induced pseudo-skyrmion phase in the antiferromagnetic kagome lattice Villalba, M. E.; Gómez Albarracín, F. A.; Rosales, H. D. Physical Review B, Vol. 100, Issue 24 https://doi.org/10.1103/physrevb.100.245106	journal	December 2019
Stability and dynamics of in-plane skyrmions in collinear ferromagnets Zarzuela, Ricardo; Bharadwaj, Venkata Krishna; Kim, Kyoung-Whan Physical Review B, Vol. 101, Issue 5 https://doi.org/10.1103/physrevb.101.054405	journal	February 2020
Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities Hayami, Satoru; Lin, Shi-Zeng; Kamiya, Yoshitomo Physical Review B, Vol. 94, Issue 17 https://doi.org/10.1103/physrevb.94.174420	journal	November 2016
Formation and stability of metastable skyrmionic spin structures with various topologies in an ultrathin film Rózsa, Levente; Palotás, Krisztián; Deák, András Physical Review B, Vol. 95, Issue 9 https://doi.org/10.1103/physrevb.95.094423	journal	March 2017
Effect of magnetic anisotropy on skyrmions with a high topological number in itinerant magnets Hayami, Satoru; Motome, Yukitoshi Physical Review B, Vol. 99, Issue 9 https://doi.org/10.1103/physrevb.99.094420	journal	March 2019
Dynamical and Reversible Control of Topological Spin Textures Stepanov, E. A.; Dutreix, C.; Katsnelson, M. I. Physical Review Letters, Vol. 118, Issue 15 https://doi.org/10.1103/physrevlett.118.157201	journal	April 2017
Magnetic Ground State Stabilized by Three-Site Interactions: $Fe / Rh (111)$ Krönlein, Andreas; Schmitt, Martin; Hoffmann, Markus Physical Review Letters, Vol. 120, Issue 20 https://doi.org/10.1103/physrevlett.120.207202	journal	May 2018
Biskyrmion lattices in centrosymmetric magnetic films Capic, Daniel; Garanin, Dmitry A.; Chudnovsky, Eugene M. Physical Review Research, Vol. 1, Issue 3 https://doi.org/10.1103/physrevresearch.1.033011	journal	October 2019
Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet Kurumaji, Takashi; Nakajima, Taro; Hirschberger, Max Science, Vol. 365, Issue 6456 https://doi.org/10.1126/science.aau0968	journal	August 2019
Spiral spin structures and skyrmions in multiferroics Kurumaji, Takashi Physical Sciences Reviews, Vol. 5, Issue 1 https://doi.org/10.1515/psr-2019-0016	journal	September 2019
Skyrmion Crystals and Phase Transitions in Magneto-Ferroelectric Superlattices: Dzyaloshinskii–Moriya Interaction in a Frustrated J1 − J2 Model Sharafullin, Ildus F.; Diep, Hung T. Symmetry, Vol. 12, Issue 1 https://doi.org/10.3390/sym12010026	journal	December 2019
B–T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo Böttcher, Marie; Heinze, Stefan; Egorov, Sergei IOP https://doi.org/10.25358/openscience-150	text	January 2018
Skyrmions with attractive interactions in an ultrathin magnetic film Rózsa, Levente; Deák, András; Simon, Eszter arXiv https://doi.org/10.48550/arxiv.1606.02464	text	January 2016
Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities Hayami, Satoru; Lin, Shi-Zeng; Kamiya, Yoshitomo arXiv https://doi.org/10.48550/arxiv.1607.07100	text	January 2016
Formation and stability of metastable skyrmionic spin structures with various topologies in an ultrathin film Rózsa, Levente; Palotás, Krisztián; Deák, András arXiv https://doi.org/10.48550/arxiv.1609.07012	text	January 2016
Skyrmion dynamics in a frustrated ferromagnetic film and current-induced helicity locking-unlocking transition Zhang, Xichao; Xia, Jing; Zhou, Yan arXiv https://doi.org/10.48550/arxiv.1703.07501	text	January 2017
Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets Hayami, Satoru; Ozawa, Ryo; Motome, Yukitoshi arXiv https://doi.org/10.48550/arxiv.1703.07690	text	January 2017
Skyrmion knots in frustrated magnets Sutcliffe, Paul arXiv https://doi.org/10.48550/arxiv.1705.10966	text	January 2017
Magnetic field gradient driven dynamics of isolated skyrmions and antiskyrmions in frustrated magnets Liang, J. J.; Yu, J. H.; Chen, J. arXiv https://doi.org/10.48550/arxiv.1712.03550	text	January 2017
Trochoidal motion and pair generation in skyrmion and antiskyrmion dynamics under spin-orbit torques Ritzmann, Ulrike; von Malottki, Stephan; Kim, Joo-Von arXiv https://doi.org/10.48550/arxiv.1803.00534	preprint	January 2018
Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet Kurumaji, Takashi; Nakajima, Taro; Hirschberger, Max arXiv https://doi.org/10.48550/arxiv.1805.10719	text	January 2018
Spin Textures induced by Quenched Disorder in a Reentrant Spin Glass: Vortices versus "Frustrated" Skyrmions Mirebeau, I.; Martin, N.; Deutsch, M. arXiv https://doi.org/10.48550/arxiv.1807.01311	text	January 2018
The dynamics of bimeron skyrmions in easy-plane magnets induced by a spin supercurrent Kim, Se Kwon arXiv https://doi.org/10.48550/arxiv.1901.00094	text	January 2019
Quantum skyrmions in frustrated ferromagnets Lohani, Vivek; Hickey, Ciarán; Masell, Jan arXiv https://doi.org/10.48550/arxiv.1901.03343	text	January 2019
Stability of Biskyrmions in Centrosymmetric Magnetic Films Capic, Daniel; Garanin, Dmitry A.; Chudnovsky, Eugene M. arXiv https://doi.org/10.48550/arxiv.1906.09202	text	January 2019
Field-induced pseudo-skyrmion phase in the antiferromagnetic kagome lattice Villalba, M. E.; Albarracín, F. A. Gómez; Rosales, H. D. arXiv https://doi.org/10.48550/arxiv.1907.01982	text	January 2019
Tunable skyrmion-skyrmion binding on the surface of a topological insulator Tiwari, Kunal L.; Lavoie, J.; Pereg-Barnea, T. arXiv https://doi.org/10.48550/arxiv.1907.03887	text	January 2019
Universality of annihilation barriers of large magnetic skyrmions in chiral and frustrated magnets Heil, Benjamin; Rosch, Achim; Masell, Jan arXiv https://doi.org/10.48550/arxiv.1907.12174	text	January 2019
Skyrmion Crystal and Phase Transition in Magneto-Ferroelectric Superlattices: Dzyaloshinskii-Moriya Interaction in a Frustrated $J_1-J_2$ Model Sharafullin, Ildus F.; Diep, H. T. arXiv https://doi.org/10.48550/arxiv.1912.12337	text	January 2019

Similar Records

Investigation of the Dzyaloshinskii-Moriya interaction and room temperature skyrmions in W/CoFeB/MgO thin films and microwires

Journal Article · Thu Jul 13 00:00:00 EDT 2017 · Applied Physics Letters · OSTI ID:1249058

Jaiswal, S.; Litzius, K.; Lemesh, I.; +10 more

Room-Temperature Skyrmions in an Antiferromagnet-Based Heterostructure

Journal Article · Fri Dec 22 00:00:00 EST 2017 · Nano Letters · OSTI ID:1249058

Yu, Guoqiang; Jenkins, Alec; Ma, Xin; +13 more

Electronic structure and the origin of the Dzyaloshinskii-Moriya interaction in MnSi

Journal Article · Mon May 02 00:00:00 EDT 2016 · Physical Review B · OSTI ID:1249058

Satpathy, S.; Shanavas, K. V.

Related Subjects

36 MATERIALS SCIENCE

Title: Ginzburg-Landau theory for skyrmions in inversion-symmetric magnets with competing interactions

Citation Formats

References (65)

Cited By (44)

Similar Records

Related Subjects