7 Current-Induced Dynamics of Chiral Magnetic Structures
177
5. I.M. Miron, K. Garello, G. Gaudin, P.J. Zermatten, M.V. Costache, S. Auffret, S. Bandiera,
B. Rodmacq, A. Schuhl, P. Gambardella, Perpendicular switching of a single ferromagnetic
layer induced by in-plane current injection. Nature 476, 189–193 (2011)
6. L. Liu, C.-F. Pai, Y. Li, H.W. Tseng, D.C. Ralph, R.A. Buhrman, Spin-Torque Switching with
the Giant Spin Hall Effect of Tantalum. Science 336, 555–558 (2012)
7. G. Catalan, J. Seidel, R. Ramesh, J.F. Scott, Domain wall nanoelectronics. Rev. Mod. Phys.
84, 119 (2012)
8. A.N. Bogdanov, D.A. Yablonskii, Thermodynamically stable “vortices” in magnetically
ordered crystals. The mixed state of magnets. Zh. Eksp. Teor. Fiz. 95, 178 (1989) [JETP
68, 101 (1989)]
9. A. Fert, N. Reyren, V. Cros, Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017)
10. W. Jiang, G. Chen, K. Liu, J. Zang, S.G. te Velthuis, A. Hoffmann, Skyrmions in magnetic
multilayers. Phys. Rep. 704, 1–49 (2017)
11. K. Everschor-Sitte, J. Masell, R.M. Reeve, M. Kläui, Perspective: Magnetic skyrmions -
Overview of recent progress in an active research field. J. Appl. Phys. 124, 240901 (2018)
12. C. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, T. Ma, S. Mankovsky, T.L.
Monchesky, M. Mostovoy, N. Nagaosa, S.S.P. Parkin, C. Pfleiderer, N. Reyren, A. Rosch, Y.
Taguchi, Y. Tokura, K. von Bergmann, J. Zang, The 2020 Skyrmionics Roadmap. J. Phys. D:
Appl. Phys. 53, 363001 (2020)
13. I.L. Bogolubsky, Three-dimensional topological solitons in the lattice model of a magnet with
competing interactions. Phys. Lett. A 126, 511–514 (1988)
14. P. Sutcliffe, Skyrmion knots in frustrated magnets. Phys. Rev. Lett. 118, 247203 (2017)
15. S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G.
Bihlmayer, S. Blügel, Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011)
16. P. Bak, M.H. Jensen, Theory of helical magnetic structures and phase transitions in MnSi and
FeGe. J. Phys. C: Solid State Phys. 13, L881 (1980)
17. M. Hoffmann, B. Zimmermann, G.P. Müller, D. Schürhoff, N.S. Kiselev, C. Melcher, S.
Blügel, Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii-Moriya interactions. Nat. Commun. 8, 308 (2017)
18. R.R. Birss, Symmetry and magnetism (North-Holland Pub, Co, 1964)
19. K.M.D. Hals, K. Everschor-Sitte, Twists in ferromagnetic monolayers with trigonal prismatic
symmetry. Phys. Rev. B 99, 104422 (2019)
20. I.A. Ado, A. Qaiumzadeh, A. Brataas, M. Titov, Chiral ferromagnetism beyond Lifshitz
invariants. Phys. Rev. B 101, 161403(R) (2020)
21. M.V. Berry, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A
392, 45–57 (1984)
22. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P.G. Niklowitz, P. Böni, Topological
Hall Effect in the A Phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009)
23. M. Lee, W. Kang, Y. Onose, Y. Tokura, N.P. Ong, Unusual Hall Effect Anomaly in MnSi
under Pressure. Phys. Rev. Lett. 102, 186601 (2009)
24. K. Everschor-Sitte, M. Sitte, Real-space Berry phases: Skyrmion soccer (invited). J. Appl.
Phys. 115, 172602 (2014)
25. J. Sampaio, V. Cros, S. Rohart, A. Thiaville, A. Fert, Nucleation, stability and current-induced
motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotechnol. 8, 839–844
(2013)
26. S. Zhang, Z. Li, Roles of nonequilibrium conduction electrons on the magnetization dynamics
of ferromagnets. Phys. Rev. Lett. 93, 127204 (2004)
27. A.P. Malozemoff, Mobility of bubbles with small numbers of Bloch lines. J. Appl. Phys. 44,
5080 (1973)
28. D.R. Rodrigues, Ar. Abanov, J. Sinova, K. Everschor-Sitte, Effective description of domain
wall strings. Phys. Rev. B 97, 134414 (2018)
177
5. I.M. Miron, K. Garello, G. Gaudin, P.J. Zermatten, M.V. Costache, S. Auffret, S. Bandiera,
B. Rodmacq, A. Schuhl, P. Gambardella, Perpendicular switching of a single ferromagnetic
layer induced by in-plane current injection. Nature 476, 189–193 (2011)
6. L. Liu, C.-F. Pai, Y. Li, H.W. Tseng, D.C. Ralph, R.A. Buhrman, Spin-Torque Switching with
the Giant Spin Hall Effect of Tantalum. Science 336, 555–558 (2012)
7. G. Catalan, J. Seidel, R. Ramesh, J.F. Scott, Domain wall nanoelectronics. Rev. Mod. Phys.
84, 119 (2012)
8. A.N. Bogdanov, D.A. Yablonskii, Thermodynamically stable “vortices” in magnetically
ordered crystals. The mixed state of magnets. Zh. Eksp. Teor. Fiz. 95, 178 (1989) [JETP
68, 101 (1989)]
9. A. Fert, N. Reyren, V. Cros, Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017)
10. W. Jiang, G. Chen, K. Liu, J. Zang, S.G. te Velthuis, A. Hoffmann, Skyrmions in magnetic
multilayers. Phys. Rep. 704, 1–49 (2017)
11. K. Everschor-Sitte, J. Masell, R.M. Reeve, M. Kläui, Perspective: Magnetic skyrmions -
Overview of recent progress in an active research field. J. Appl. Phys. 124, 240901 (2018)
12. C. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, T. Ma, S. Mankovsky, T.L.
Monchesky, M. Mostovoy, N. Nagaosa, S.S.P. Parkin, C. Pfleiderer, N. Reyren, A. Rosch, Y.
Taguchi, Y. Tokura, K. von Bergmann, J. Zang, The 2020 Skyrmionics Roadmap. J. Phys. D:
Appl. Phys. 53, 363001 (2020)
13. I.L. Bogolubsky, Three-dimensional topological solitons in the lattice model of a magnet with
competing interactions. Phys. Lett. A 126, 511–514 (1988)
14. P. Sutcliffe, Skyrmion knots in frustrated magnets. Phys. Rev. Lett. 118, 247203 (2017)
15. S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G.
Bihlmayer, S. Blügel, Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713–718 (2011)
16. P. Bak, M.H. Jensen, Theory of helical magnetic structures and phase transitions in MnSi and
FeGe. J. Phys. C: Solid State Phys. 13, L881 (1980)
17. M. Hoffmann, B. Zimmermann, G.P. Müller, D. Schürhoff, N.S. Kiselev, C. Melcher, S.
Blügel, Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii-Moriya interactions. Nat. Commun. 8, 308 (2017)
18. R.R. Birss, Symmetry and magnetism (North-Holland Pub, Co, 1964)
19. K.M.D. Hals, K. Everschor-Sitte, Twists in ferromagnetic monolayers with trigonal prismatic
symmetry. Phys. Rev. B 99, 104422 (2019)
20. I.A. Ado, A. Qaiumzadeh, A. Brataas, M. Titov, Chiral ferromagnetism beyond Lifshitz
invariants. Phys. Rev. B 101, 161403(R) (2020)
21. M.V. Berry, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A
392, 45–57 (1984)
22. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P.G. Niklowitz, P. Böni, Topological
Hall Effect in the A Phase of MnSi. Phys. Rev. Lett. 102, 186602 (2009)
23. M. Lee, W. Kang, Y. Onose, Y. Tokura, N.P. Ong, Unusual Hall Effect Anomaly in MnSi
under Pressure. Phys. Rev. Lett. 102, 186601 (2009)
24. K. Everschor-Sitte, M. Sitte, Real-space Berry phases: Skyrmion soccer (invited). J. Appl.
Phys. 115, 172602 (2014)
25. J. Sampaio, V. Cros, S. Rohart, A. Thiaville, A. Fert, Nucleation, stability and current-induced
motion of isolated magnetic skyrmions in nanostructures. Nat. Nanotechnol. 8, 839–844
(2013)
26. S. Zhang, Z. Li, Roles of nonequilibrium conduction electrons on the magnetization dynamics
of ferromagnets. Phys. Rev. Lett. 93, 127204 (2004)
27. A.P. Malozemoff, Mobility of bubbles with small numbers of Bloch lines. J. Appl. Phys. 44,
5080 (1973)
28. D.R. Rodrigues, Ar. Abanov, J. Sinova, K. Everschor-Sitte, Effective description of domain
wall strings. Phys. Rev. B 97, 134414 (2018)