176
J. Masell and K. Everschor-Sitte
rana modes localize at skyrmions [110] or compound structures of superconducting
vortices and skyrmions [111–113]. This might provide a path to perform the key
operation of topological quantum computing, i.e., braiding of the localized modes
with a non-Abelian statistics, via the manipulation of magnetic textures.
7.7 Conclusion
This book chapter presented an introduction to current-induced dynamics of chiral
magnetic structures. We briefly summarized the basic concepts for deriving a continuum theory of magnetization dynamics in Sect. 7.2 and introduced domain walls,
(anti-)skyrmions, and hopfions as examples for magnetic solitons in Sect. 7.3. In the
main part of this chapter, we focused on the manipulation of magnetic textures by
spin-troques, both due to spin-transfer and spin-orbit mechanisms. We reviewed (i)
selected creation processes for domain walls and skyrmions in Sect. 7.4 and (ii) the
motion of the above solitons in Sect. 7.5 with a particular focus on the generalized
Thiele method. Finally, in Sect. 7.6 we summarized already implemented or theoretically suggested applications of magnetic textures which are manipulated by electric
currents.
The field of spintronics, which explores the interplay of electric currents and
the magnetization, has shown an enormous theoretical and experimental progress
in the past years and a vast variety of possible new routes have emerged, including
antiferromagnetic materials which are not discussed in this chapter. We can look
forward with excitement to the future of current-induced magnetization dynamics,
what new physics and which new quasi-particles will be revealed in the future, and
how spintronics might continue contributing to our everyday life.
Acknowledgements We thank D. R. Rodrigues for fruitful discussions. JM is supported as
an Alexander von Humboldt/JSPS International Research Fellow (Project No. 19F19815). KES
acknowledges funding from the German Research Foundation (DFG) Project No. 320163632
(Emmy Noether), No. 403233384 (SPP 2137 Skyrmionics), No. 268565370 (TRR 173, B12), as
well as from the Emergent AI Center funded by the Carl-Zeiss-Stiftung.
References
1. I.E. Dzyaloshinskii, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958)
2. T. Moriya, Anisotropic Superexchange Interaction and Weak Ferromagnetism. Phys. Rev.
120, 91 (1960)
3. J.C. Slonczewski, Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater.
159, L1–L7 (1996)
4. L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev.
B 54, 9353 (1996)
J. Masell and K. Everschor-Sitte
rana modes localize at skyrmions [110] or compound structures of superconducting
vortices and skyrmions [111–113]. This might provide a path to perform the key
operation of topological quantum computing, i.e., braiding of the localized modes
with a non-Abelian statistics, via the manipulation of magnetic textures.
7.7 Conclusion
This book chapter presented an introduction to current-induced dynamics of chiral
magnetic structures. We briefly summarized the basic concepts for deriving a continuum theory of magnetization dynamics in Sect. 7.2 and introduced domain walls,
(anti-)skyrmions, and hopfions as examples for magnetic solitons in Sect. 7.3. In the
main part of this chapter, we focused on the manipulation of magnetic textures by
spin-troques, both due to spin-transfer and spin-orbit mechanisms. We reviewed (i)
selected creation processes for domain walls and skyrmions in Sect. 7.4 and (ii) the
motion of the above solitons in Sect. 7.5 with a particular focus on the generalized
Thiele method. Finally, in Sect. 7.6 we summarized already implemented or theoretically suggested applications of magnetic textures which are manipulated by electric
currents.
The field of spintronics, which explores the interplay of electric currents and
the magnetization, has shown an enormous theoretical and experimental progress
in the past years and a vast variety of possible new routes have emerged, including
antiferromagnetic materials which are not discussed in this chapter. We can look
forward with excitement to the future of current-induced magnetization dynamics,
what new physics and which new quasi-particles will be revealed in the future, and
how spintronics might continue contributing to our everyday life.
Acknowledgements We thank D. R. Rodrigues for fruitful discussions. JM is supported as
an Alexander von Humboldt/JSPS International Research Fellow (Project No. 19F19815). KES
acknowledges funding from the German Research Foundation (DFG) Project No. 320163632
(Emmy Noether), No. 403233384 (SPP 2137 Skyrmionics), No. 268565370 (TRR 173, B12), as
well as from the Emergent AI Center funded by the Carl-Zeiss-Stiftung.
References
1. I.E. Dzyaloshinskii, A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241–255 (1958)
2. T. Moriya, Anisotropic Superexchange Interaction and Weak Ferromagnetism. Phys. Rev.
120, 91 (1960)
3. J.C. Slonczewski, Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater.
159, L1–L7 (1996)
4. L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev.
B 54, 9353 (1996)