References
- A. Malozemoff and J. Slonzewski, Magnetic Domain Walls in Bubble Materials, Academic, New York (1979).
- A. Hubert and R. Schafer, Magnetic Domains: The Analysis of Magnetic Microstructure, Springer, Berlin (1998).
- T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, and T. Ono, Science 289, 930 (2000). https://doi.org/10.1126/science.289.5481.930
- A. Wachowiak, J. Wiebe, M. Bode, O. Pietzsch, M. Morgenstern, and R. Wiesendanger, Science 298, 577 (2002). https://doi.org/10.1126/science.1075302
- K. Shigeto, T. Okuno, K. Mibu, T. Shinjo, and T. Ono, Appl. Phys. Lett. 80, 4190 (2002). https://doi.org/10.1063/1.1483386
- K.-S. Lee, B.-W. Kang, Y.-S. Yu, and S.-K. Kim, Appl. Phys. Lett. 85, 1568 (2004). https://doi.org/10.1063/1.1784892
- K.-S. Lee, S. Choi, and S.-K. Kim, Appl. Phys. Lett. 87, 192502 (2005). https://doi.org/10.1063/1.2128478
- B. Van Waeyenberge, A. Puzic, H. Stoll, K. W. Chou, T. Tyliszczak, R. Hertel, M. Fahnle, H. Bruckl, K. Rott, G. Reiss, I. Neudecker, D. Weiss, C. H. Back, and G. Schutz, Nature 444, 461 (2006). https://doi.org/10.1038/nature05240
- R. Hertel and C. Schneider, Phys. Rev. Lett. 97, 177202 (2006). https://doi.org/10.1103/PhysRevLett.97.177202
- K. Y. Guslienko, B. A. Ivanov, V. Novosad, Y. Otani, H. Shima, and K. Fukamichi, J. Appl. Phys. 91, 8037 (2002). https://doi.org/10.1063/1.1450816
- M. Buess, R. Hollinger, T. Haug, K. Perzlmaier, U. Krey, D. Pescia, M. R. Scheinfein, D. Weiss, and C. H. Back, Phys. Rev. Lett. 93, 077207 (2004). https://doi.org/10.1103/PhysRevLett.93.077207
- H. Wang and C. E. Campbell, Phys. Rev. B 76, 220407(R) (2007). https://doi.org/10.1103/PhysRevB.76.220407
- R. P. Cowburn, Nature Mater. 6, 255 (2007). https://doi.org/10.1038/nmat1877
- J. Thomas, Nature Nanotechnol. 2, 206 (2007). https://doi.org/10.1038/nnano.2007.92
- K.-S. Lee, M.-W. Yoo, Y.-S. Choi, and S.-K. Kim, Phys. Rev. Lett. 106, 147201 (2011). https://doi.org/10.1103/PhysRevLett.106.147201
- M. Kammerer, M. Weigand, M. Curcic, M. Noske, M. Sproll, A. Vansteenkiste, B. Van Waeyenberge, H. Stoll, G. Woltersdorf, C. H. Back, and G. Schuetz, Nature Commun. 2, 279 (2011). https://doi.org/10.1038/ncomms1277
- R. Wang and X. Dong, Appl. Phys. Lett. 100, 082402 (2012). https://doi.org/10.1063/1.3687909
- M.-W. Yoo, J. Lee, and S.-K. Kim, Appl. Phys. Lett. 100, 172413 (2012). https://doi.org/10.1063/1.4705690
- S.-K. Kim, K.-S. Lee, Y.-S. Yu, and Y.-S. Choi, Appl. Phys. Lett. 92, 022509 (2008). https://doi.org/10.1063/1.2807274
- S. Bohlens, B. Kruger, A. Drews, M. Bolte, G. Meier, and D. Pfannkuche, Appl. Phys. Lett. 93, 142508 (2008). https://doi.org/10.1063/1.2998584
- S. Barman, A. Barman, and Y. Otani, IEEE Trans. Magn. 46, 1342 (2010). https://doi.org/10.1109/TMAG.2010.2040587
- H. Jung, Y.-S. Choi, K.-S. Lee, D.-S. Han, Y.-S. Yu, M.Y. Im, P. Fischer, and S.-K. Kim, ACS Nano 6, 3712 (2012). https://doi.org/10.1021/nn3000143
- D.-S. Han, A. Vogel, H. Jung, K.-S. Lee, M. Weigand, H. Stoll, G. Schutz, P. Fischer, G. Meier, and S.-K. Kim, Sci. Rep. 3, 2262 (2013). https://doi.org/10.1038/srep02262
- T. H. R. Skyrme, Nucl. Phys. 31, 556 (1962). https://doi.org/10.1016/0029-5582(62)90775-7
- A. A. Belavin and A. M. Polyakov, JETP Lett. 22, 245 (1975).
- S. Muhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Boni, Science 323, 915 (2009). https://doi.org/10.1126/science.1166767
- X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Nature 465, 901 (2010). https://doi.org/10.1038/nature09124
- S. Heinze, K. V. Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendager, G. Bihlmayer, and S. Blugel, Nature Physics 7, 713 (2011). https://doi.org/10.1038/nphys2045
- A. Fert, V. Cros, and J. Sampaio, Nature Nanotech. 8, 152 (2013). https://doi.org/10.1038/nnano.2013.29
- I. E. Dzyaloshinskii, J. Phys. Chem. Sol. 4, 241 (1958). https://doi.org/10.1016/0022-3697(58)90076-3
- T. Moriya, Phys. Rev. 120, 91 (1960). https://doi.org/10.1103/PhysRev.120.91
- X. Z. Yu, N. Kanazawa, W. Z. Zhang, T. Nagai, K. Kimoto, Y. Matsui, Y. Onose, and Y. Tokura, Nature Commun. 3, 988 (2012). https://doi.org/10.1038/ncomms1990
- J. Iwasaki, M. Mochizuki, and N. Nagaosa, Nature Nanotech. 8, 742 (2013). https://doi.org/10.1038/nnano.2013.176
- O. Tretiakov and O. Tchernyshyov, Phys. Rev. B 75, 012408 (2007). https://doi.org/10.1103/PhysRevB.75.012408
- E. E. Huber Jr., D. O. Smith, and J. B. Goodenough, J. Appl. Phys. 29, 294 (1958). https://doi.org/10.1063/1.1723105
- The version of the OOMMF code used is 1.2a4. See http://math.nist.gov/oommf.
- L. D. Landau and E. M. Lifshitz, Phys. Z. Sowjetunion 8, 153 (1935).
- T. L. Gilbert, Phys. Rev. 100, 1243 (1955).
- J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996). https://doi.org/10.1016/0304-8853(96)00062-5
- Y.-S. Choi, M.-W. Yoo, K.-S. Lee, Y.-S. Yu, H. Jung, and S.-K. Kim, Appl. Phys. Lett. 96, 072507 (2010). https://doi.org/10.1063/1.3310017
- J.-G. Caputo, Y. Gaididei, F. G. Mertens, and D. D. Sheka, Phys. Rev. Lett. 98, 056604 (2007). https://doi.org/10.1103/PhysRevLett.98.056604
- D. D. Sheka, Y. Gaididei, and F. G. Mertens, Appl. Phys. Lett. 91, 082509 (2007). https://doi.org/10.1063/1.2775036
- Y. Liu, H. He, and Z. Zhang, Appl. Phys. Lett. 91, 242501 (2007). https://doi.org/10.1063/1.2822436
- O. M. Volkov, V. P. Kravchuk, D. D. Sheka, and Y. Gaididei, Phys. Rev. Lett. 84, 052404 (2011).
- Y. Gaididei, O. M. Volkov, V. P. Kravchuk, and D. D. Sheka, Phys. Rev. B 86, 144401 (2012). https://doi.org/10.1103/PhysRevB.86.144401
- B. Binz, A. Vishwanath, Physica B 403, 1336 (2008). https://doi.org/10.1016/j.physb.2007.10.136