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Strings and skyrmions on domain walls

Vladimir Bychkov

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

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Michael Kreshchuk

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

Department of Physics, Tufts University, Medford, MA 02155, USA

E-mail Address: kreshchu@physics.umn.edu

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, and

Evgeniy Kurianovych

School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA

E-mail Address: kuria014@umn.edu

Corresponding author.

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https://doi.org/10.1142/S0217751X18501117Cited by:6 (Source: Crossref)

Abstract

We address a simple model allowing the existence of domain walls with orientational moduli localized on them. Within this model, we discuss an analytic solution and explore it in the context of previously known results. We discuss the existence of one-dimensional domain walls localized on two-dimensional ones, and construct the corresponding effective action. In the low-energy limit, which is the $𝕆 (3)$ sigma-model, we discuss the existence of skyrmions localized on domain walls, and provide a solution for a skyrmion configuration, based on an analogy with instantons. We perform symmetry analysis of the initial model and of the low-energy theory on the domain wall worldvolume.

Keywords:

PACS: 11.10.Lm, 11.10.Nx, 11.27.+d

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References

1. A. Hanany and D. Tong, J. High Energy Phys. 0307, 037 (2003), arXiv:hep-th/0306150. Web of Science, ADS, Google Scholar
2. R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi and A. Yung, Nucl. Phys. B 673, 187 (2003), arXiv:hep-th/0307287. Web of Science, ADS, Google Scholar
3. M. Shifman and A. Yung, Phys. Rev. D 70, 045004 (2004), arXiv:hep-th/0403149. Web of Science, ADS, Google Scholar
4. E. Witten, Nucl. Phys. B 249, 557 (1985). Web of Science, ADS, Google Scholar
5. M. Shifman, Phys. Rev. D 87, 025025 (2013), arXiv:1212.4823 [hep-th]. Web of Science, ADS, Google Scholar
6. M. Shifman and E. Kurianovych, Int. J. Mod. Phys. A 29, 1450193 (2014), arXiv:1407.7144 [hep-th]. Link, Web of Science, Google Scholar
7. V. A. Gani, M. A. Lizunova and R. V. Radomskiy, J. High Energy Phys. 04, 043 (2016), arXiv:1601.07954 [hep-th]. ADS, Google Scholar
8. V. A. Gani, M. A. Lizunova and R. V. Radomskiy, J. Phys.: Conf. Ser. 675, 012020 (2016), arXiv:1602.04446 [hep-th]. Google Scholar
9. S. Monin, M. Shifman and A. Yung, Phys. Rev. D 88, 025011 (2013), arXiv:1305.7292 [hep-th]. Web of Science, ADS, Google Scholar
10. R. Rajaraman, Solitons and Instantons (Elsevier, Amsterdam, 1996). Google Scholar
11. R. Auzzi, M. Shifman and A. Yung, Phys. Rev. D 74, 045007 (2006), arXiv:hep-th/0606060. Web of Science, ADS, Google Scholar
12. M. Shifman, Advanced Topics in Quantum Field Theory (Cambridge University Press, 2012). Google Scholar
13. M. Nitta, Phys. Rev. D 87, 025013 (2013), arXiv:1210.2233 [hep-th]. Web of Science, ADS, Google Scholar
14. M. Nitta, Nucl. Phys. B 872, 1 (2013), arXiv:1211.4916 [hep-th]. Web of Science, Google Scholar
15. M. Nitta, Phys. Rev. D 86, 125004 (2012), arXiv:1207.6958 [hep-th]. Web of Science, ADS, Google Scholar
16. M. Nitta, Phys. Rev. D 92, 045010 (2015), arXiv:1503.02060 [hep-th]. Web of Science, ADS, Google Scholar
17. S. B. Gudnason and M. Nitta, Phys. Rev. D 89, 085022 (2014), arXiv:1403.1245 [hep-th]. Web of Science, ADS, Google Scholar
18. A. Kudryavtsev, B. Piette and W. J. Zakrzewski, Nonlinearity 11, 4 (1998), arXiv:hep-th/9709187. Web of Science, Google Scholar
19. Y. Zhou and M. Ezawa, Nat. Commun. 5, 4652 (2014), arXiv:1404.3350 [cond-mat.str-el]. Web of Science, ADS, Google Scholar
20. G. Seibold, Phys. Rev. B 58, 15520 (1998), arXiv:cond-mat/9809113. Web of Science, ADS, Google Scholar
21. P. Jennings and P. Sutcliffe, J. Phys. A 46, 465401 (2013), arXiv:1305.2869 [hep-th]. Google Scholar
22. N. Blyankinshtein, Phys. Rev. D 93, 065030 (2016), arXiv:1510.07935 [hep-th]. Web of Science, ADS, Google Scholar
23. M. Ezawa, Phys. Rev. Lett. 105, 197202 (2010), arXiv:1007.4048 [cond-mat.str-el]. Web of Science, ADS, Google Scholar
24. U. Parts, E. V. Thuneberg, G. E. Volovik, J. H. Koivuniemi, V. M. H. Ruutu, M. Heinila, J. M. Karimäki and M. Krusius, Phys. Rev. Lett. 72, 3839 (1994). Web of Science, ADS, Google Scholar
25. M. T. Heinila and G. E. Volovik, Phys. B: Condens. Matter 210, 300 (1995). Web of Science, ADS, Google Scholar
26. H. Watanabe and H. Murayama, Phys. Rev. Lett. 112, 191804 (2014), arXiv:1401.8139 [hep-th]. Web of Science, ADS, Google Scholar
27. N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka and R. Wiesendanger, Science 341, 6146 (2013). Web of Science, Google Scholar
28. U. K. Rossler, A. N. Bogdanov and C. Pfleiderer, Nature 442, 797 (2006). Web of Science, ADS, Google Scholar
29. X. Zhang, M. Ezawa and Y. Zhou, Sci. Rep. 5, 9400 (2015), arXiv:1410.3086 [cond-mat.mes-hall]. Web of Science, Google Scholar
30. Y. Zhou, E. Iacocca, A. Awad, R. K. Dumas, F. C. Zhang, H. B. Braun and J. Akerman, Nat. Commun. 6, 8193 (2015). Web of Science, ADS, Google Scholar
31. M. J. Benitez, A. Hrabec, A. P. Mihai, T. A. Moore, G. Burnell, D. McGrouther, C. H. Marrows and S. McVitie, Nat. Commun. 6, 8957 (2015). Web of Science, ADS, Google Scholar
32. O. Heinonen, W. Jiang, H. Somaily, S. G. E. te Velthuis and A. Hoffmann, Phys. Rev. B 93, 094407 (2016), arXiv:1511.04630 [cond-mat.mes-hall]. Web of Science, ADS, Google Scholar
33. O. Boulle et al., Nat. Nanotechnol. 11, 449 (2016). Web of Science, ADS, Google Scholar
34. R. Wiesendanger, Nat. Rev. Mater. 1, 16044 (2016). Web of Science, ADS, Google Scholar
35. N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013). Web of Science, ADS, Google Scholar
36. K.-W. Moon et al., Sci. Rep. 5, 9166 (2015). Web of Science, Google Scholar
37. A. M. Polyakov and A. A. Belavin, JETP Lett. 22, 245 (1975) [Pisma Zh. Eksp. Teor. Fiz. 22, 503 (1975)]. Web of Science, ADS, Google Scholar
38. A. A. Belavin, A. M. Polyakov, A. S. Schwartz and Yu. S. Tyupkin, Phys. Lett. B 59, 85 (1975). Web of Science, ADS, Google Scholar
39. V. A. Novikov, M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Phys. Rep. 116, 103 (1984). Web of Science, ADS, Google Scholar
40. N. D. Vlasii, C. P. Hofmann, F.-J. Jiang and U.-J. Wiese, Phys. Rev. B 86, 155113 (2012), arXiv:1205.3677 [cond-mat.str-el]. Web of Science, ADS, Google Scholar
41. P. Olver, Applications of Lie Groups to Differential Equations, 2nd edn. (Springer, 2000). Google Scholar
42. B. J. Cantwell, Introduction to Symmetry Analysis (Cambridge University Press, 2002). Google Scholar