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Approximate analytic expression for the Skyrmions crystal

Nicolás Grandi

Instituto de Fisica de La Plata - CONICET, Departamento de Fisica - UNLP, C.C. 67, 1900 La Plata, Argentina

E-mail Address: grandi@fisica.unlp.edu.ar

Corresponding author.

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and

Mauricio Sturla

Instituto de Fisica de La Plata - CONICET, Departamento de Fisica - UNLP, C.C. 67, 1900 La Plata, Argentina

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https://doi.org/10.1142/S021797921850008XCited by:1 (Source: Crossref)

Abstract

We find approximate solutions for the two-dimensional nonlinear $Σ$ -model with Dzyalioshinkii–Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.

Keywords:

PACS: 75.10.Hk, 75.70.-i, 12.39.Dc

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References

1. D. C. Wright and N. D. Mermin, Rev. Mod. Phys. 61(2), 385 (1989). Web of Science, ADS, Google Scholar
2. S. Sondhi et al., Phys. Rev. B 47, 16419 (1993). Web of Science, ADS, Google Scholar
3. T.-L. Ho, Phys. Rev. Lett. 81, 742 (1998). Web of Science, ADS, Google Scholar
4. X. Yu et al., Nature 465, 901 (2010). Web of Science, ADS, Google Scholar
5. S. Mühlbauer et al., Science 323, 915 (2009). Web of Science, ADS, Google Scholar
6. S. Heinze et al., Nat. Phys. 7, 713 (2011). Web of Science, Google Scholar
7. C. Pfleiderer, Nat. Phys. 7, 673 (2011). Web of Science, Google Scholar
8. F. Jonietz et al., Science 330, 1648 (2010). Web of Science, ADS, Google Scholar
9. N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013). Web of Science, ADS, Google Scholar
10. J. Sampaio et al., Nat. Nanotechnol. 8, 839 (2013). Web of Science, ADS, Google Scholar
11. R. Tomasello et al., Sci. Rep. 4, 6784 (2014). Web of Science, Google Scholar
12. Y. S. Lin, P. J. Grundy and E. A. Giess, Appl. Phys. Lett. 23, 485 (1973). Web of Science, ADS, Google Scholar
13. T. Okubo, S. Chung and H. Kawamura, Phys. Rev. Lett. 108, 017206 (2012). Web of Science, ADS, Google Scholar
14. I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). Web of Science, ADS, Google Scholar
15. T. Moriya, Phys. Rev. Lett. 4, 228 (1960). Web of Science, ADS, Google Scholar
16. J. H. Han et al., Phys. Rev. B 82, 094429 (2010). Web of Science, ADS, Google Scholar
17. B. Lebech, J. Bernhard and T. Freltoft, J. Phys. Condens. Matter 1, 6105 (1989). Web of Science, ADS, Google Scholar
18. M. Uchida et al., Phys. Rev. B 77, 184402 (2008). Web of Science, ADS, Google Scholar
19. X. Yu et al., Nature Mater. 10, 106 (2011). Web of Science, ADS, Google Scholar
20. H. Wilhelm et al., Phys. Rev. Lett. 107, 127203 (2011). Web of Science, ADS, Google Scholar
21. Y. Ishikawa et al., Solid State Commun. 19, 525 (1976). Web of Science, ADS, Google Scholar
22. Y. Ishikawa and M. Arai, J. Phys. Soc. Jpn. 53, 2726 (1984). ADS, Google Scholar
23. S. Grigoriev et al., Phys. Rev. B 79, 144417 (2009). Web of Science, ADS, Google Scholar
24. B. Lebech et al., J. Magn. Magn. Mater. 140, 119 (1995). Web of Science, ADS, Google Scholar
25. C. Pfleiderer et al., Nature 427, 227 (2004). Web of Science, ADS, Google Scholar
26. M. Janoschek et al., Phys. Rev. B 87, 134407 (2013). Web of Science, ADS, Google Scholar
27. K. Shibata et al., Nat. Nanotechnol. 8, 723 (2013). Web of Science, ADS, Google Scholar
28. J. Beille, J. Voiron and M. Roth, Solid State Commun. 47, 399 (1983). Web of Science, ADS, Google Scholar
29. S. Grigoriev et al., Phys. Rev. B 76, 224424 (2007). Web of Science, ADS, Google Scholar
30. S. Grigoriev et al., Phys. Rev. Lett. 102, 037204 (2009). Web of Science, ADS, Google Scholar
31. Y. Onose et al., Phys. Rev. B 72, 224431 (2005). Web of Science, ADS, Google Scholar
32. A. Bogdanov and D. Yablonskii, Zh. Eksp. Teor. Fiz 95, 182 (1989). Google Scholar
33. A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994). Web of Science, ADS, Google Scholar
34. U. Röler, A. Bogdanov and C. Pfleiderer, Nature 442, 797 (2006). Web of Science, ADS, Google Scholar
35. S. D. Yi et al., Phys. Rev. B 80, 054416 (2009). Web of Science, ADS, Google Scholar
36. J. Zang et al., Phys. Rev. Lett. 107 (2011). Web of Science, Google Scholar