Skip to main content
Log in

Skyrmion-(non)crystal structure stabilized by dipolar interaction

  • Original Article
  • Published:
Rare Metals Aims and scope Submit manuscript

Abstract

We report a numerical study on the role of long-range dipolar interaction played on the creation and stabilization of skyrmion-(non)crystal structure in chiral ferromagnetic thin films without any anisotropies, based on a Monte-Carlo simulation method. With the increase of external magnetic field, the microscopic spin configuration is transformed from a spin-spiral stripe or labyrinth structure, depending on the strength of dipolar interaction, into a skyrmion-(non)crystal structure, and then into a skyrmion-gas structure, and finally into a ferromagnetic state. Interestingly, with the increase of dipolar interaction, the skyrmion-crystal structure evolves from a triangular arrangement into a square arrangement with the change of skyrmion shape from circle to square. For larger dipolar interactions, the skyrmion-crystal structure loses the regular arrangements and the skyrmions, remaining topological, exhibit different shapes and sizes and squeeze with each other, whose distributions are analogous to a non-crystal structure. Therefore, different skyrmion-(non)crystal structures are stabilized in different ranges of dipolar interactions, which further promotes the applications of skyrmions as non-volatile information carriers.

Graphical abstract

摘要

我们报道了一项基于蒙特卡洛模拟方法的在无任何各向异性的手性铁磁薄膜体系中, 长程偶极相互作用在斯格明子(非)晶体结构的产生和稳定方面所起的作用的数值研究工作。结果表明, 随着外磁场的增强, 体系微观自旋构型从自旋螺旋条纹结构或迷宫结构, 取决于偶极作用大小, 演变为斯格明子 (非) 晶体结构, 然后转变为斯格明子气体结构, 最终, 演化为铁磁结构。有趣的是, 随着偶极作用的增大, 斯格明子晶体结构会由三角格点的排列方式转变为正方格点, 同时斯格明子的形状也由圆形转变为正方形。在大的偶极作用下, 斯格明子晶体结构失去格点的规则排列方式, 且仍然是拓扑性的斯格明子表现出不同的形状和尺寸, 并彼此挤压在一起, 其结构分布类似于非晶体结构。因此, 我们得出结论, 不同的斯格明子 (非) 晶体结构稳定在不同的偶极作用范围内, 此项工作将进一步推动斯格明子作为非易失性信息载体的应用。

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Fert A, Cros V, Sampaio J. Skyrmions on the track. Nat Nanotech. 2013;8(3):152.

    Article  CAS  Google Scholar 

  2. Woo S, Litzius K, Krüger B, Im MY, Caretta L, Richter K, Mann M, Krone A, Reeve RM, Weigand M, Agrawal P, Lemesh I, Mawass MA, Fischer P, Kläui M, Beach GSD. Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets. Nat Mater. 2016;15(5):501.

    Article  CAS  Google Scholar 

  3. Jiang W, Chen G, Liu K, Zang J, te Velthuis SGE, Hoffmann A. Skyrmions in magnetic multilayers. Phys Rep. 2017;704:1.

    Article  Google Scholar 

  4. Zhang X, Zhou Y, Song KM, Park TE, Xia J, Ezawa M, Liu X, Zhao W, Zhao G, Woo S. Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications. J Phys Condens Matter. 2020;32(14):143001.

    Article  CAS  Google Scholar 

  5. Belavin AA, Polyakov AM. Metastable states of two-dimensional isotropic ferromagnets. JETP Lett. 1975;22:245.

    Google Scholar 

  6. Nagaosa N, Tokura Y. Topological properties and dynamics of magnetic skyrmions. Nat Nanotech. 2013;8(12):899.

    Article  CAS  Google Scholar 

  7. Neubauer A, Pfleiderer C, Binz B, Rosch A, Ritz R, Niklowitz PG, Böni P. Topological hall effect in the a phase of MnSi. Phys Rev Lett. 2009;102(18):186602.

    Article  CAS  Google Scholar 

  8. Qin PX, Yan H, Wang XN, Feng ZX, Guo HX, Zhou XR, Wu HJ, Zhang X, Leng ZGG, Chen HY, Liu ZQ. Noncollinear spintronics and electric-field control: a review. Rare Met. 2020;39(2):95.

    Article  CAS  Google Scholar 

  9. Bogdanov AN, Yablonskii DA. Thermodynamically stable ‘vortices’ in magnetically ordered crystals. The mixed state of magnets. Sov Phys JETP. 1989;68:101.

    Google Scholar 

  10. Mühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Böni P. Skyrmion lattice in a chiral magnet. Science. 2009;323(5916):915.

    Article  Google Scholar 

  11. Dzyaloshinskii IE. Theory of helicoidal structures in antiferromagnets. Sov Phys JETP. 1964;19:960.

    Google Scholar 

  12. Yu XZ, Onose Y, Kanazawa N, Park JH, Han JH, Matsui Y, Nagaosa N, Tokura Y. Real-space observation of a two-dimensional skyrmion crystal. Nature (London). 2010;465(7300):901.

    Article  CAS  Google Scholar 

  13. Wei WS, He ZD, Qu Z, Du HF. Dzyaloshinsky-Moriya interaction (DMI)-induced magnetic skyrmion materials. Rare Met. 2021;40(11):3076.

    Article  CAS  Google Scholar 

  14. Kézsmárki I, Bordács S, Milde P, Neuber E, Eng LM, White JS, Rønnow HM, Dewhurst CD, Mochizuki M, Yanai K, Nakamura H, Ehlers D, Tsurkan V, Loidl A. Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8. Nature Mater. 2015;14(11):1116.

    Article  Google Scholar 

  15. Seki S, Yu XZ, Ishiwata S, Tokura Y. Observation of skyrmions in a multiferroic material. Science. 2012;336(6078):198.

    Article  CAS  Google Scholar 

  16. Wiesendanger R. Nanoscale magnetic skyrmions in metallic films and multilayers: a new twist for spintronics. Nat Rev Mater. 2016;1(7):16044.

    Article  CAS  Google Scholar 

  17. Moriya T. Anisotropic superexchange interaction and weak ferromagnetism. Phys Rev. 1960;120(1):91.

    Article  CAS  Google Scholar 

  18. Heinze S, Bergmann KVON, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blügel S. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat Phys. 2011;7(9):713.

    Article  CAS  Google Scholar 

  19. Bader SD. Colloquium: opportunities in nanomagnetism. Rev Mod Phys. 2006;78(1):1.

    Article  CAS  Google Scholar 

  20. Boulle O, Vogel J, Yang H, Pizzini S, Souza Chaves DDE, Locatelli A, Menteş TO, Sala A, Buda-Prejbeanu LD, Klein O, Belmeguenai M, Roussigné Y, Stashkevich A, Chérif SM, Aballe L, Foerster M, Chshiev M, Auffret S, Miron IM, Gaudin G. Room-temperature chiral magnetic skyrmions in ultrathin magnetic nanostructures. Nat Nanotech. 2016;11(5):449.

    Article  CAS  Google Scholar 

  21. Moreau-Luchaire C, Moutafis C, Reyren N, Sampaio J, Vaz CAF, Horne NVAN, Bouzehouane K, Garcia K, Deranlot C, Warnicke P, Wohlhüter P, George JM, Weigand M, Raabe J, Cros V, Fert A. Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmions at room temperature. Nat Nanotech. 2016;11(5):444.

    Article  CAS  Google Scholar 

  22. Khanh ND, Nakajima T, Yu X, Gao S, Shibata K, Hirschberger M, Yamasaki Y, Sagayama H, Nakao H, Peng L, Nakajima K, Takagi R, Arima T, Tokura Y, Seki S. Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet. Nat Nanotechnol. 2020;15(6):444.

    Article  CAS  Google Scholar 

  23. Utesov OI. Thermodynamically stable skyrmion lattice in a tetragonal frustrated antiferromagnet with dipolar interaction. Phys Rev B. 2021;103(6):064414.

    Article  CAS  Google Scholar 

  24. Komatsu H, Nonomura Y, Nishino M. Phase diagram of the two-dimensional dipolar Heisenberg model with Dzyaloshinskii-Moriya interaction and Ising anisotropy. Phys Rev B. 2021;103(21):214404.

    Article  CAS  Google Scholar 

  25. Lin SZ, Saxena A, Batista CD. Skyrmion fractionalization and merons in chiral magnets with easy-plane anisotropy. Phys Rev B. 2015;91(22):224407.

    Article  Google Scholar 

  26. Sui MX, Zhang ZB, Chi XD, Zhang JY, Hu Y. Dense skyrmion crystal stabilized through interfacial exchange coupling: role of in-plane anisotropy. Front Phys. 2021;16(2):23501.

    Article  Google Scholar 

  27. Zhang ZB, Hu Y. Zero-field skyrmions in FeGe thin films stabilized through attaching a perpendicularly magnetized single-domain Ni layer. Chin Phys B. 2021;30(7):077503.

    Article  CAS  Google Scholar 

  28. Rohart S, Thiaville A. Skyrmion confinement in ultrathin film nanosturctures in the presence Dzyaloshinskii-Moriya interaction. Phys Rev B. 2013;88(18):184422.

    Article  Google Scholar 

  29. Büttner F, Lemesh I, Beach GSD. Theory of isolated magnetic skyrmions: from fundamentals to room temperature applications. Sci Rep. 2018;8(1):4464.

    Article  Google Scholar 

  30. Bogdanov AN, Panagopoulos C. Physical foundations and basic properties of magnetic skyrmions. Nat Rev Phys. 2020;2(9):249.

    Article  Google Scholar 

  31. Lucassen J, Meijer MJ, Jong MCHDE, Duine RA, Swagten HJM, Koopmans B, Lavrijsen R. Stabilizing chiral spin structures via an alternating Dzyaloshinskii-Moriya interaction. Phys Rev B. 2020;102(1):014451.

    Article  CAS  Google Scholar 

  32. Bernand-Mantel A, Muratov CB, Simon TM. Unraveling the role of dipolar versus Dzyaloshinskii-Moriya interactions in stabilizing compact magnetic skyrmions. Phys Rev B. 2020;101(4):045416.

    Article  CAS  Google Scholar 

  33. Nishikawa Y, Hukushima K, Krauth W. Solid-liquid transition of skyrmions in a two-dimensional chiral magnet. Phys Rev B. 2019;99(6):064435.

    Article  CAS  Google Scholar 

  34. Simon E, Palotás K, Rózsa L, Udvardi L, Szunyogh L. Formation of magnetic skyrmions with tunable properties in PdFe bilayer deposited on Ir(111). Phys Rev B. 2014;90(9):094410.

    Article  CAS  Google Scholar 

  35. Ummelen FC, Lichtenberg T, Swagten HJM, Koopmans B. Controlling skyrmion bubble confinement by dipolar interactions. Appl Phys Lett. 2019;115(10):102402.

    Article  Google Scholar 

  36. Lu Q, Hu Y. Temperature dependence of dipole-induced exchange bias. Nanotechnology. 2020;31(30):305703.

    Article  CAS  Google Scholar 

  37. d’Albuquerque e Castro J, Altbir D, Retamal JC, Vargas P. Scaling approach to the magnetic phase diagram of nanosized systems. Phys Rev Lett. 2002;88(23):237202.

    Article  Google Scholar 

  38. Vargas P, Altbir D, d’Albuquerque e Castro J. Fast Monte Carlo method for magnetic nanoparticles. Phys. Rev. B, 2006; 73 (9): 092417

  39. Sasaki M, Matsubara F. Stochastic cutoff method for long-range interacting systems. J Phys Soc Jpn. 2008;77(2):024004.

    Article  Google Scholar 

  40. Yu H, Xiao J, Schultheiss H. Magnetic texture based magnonics. Phys Rep. 2021;905:1.

    Article  CAS  Google Scholar 

  41. Hu Y, Chi XD, Li X, Liu Y, Du A. Creation and annihilation of skyrmions in the frustrated magnets with competing exchange interactions. Sci Rep. 2017;7(1):16079.

    Article  Google Scholar 

Download references

Acknowledgements

This study was financially supported by the National Natural Science Foundation of China (No. 11774045) and the Joint Research Fund Liaoning-Shenyang National Laboratory for Materials Science (No. 20180510008).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong Hu.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sui, MX., Hu, Y. Skyrmion-(non)crystal structure stabilized by dipolar interaction. Rare Met. 41, 3160–3169 (2022). https://doi.org/10.1007/s12598-022-02040-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12598-022-02040-y

Keywords

Navigation