Formation and annihilation of magnetic skyrmions on a square lattice Heisenberg Ferromagnet: the role played by the pure and random anisotropy configurations

References

• T.H.R. Skyrme, A nonlinear field theory, Proc. R. Soc. Lond. A 260 (1961), pp. 127–138.
   Web of Science ®Google Scholar
• T.H.R. Skyrme, A unified field theory of mesons and baryons, Nuclear Phys. 31 (1962), pp. 556–569.
   Web of Science ®Google Scholar
• A. Bogdanov and A. Hubert, Thermodynamically stable magnetic vortex states in magnetic crystals, J. Magn. Magn. Mater. 138 (1994), pp. 255–269.
   Web of Science ®Google Scholar
• A.N. Bogdanov and D.A. Yablonsky, Thermodynamically stable ‘vortices’ in magnetically ordered crystals. The mixed state of magnets, Sov. Phys. JETP 95 (1989), pp. 178–182.
   Google Scholar
• S. Buhrandt and L. Fritz, Skyrmion lattice phase in three-dimensional chiral magnets from Monte Carlo simulations, Phys. Rev. B 88 (2013), p. 195137.
   Web of Science ®Google Scholar
• S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Böni, Skyrmion lattice in a chiral magnet, Science 323 (2009), pp. 915–919.
   PubMed Web of Science ®Google Scholar
• A. Bauer and C. Pfleiderer, Magnetic phase diagram of MnSi inferred from magnetization and ac susceptibility, Phys. Rev. B 85 (2012), p. 214418.
   Web of Science ®Google Scholar
• A. Bauer, M. Garst, and C. Pfleiderer, Specific heat of the Skyrmion lattice phase and field-induced tricritical point in MnSi, Phys. Rev. Lett. 110 (2013), p. 177207.
   PubMed Web of Science ®Google Scholar
• A. Bauer, A. Neubauer, C. Franz, W. Münzer, M. Garst, and C. Pfleiderer, Quantum phase transitions in single-crystal Mn1−xFexSi and Mn1−xCoxSi: Crystal growth, magnetization, ac susceptibility, and specific heat, Phys. Rev. B 82 (2010), p. 064404.
   Web of Science ®Google Scholar
• X.Z. Yu, Y. Onose, N. Kanazawa, J.H. Park, J.H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Real-space observation of a two-dimensional skyrmion crystal, Nature 465 (2010), pp. 901–904.
   PubMed Web of Science ®Google Scholar
• M. Janoschek, M. Garst, A. Bauer, P. Krautscheid, R. Georgii, P. Böni, and C. Pfleiderer, Fluctuation-induced first-order phase transition in Dzyaloshinskii–Moriya helimagnets, Phys. Rev. B87 (2013), p. 134407.
   Web of Science ®Google Scholar
• K. Karube, J.S. White, D. Morikawa, C.D. Dewhurst, R. Cubitt, A. Kikkawa, X. Yu, Y. Tokunaga, T. Arima, H.M. Ronnow, Y. Tokura, and Y. Taguchi, Disordered skyrmion phase stabilized by magnetic frustration in a chiral magnet, Sci. Adv. 4 (2018), p. 7043.
   Web of Science ®Google Scholar
• S.X. Huang and C.L. Chien, Extended skyrmion phase in epitaxial FeGe(111) thin films, Phys. Rev. Lett. 108 (2012), p. 267201.
   PubMed Web of Science ®Google Scholar
• D. Kechrakos, A. Patsopoulos, and L. Tzannetou, Magnetic skyrmions in cylindrical ferromagnetic nanostructures with chiral interactions, Phys. Rev. B 102 (2019), p. 054439.
   Web of Science ®Google Scholar
• E. van Walsem, R.A. Duine, J. Lucassen, R. Lavrijsen, and H.J.M. Swagten, Structural transitions of skyrmion lattices in synthetic antiferromagnets, Phys. Rev. B 100 (2019), p. 064402.
   Web of Science ®Google Scholar
• S.D. Yi, S. Onoda, N. Nagaosa, and J.H. Han, Skyrmions and anomalous Hall effect in a Dzyaloshinskii–Moriya spiral magnet, Phys. Rev. B 80 (2009), p. 054416.
   Web of Science ®Google Scholar
• G. Bannasch and W. Selke, Heisenberg antiferromagnets with exchange and cubic anisotropies, J. Phys. Conf. Ser. 200 (2010), p. 022057. Depending on the sign of the cubic anisotropy term, the spins prefer one of the diagonal directions of the lattice. For details, please see.
   Google Scholar
• T. Okubo, S. Chung, and H. Kawamura, Multiple-q states and the skyrmion lattice of the triangular-lattice Heisenberg antiferromagnet under magnetic fields, Phys. Rev. Lett. 108 (2012), p. 017206.
   PubMed Web of Science ®Google Scholar
• A.O. Leonov and M. Mostovoy, Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet, Nature Commun. 6 (2015), p. 8275.
   PubMed Web of Science ®Google Scholar
• H.D. Rosales, D.C. Cabra, and P. Pujol, Three-sublattice skyrmion crystal in the antiferromagnetic triangular lattice, Phys. Rev. B 92 (2015), p. 214439.
   Web of Science ®Google Scholar
• R. Keesman, M. Raaijmakers, A.E. Baerends, G.T. Barkema, and R.A. Duine, Skyrmions in square-lattice antiferromagnets, Phys. Rev. B 94 (2016), p. 054402.
   Web of Science ®Google Scholar
• L. Rózsa, E. Simon, K. Palotás, L. Udvardi, and L. Szunyogh, Complex magnetic phase diagram and skyrmion lifetime in an ultrathin film from atomistic simulations, Phys. Rev. B 93 (2016), p. 024417.
   Web of Science ®Google Scholar
• J. Chen, W.P. Cai, M.H. Qin, S. Dong, X.B. Lu, X.S. Gao, and J.-M. Liu, Helical and skyrmion lattice phases in three-dimensional chiral magnets: Effect of anisotropic interactions, Sci. Rep. 7 (2017), p. 7392.
   PubMed Web of Science ®Google Scholar
• E.A.S. Oliveira, R.L. Silva, R.C. Silva, and A.R. Pereira, Effects of second neighbor interactions on skyrmion lattices in chiral magnets, J. Phys. Condens. Matter 29 (2017), p. 205801.
   PubMed Web of Science ®Google Scholar
• M. Mohylina and M. Zukovic, Emergence of a skyrmion phase in a frustrated Heisenberg antiferromagnet with Dzyaloshinskii–Moriya interaction, Acta Phys. Pol. A 137 (2019), pp. 616–618.
   Web of Science ®Google Scholar
• J. Yu, W. Li, Z. Huang, J. Liang, J. Chen, D. Chen, Z. Hou, and M. Qin, Skyrmion crystals in frustrated Shastry–Sutherland magnets, Phys. Status Solidi. RRL 13 (2019), p. 1900161.
   Google Scholar
• Z. Liu and H. Ian, Ferromagnetic sublattices of antiferromagnetic skyrmion crystals formed in two-dimensional square lattices, Superlattice Microst. 126 (2019), pp. 25–31.
   Web of Science ®Google Scholar
• G. Pradhan, B. Ojha, and S. Bedanta, Effect of random anisotropy in stabilization of skyrmions and antiskyrmions, J. Magn. Magn. Mater. 528 (2021), p. 167805.
   Web of Science ®Google Scholar
• X. Gong, H.Y. Yuan, and X.R. Wang, Current-driven skyrmion motion in granular films, Phys. Rev. B 101 (2020), p. 064421.
   Web of Science ®Google Scholar
• C. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, T. Ma, S. Mankovsky, T.L. Monchesky, M. Mostovoy, N. Nagaosa, S.S.P. Parkin, C. Pfleiderer, N. Reyren, A. Rosch, Y. Taguchi, Y. Tokura, K. von Bergmann, and J. Zang, The 2020 skyrmionics roadmap, J. Phys. D: Appl. Phys.53 (2020), p. 363001.
   Web of Science ®Google Scholar
• J. Liang, W. Wang, H. Du, A. Hallal, K. Garcia, M. Chshiev, A. Fert, and H. Yang, Very large Dzyaloshinskii–Moriya interaction in two-dimensional Janus manganese dichalcogenides and its application to realize skyrmion states, Phys. Rev. B 101 (2020), p. 184401.
   Web of Science ®Google Scholar
• M. Böttcher, S. Heinze, S. Egorov, J. Sinova, and B. Dupé, B-T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo, New J. Phys. 20 (2018), p. 103014.
   Web of Science ®Google Scholar
• G. Yin, Y. Li, L. Kong, R.K. Lake, C.L. Chien, and J. Zang, Topological charge analysis of ultrafast single skyrmion creation, Phys. Rev. B 93 (2016), p. 174403.
   Web of Science ®Google Scholar
• A.E. Clark, High-field magnetization and coercivity of amorphous rare-earth- Fe2 alloys, Appl. Phys. Lett.23 (1973), pp. 642–644.
   Web of Science ®Google Scholar
• J.J. Rhyne, J.H. Schelleng, and N.C. Koon, Anomalous magnetization of amorphous TbFe2, GdFe2 and YFe2, Phys. Rev. B 10 (1974), pp. 4672–4679.
   Web of Science ®Google Scholar
• M.E.J. Newman and G.T. Barkema, Monte Carlo Methods in Statistical Physics, Oxford University Press, 2001.
   Google Scholar
• V. Kapitan, E. Vasiliev, and A. Perzhu, Computer simulation of magnetic Skyrmions, Proceedings 46 (2020), p. 6.
   Google Scholar
• H.T. Diep, S. El Hog, and A. Bailly-Reyre, Skyrmion crystals: Dynamics and phase transition, AIP. Adv. 8 (2018), p. 055707.
   Web of Science ®Google Scholar
• M.C. Ambrose and R.L. Stamps, Melting of hexagonal skyrmion states in chiral magnets, New J. Phys. 15 (2013), p. 053003.
   Web of Science ®Google Scholar
• S. von Malottki, B. Dupé, P.F. Bessarab, A. Delin, and S. Heinze, Enhanced skyrmion stability due to exchange frustration, Sci. Rep. 7 (2017), p. 12299.
   PubMed Web of Science ®Google Scholar
• M. Fattouhi, M.Y. El Hafidi, and M. El Hafidi, Formation of a hexagonal skyrmion lattice assisted by magnetic field in CeFeB ultrathin films, J. Magn. Magn. Mater. 495 (2020), p. 165870.
   Web of Science ®Google Scholar
• A. Siemens, Y. Zhang, J. Hagemeister, E.Y. Vedmedenko, and R. Wiesendanger, Minimal radius of magnetic skyrmions: Statics and dynamics, New J. Phys. 18 (2018), p. 045021.
   Web of Science ®Google Scholar
• A. Fert, V. Cros, and J. Sampaio, Skyrmions on the track, Nature Nanotech 8 (2013), p. 152–156.
   PubMed Web of Science ®Google Scholar
• X.S. Wang, H.Y. Yuan, and X.R. Wang, A theory on skyrmion size, Commun. Phys. 1 (2018), p. 31.
   Web of Science ®Google Scholar