Magnetic textures with particle properties beyond skyrmions: chiral bobbers, globules, and hopfions

Magnetic crystals with competing interactions allow the existence of localized in space magnetic textures possessing a lot of similarities to ordinary particles meaning that they can move and interact with each other: attract, repel or collide and annihilate.
First, I will discuss the chiral magnets where the competition between the Heisenberg exchange and the Dzyaloshinsky-Moriya interactions leads to the emergence of magnetic skyrmions. Recently we have shown that besides ordinary skyrmion [1], the micromagnetic functional for a 2D chiral magnet, strictly speaking, admits an infinite number of solutions with different topological charges, energies, static and dynamical properties [2,3].
We have shown theoretically [4] and experimentally [5] that in 3D crystals of isotropic chiral magnets besides skyrmion tubes (SkTs) penetrating through the whole sample, there are also other types of solutions, so-called hybrid solitons (HSs) [5]. HS can be thought of as a SkT with one end – chiral bobber [5,6] or two ends – magnetic globule [6], where the ends of the skyrmion tube are magnetic singularities – Bloch points.
In the final part of the talk, I will discuss true 3D to topological magnetic solitons or magnetic hopfions [7,8]. The magnetic hopfions can be thought of as closed SkTs. Such tubes in general have the shape of complex mathematical knots. I will present the micromagnetic functional [8] and magnetic interactions allowing the stability of these objects and discuss some static and dynamic properties of these objects.

[1] A. N. Bogdanov & D. A. Yablonskii, Sov. Phys. JETP 68, 101 (1989).
[2] F. N. Rybakov & N. S. Kiselev, Phys. Rev. B 99, 064437 (2019).
[3] V. Kuchkin, et al., Phys. Rev. B 102, 144422 (2020).
[4] F. N. Rybakov, et al., Phys. Rev. Lett. 115, 117201 (2015).
[5] F. Zheng, et al., Nat. Nanotechnol. 13 451 (2018).
[6] G. P. Müller, et al., Phys. Rev. B 101, 184405 (2020).
[7] http://hopfion.com/
[8] F. N. Rybakov, et al., arXiv:1904.00250.