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The lower image shows an over-focused Lorentz TEM image calculated for the above spin texture for an electron beam that is parallel to the z axis. The spin textures are visualized in the form of isosurfaces where m z = 0. Periodic boundary conditions are applied in the x– y plane. The lateral size of the simulated domain is 512 × 512 nm 2. 1) are statically stable states and are therefore fundamentally different from the dynamic antiskyrmions that have been discussed earlier 13, 14, 15.Ī, Micromagnetic simulation of a plate of thickness t = 50 nm of an isotropic chiral magnet that supports a skyrmion, an antiskyrmion, a skyrmion–antiskyrmion pair and a skyrmionium in a perpendicular magnetic field. It is important to note that the isolated antiskyrmion and skyrmion–antiskyrmion pair (Fig. The 3D spin textures are visualized by means of isosurfaces and a standard colour code for spin directions. 1a,b) (for illustrative purposes, the different spin textures are combined in a single simulated domain in an optimal field at which all of them are stable). Figure 1a illustrates statically stable solutions for a skyrmion, an antiskyrmion, a skyrmionium and a representative skyrmion–antiskyrmion pair obtained by micromagnetic calculations (Methods and Extended Data Fig. We begin by checking the stability of such a solution for a film of finite thickness with a three-dimensional (3D) model, taking into account demagnetizing fields. In particular, it was shown that there is a stable solution for a skyrmion antiparticle-an antiskyrmion-which is characterized by opposite chirality in different spatial directions 3. Recent theoretical studies 3, 12 of a 2D model of an isotropic chiral magnet have revealed many intriguing effects. As a result of conical modulations, a cross section of an isolated skyrmion tube resembles a two-dimensional (2D) skyrmion in a tilted ferromagnetic vacuum 11. Skyrmions in isotropic chiral magnets typically take the form of vortex-like tubes or strings, which penetrate through the entire sample thickness.
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In such systems, DMI is predicted to favour skyrmion solutions of fixed chirality 6, in agreement with experimental observations 7, 8, 9, 10.
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Since cubic anisotropy in such crystals is typically negligibly small and, to a first approximation, Heisenberg exchange and DMI are assumed to be isotropic, it is common to refer to them as isotropic chiral magnets. The stability of magnetic skyrmions in B20-type crystals results from competition between Heisenberg exchange and chiral Dzyaloshinskii–Moriya interaction (DMI) 4, 5. Our findings provide a new platform for the fundamental studies of particles and antiparticles based on magnetic solids and open new perspectives for practical applications of thin films of isotropic chiral magnets. Our observations are highly reproducible and are fully consistent with micromagnetic simulations. Here we report the creation and annihilation of skyrmion–antiskyrmion pairs in an exceptionally thin film of the cubic chiral magnet of B20-type FeGe observed using transmission electron microscopy. However, experimental verification of such particle–antiparticle pair production and annihilation processes has been lacking. Theoretically, magnetic topological solitons with opposite values of Q, such as skyrmions 2 and their antiparticles (namely, antiskyrmions), are expected to be able to continuously merge and annihilate 3. A similar behaviour is predicted for magnetic solitons 1-localized spin textures that can be distinguished by their topological index Q. A fundamental property of particles and antiparticles (such as electrons and positrons, respectively) is their ability to annihilate one another.