Turning a chiral skyrmion inside out

Abstract

The stability of two-dimensional chiral skyrmions in a tilted magnetic field is studied. It is shown that by changing the direction of the field and its magnitude, one can continuously transform chiral skyrmion into a skyrmion with opposite polarity and vorticity. This turned inside out skyrmion can be considered as an antiparticle for ordinary axisymmetric skyrmion. For any tilt angle of the magnetic field, there is a range of its absolute values where two types of skyrmions may coexist. In a tilted field the potentials for inter-skyrmion interactions are characterized by the presence of local minima suggesting attractive interaction between the particles. The potentials of inter-particle interactions also have so-called fusion channels allowing either annihilation of two particles or the emergence of a new particle. The presented results are general for a wide class of magnetic crystals with both easy-plane and easy-axis anisotropy.Chiral magnetic skyrmions (Sks) are localized magnetic vortices [1], which can be stabilized in materials with competing the Heisenberg exchange and the Dzyaloshinskii-Moriya interaction (DMI) [2, 3]. In the most general case, the stability of chiral Sks requires the presence of a potential energy term as the interaction with an external magnetic field and/or the magnetocrystalline anisotropy. The latter plays an important role in the case of thin films and multilayer systems [4]. Such systems are typically well-described by the twodimensional (2D) model of chiral magnet, which is also often utilized for so-called quasi-2D crystals -bulk crystals of particular symmetry allowing DMI between spins contained in specific crystallographic planes, for instance GaV 4 S 8 alloy [5]. The majority of studies associated with the stability of Sks [6][7][8][9][10][11][12], their interactions, dynamics and transport properties, have been carried out for the regime when the external magnetic field is applied perpendicularly to the plane of the 2D magnet. The number of studies related to the case of a tilted field is limited [13][14][15][16][17][18][19][20][21]. These publications are mainly related to Sk lattices, their dynamical properties [13][14][15] and phase transitions [16][17][18][19][20][21]. The properties of isolated Sks have been partially discussed in Refs. [16,19]. In this letter, we report a number of fundamentally new phenomena occurring upon applyinga tiltedmagnetic fieldto chiral Sks.We estimate the stability of Sks by means of a direct energy minimization of the micromagnetic functional [1]:where n = M(r)/M s is a continuous unit vector field, M s is a saturation magnetization, A and D are the micromagnetic constants for isotropic exchange and DMI, respectively. It is assumed that magnetization remains homogeneous along the thickness, t. The DMI term w(n) is defined by combinations of Lifshitz invariants, ΛThe re-sults presented in this letter are valid for a wide class of chiral magnets of different crystal symmetries with: Néeltype modulations [22][23][24] The last term in (1) r...

Magnetic particle-antiparticle creation and annihilation

“…A fundamental property of particles and antiparticles, such as electrons and positrons, is their ability to annihilate one another. Similar behavior is predicted for magnetic solitons 1 -localized spin textures that can be distinguished by their topological index Q. Theoretically, magnetic topological solitons with opposite values of Q, such as skyrmions 2 and their antiparticlesantiskyrmions -are expected to be able to merge continuously and to annihilate 3 . However, experimental verification of such particle-antiparticle pair production and annihilation processes has been lacking.…”

Geometry and symmetry in skyrmion dynamics

“…It parametrises the unoriented direction of the eigenvector for λ 1 relative to the x-axis. Under rotation of a configuration by ϕ according to (7), the angle ψ shifts to ψ + ϕ, see again Fig. 2.…”

“…The Lifshitz invariant in crystals with point group D 2d has rotational symmetry 1 like the invariants in Neel and Bloch-type systems. In this case, however, the rotation in spin space should have the opposite direction to that given in (7). Since the dispersion tensor Γ is invariant under rotations in spin space, the transformation rule (8) of Γ is unchanged and the results of our theoretical analysis are fully applicable for solitons in these systems 17 when accompanied by the exchange of particles and anti-particles (Q → −Q).…”

“…2a, b. When the transformation (7) with ϕ = 2π/k is trivial for some positive integers k, so that n = n (possibly up to translation), we say that the spin texture has a rotational symmetry of order k s = max(k).…”

“…Only recently, new classes of skyrmion solutions with diverse morphology and arbitrary topological charge have been reported. [5][6][7][8]26 The static properties of so-called skyrmion bags 5,6 and skyrmions with chiral kinks 7,8 belonging to these newly discovered classes of skyrmions are now quite well understood.…”