Chiral magnets are an emerging class of topological matter harboring localized and topologically protected vortex-like magnetic textures called skyrmions, which are currently under intense scrutiny as an entity for information storage and processing. Here, on the level of micromagnetics we rigorously show that chiral magnets can not only host skyrmions but also antiskyrmions as least energy configurations over all non-trivial homotopy classes. We derive practical criteria for their occurrence and coexistence with skyrmions that can be fulfilled by (110)-oriented interfaces depending on the electronic structure. Relating the electronic structure to an atomistic spin-lattice model by means of density functional calculations and minimizing the energy on a mesoscopic scale by applying spin-relaxation methods, we propose a double layer of Fe grown on a W(110) substrate as a practical example. We conjecture that ultra-thin magnetic films grown on semiconductor or heavy metal substrates with C 2v symmetry are prototype classes of materials hosting magnetic antiskyrmions.

Magnets without inversion symmetry are a prime example of a solid-state system featuring topological solitons on the nanoscale, and a promising candidate for novel spintronic applications. Magnetic chiral skyrmions are localized vortex-like structures, which are stabilized by antisymmetric exchange interaction, the so-called Dzyaloshinskii-Moriya interaction. In continuum theories, the corresponding energy contribution is, in contrast to the classical Skyrme mechanism from nuclear physics, of linear gradient dependence and breaks the chiral symmetry. In the simplest possible case of a ferromagnetic energy in the plane, including symmetric and antisymmetric exchange and Zeeman interaction, we show that the least energy in a class of fields with unit topological charge is attained provided the Zeeman field is sufficiently large.

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We investigate the magnetization dynamics in soft ferromagnetic films with small damping. In this case, the gyrotropic nature of Landau-Lifshitz-Gilbert dynamics and the shape anisotropy effects from stray-field interactions effectively lead to a wave-type dynamics for the in plane magnetization. We apply this result to study the motion of Néel walls in thin films and prove the existence of a traveling wave solution under a small constant forcing.

Abstract. This paper is concerned with the analysis of a numerical algorithm for the approximate solution of a class of nonlinear evolution problems that arise as L 2 gradient flow for the Modica-Mortola regularization of the functionalHere γ is the interfacial energy per unit length or unit area, T d is the flat torus in R d , and σ is a nonnegative Fourier multiplier, that is continuous on R d , symmetric in the sense that σ(ξ) = σ(−ξ) for all ξ ∈ R d and that decays to zero at infinity. Such functionals feature in mathematical models of pattern-formation in micromagnetics and models of diblock copolymers. The resulting evolution equation is discretized by a Fourier spectral method with respect to the spatial variables and a modified Crank-Nicolson scheme in time. Optimal-order a priori bounds are derived on the global error in the ∞ (0, T ; L 2 (T d )) norm.

We prove existence, uniqueness and asymptotics of global smooth solutions for the Landau-Lifshitz-Gilbert equation in dimension n ≥ 3, valid under a smallness condition of initial gradients in the L n norm. The argument is based on the method of moving frames that produces a covariant complex Ginzburg-Landau equation, and a priori estimates that we obtain by the method of weighted-in-time norms as introduced by Fujita and Kato.

We examine lower order perturbations of the harmonic map problem from R 2 to S 2 including chiral interaction in form of a helicity term that prefers modulation, and a potential term that enables decay to a uniform background state. Energy functionals of this type arise in the context of magnetic systems without inversion symmetry. In the almost conformal regime, where these perturbations are weighted with a small parameter, we examine the existence of relative minimizers in a non-trivial homotopy class, so-called chiral skyrmions, strong compactness of almost minimizers, and their asymptotic limit. Finally we examine dynamic stability and compactness of almost minimizers in the context of the Landau-Lifshitz-Gilbert equation including spin-transfer torques arising from the interaction with an external current.

We establish the existence of partially regular weak solutions for the Landau-Lifshitz equation in three space dimensions for smooth initial data of finite Dirichlet energy. The construction is based on Ginzburg-Landau approximation. The new key ingredient is a nonlocal representation formula for the penalty term that permits us to take advantage of the special trilinear structure of the limiting nonlinearity.