The creation and annihilation of magnetic skyrmions are mediated by three dimensional topological defects known as Bloch points. Investigation of such dynamical processes is important both for understanding the emergence of exotic topological spin textures, and for future engineering of skyrmions in technological applications. However, while the annihilation of skyrmions has been extensively investigated in two dimensions, in three dimensions the phase transitions are considerably more complex. We report field-dependent experimental measurements of metastable skyrmion lifetimes in an archetypal chiral magnet, revealing two distinct regimes. Comparison to supporting three-dimensional geodesic nudged elastic band simulations demonstrates that these correspond to skyrmion annihilation into either the helical or conical states, each exhibiting a different transition mechanism. The results highlight that the lowest energy magnetic configuration of the system plays a crucial role when considering the emergence of topological spin structures via defect-mediated dynamics, and their stability in future devices.
A skyrmion crystal has internal degrees of freedom in terms of vorticity and helicity, which gives rise to fascinating types of skyrmion phases (Néel, Bloch, and anti-skyrmion). We show how the degeneracy lifting in tetragonal skyrmion crystals occurs in centrosymmetric itinerant magnets by focusing on microscopic interactions through the Fermi surface instability. We demonstrate that four types of skyrmion crystals can be realized according to the signs of the anisotropic Ruderman-Kittel-Kasuya-Yosida interaction, which are sensitive to band structures, electron fillings, atomic orbitals, and…
We present a microscopic electronic description of how antiskyrmions can be stabilized in a Dresselhaus spin-orbit coupled magnetic metal. Furthermore, we show that the antiskyrmions can be tuned into Bloch skyrmions via a change in sign of hopping integral. The results are based on the state of the art hybrid Monte Carlo simulations. Origin of such topological textures is understood via an effective spin-only model. Our results uncover a novel connection between two very distinct topological spin textures of immense current interest, and present a microscopic explanation of skyrmion formation…
The influence of the geometrical curvature of chiral magnetic films on the static and dynamic properties of hosted skyrmions are studied theoretically. We predict the effects of the curvature-induced drift of skyrmions under the action of the curvature gradients without any external stimuli. The strength of the curvature-induced driving force essentially depends on the skyrmion type, Neel or Bloch, while the trajectory of motion is determined by the type of magnetic ordering: ferro- or antiferromagnetic. When moving on the surface, skyrmions undergo deformations that depend on the type of skyr…
Magnetic skyrmions are whirls in the magnetization whose topological winding number promises stability against thermal fluctuations and defects. They can only decay via singular spin configurations. We analyze the corresponding energy barriers of skyrmions in a magnetic monolayer for two distinct stabilization mechanisms, i.e., Dzyaloshinskii-Moriya interaction (DMI) and competing interactions. Based on our numerically calculated collapse paths on an atomic lattice, we derive analytic expressions for the saddle point textures and energy barriers of large skyrmions. The sign of the spin stiffne…
The evolution of skyrmion crystal encapsulates skyrmion critical behaviors, such as nucleation, deformation and annihilation. Here, we achieve a tunable evolution of artificial skyrmion crystal in nanostructured synthetic antiferromagnet multilayers, which are comprised of perpendicular magnetic multilayers and nanopatterned arrays of magnetic nanodots. The out-of-plane magnetization hysteresis loops and first-order reversal curves show that the nucleation and annihilation of the artificial skyrmion can be controlled by tuning the diameter of and spacing between the nanodots. Moreover, when th…
Ferromagnets in contact with a topological insulator have become appealing candidates for spintronics due to the presence of Dirac surface states with spin-momentum locking. Because of this bilayer Bi$_2$Se$_3$-EuS structures, for instance, show a finite magnetization at the interface at temperatures well exceeding the Curie temperature of bulk EuS. Here we determine theoretically the effective magnetic interactions at a topological insulator-ferromagnet interface {\it above} the magnetic ordering temperature. We show that by integrating out the Dirac fermion fluctuations an effective Dzyalosh…
Skyrmions are small magnetic quasiparticles, which are uniquely characterized by their topological charge and their helicity. In this Rapid Communication, we show via calculations how both properties can be determined without relying on real-space imaging. The orbital magnetization and topological Hall conductivity measure the arising magnetization due to the circulation of electrons in the bulk and the occurrence of topologically protected edge channels due to the emergent field of a skyrmion crystal. Both observables quantify the topological Hall effect and distinguish skyrmions from antisky…
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 -- localized spin textures that can be distinguished by their topological index $Q$. Theoretically, magnetic topological solitons with opposite values of $Q$, such as skyrmions and their antiparticles -- antiskyrmions -- are expected to be able to merge continuously and to annihilate. However, experimental verification of such particle-antiparticle pair production and annihilation processes has been lacking. Here…
Geometrically frustrated magnets provide abundant opportunities for discovering complex spin textures, which sometimes yield unconventional electromagnetic responses in correlated electron systems. It is theoretically predicted that magnetic frustration may also promote a topologically nontrivial spin state, i.e., magnetic skyrmions, which are nanometric spin vortices. Empirically, however, skyrmions are essentially concomitant with noncentrosymmetric lattice structures or interfacial-symmetry-breaking heterostructures. Here, we report the emergence of a Bloch-type skyrmion state in the frustr…
We report scanning transmission X-ray microscopy of mixed helical and skyrmion magnetic states in thin FeGe lamellae. This imaging of the out-of-plane magnetism allows clear identification of the different magnetic states, and reveals details about the coexistence of helical and skyrmion states. In particular, our data show that finite length helices are continuously deformable down to the size of individual skyrmions and are hence topologically equivalent to skyrmions. Furthermore, we observe transition states between helical and skyrmion states across the thickness of the lamella that are ev…
Broadband microwave spectroscopy has been performed on single-crystalline GaV$_4$S$_8$, which exhibits a complex magnetic phase diagram including cycloidal, Néel-type skyrmion lattice, as well as field-polarized ferromagnetic phases below 13 K. At zero and small magnetic fields two collective modes are found at 5 and 15 GHz, which are characteristic of the cycloidal state in this easy-axis magnet. In finite fields, entering the skyrmion lattice phase, the spectrum transforms into a multi-mode pattern with absorption peaks near 4, 8, and 15 GHz. The spin excitation spectra in GaV$_4$S$_8$ and t…
Multiple intriguing phenomena have recently been discovered in tetragonal Heusler compounds, where $D_{2d}$ symmetry sets a unique interplay between Dzyaloshinskii-Moriya (DM) and magnetic dipolar interactions. In the prototype $D_{2d}$ compound Mn$_{1.4}$PtSn, this has allowed the stabilization of exotic spin textures such as first-reported anti-skyrmions or elliptic Bloch-type skyrmions. While less attention has so far been given to the low-field spiral state, this remains extremely interesting as a simplest phase scenario on which to investigate the complex hierarchy of magnetic interaction…
Magnetic skyrmions are novel topological spin textures on the nanoscale, and significant efforts have been taken to improve their zero-field density at room temperature (RT). In this work, we reported an approach of improving zero-field skyrmion density in [Pt/Co/Fe/Ir]2 multilayers at RT by using the first-order reversal curve (FORC) technique. Firstly, we investigated the nucleation and annihilation mechanism of magnetic skyrmions using polar magneto-optical Kerr effect measurement. Secondly, the FORC technique was used to obtain information on the irreversible or reversible behaviors in the…
We theoretically study noncoplanar spin textures in polar magnetic conductors. Starting from the Kondo lattice model with the Rashba spin-orbit coupling, we derive an effective spin model with generalized Ruderman-Kittel-Kasuya-Yosida interactions including the anisotropic and antisymmetric exchange interactions. By performing simulated annealing for the effective model, we find that a vortex crystal of Néel type is stabilized even in the absence of a magnetic field. Moreover, we demonstrate that a Bloch-type vortex crystal, which is usually associated with the Dresselhaus spin-orbit coupling,…
We report simulation results of skyrmions on fluctuating 2D lattices, where the vertices ${\bf r}_i (\in {\bf R}^3)$ are treated as a dynamical variable and, hence, there is no crystalline structure. On the fluctuating surfaces, an external magnetic field perpendicular to the surface, Dzyaloshinskii-Moriya and ferromagnetic interactions are assumed in addition to the Helfrich-Polyakov Hamiltonian for membranes. The surface (or frame) tension $τ$ is calculated under both isotropic and uniaxial strain conditions, and this calculation clarifies a non-trivial dependence of $τ$ on the skyrmion, str…
We investigate the skyrmion formation process in nano-structured FeGe Hall-bar devices by measurements of topological Hall effect, which extracts the winding number of a spin texture as an emergent magnetic field. Step-wise profiles of topological Hall resistivity are observed in the course of varying the applied magnetic field, which arise from instantaneous changes in the magnetic nano-structure such as creation, annihilation, and jittering motion of skyrmions. The discrete changes in topological Hall resistivity demonstrate the quantized nature of emergent magnetic flux inherent in each sky…
The current-driven motion of a domain wall (DW) in a ferromagnet with many Bloch lines (BLs) via the spin transfer torque is studied theoretically. It is found that the motion of BLs changes the current-velocity ($j$-$v$) characteristic dramatically. Especially, the critical current density to overcome the pinning force is reduced by the factor of the Gilbert damping coefficient $α$ even compared with that of a skyrmion. This is in sharp contrast to the case of magnetic field driven motion, where the existence of BLs reduces the mobility of the DW.
We introduce a family of models for magnetic skyrmions in the plane for which infinitely many solutions can be given explicitly. The energy defining the models is bounded below by a linear combination of degree and total vortex strength, and the configurations attaining the bound satisfy a first order Bogomol'nyi equation. We give explicit solutions which depend on an arbitrary holomorphic function. The simplest solutions are the basic Bloch and Néel skyrmions, but we also exhibit distorted and rotated single skyrmions as well as line defects, and configurations consisting of skyrmions and ant…
