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We present micromagnetic simulations on resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 32 mT coinciding with a transition from Hopfions to magnetic torons. The modes exhibit characteristic amplitudes in frequency space accompanied by unique localization patterns in real space, and are found to be robust to damping around topological features, particularly vortex lines in Hopfions and Bloch points in torons. The marked differences in spin wave spectra between Hopfions, torons and target skyrmions can serve as fingerprints in future experimental validation studies of these novel 3d topological spin textures.
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The study of skyrmion/antiskyrmion motion in magnetic materials is very important in particular for the spintronics applications. In this work, we study the dynamics of isolated skyrmions and antiskyrmions in frustrated magnets driven by magnetic field gradient, using the Landau-Lifshitz-Gilbert simulations on the frustrated classical Heisenberg model on the triangular lattice. A Hall-like motion induced by the gradient is revealed in bulk system, similar to that in the well-studied chiral magnets. More interestingly, our work suggests that the lateral confinement in nano-stripes of the frustrated system can completely suppress the Hall motion and significantly speed up the motion along the gradient direction. The simulated results are well explained by the Thiele theory. It is demonstrated that the acceleration of the motion is mainly determined by the Gilbert damping constant, which provides useful information for finding potential materials for skyrmion-based spintronics.
The influence of temperature on the magnetic-field-driven domain wall (DW) motion is investigated in GdFeCo ferrimagnets with perpendicular magnetic anisotropy (PMA). We find that the depinning field strongly depends on temperature. Moreover, it is also found that the saturation magnetization exhibits a similar dependence on temperature to that of depinning field. From the creep-scaling criticality, a simple relation between the depinning field and the properties of PMA is clearly identified theoretically as well as experimentally. Our findings open a way for a better understanding how the magnetic properties influence on the depinning field in magnetic system and would be valuably extended to depinning studies in other system.
Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search of hopfions in real physical systems is going on for nearly half a century, starting with the seminal work of Faddeev. But so far realizations in solids are missing. Here, we present a theory that identifies magnetic materials featuring hopfions as stable states without the assistance of confinement or external fields. Our results are based on an advanced micromagnetic energy functional derived from a spin-lattice Hamiltonian. Hopfions appear as emergent particles of the classical Heisenberg model. Magnetic hopfions represent three-dimensional particle-like objects of nanometre-size dimensions opening the gate to a new generation of spintronic devices in the framework of a truly three-dimensional architecture. Our approach goes beyond the conventional phenomenological models. We derive material-realistic parameters that serve as concrete guidance in the search of magnetic hopfions bridging computational physics with materials science.
Magnetic skyrmion motion induced by an electric current has drawn much interest because of its application potential in next-generation magnetic memory devices. Recently, unidirectional skyrmion motion driven by an oscillating magnetic field was also demonstrated on large (20 micrometer) bubble domains with skyrmion topology. At smaller length scale which is more relevant to high-density memory devices, we here show by numerical simulation that a skyrmion of a few tens of nanometers could also be driven by high-frequency field oscillations but with the motion direction different from the tilted oscillating field direction. We found that high-frequency field for small size skyrmions could excite skyrmion resonant modes and that a combination of different modes would result in the final skyrmion motion with a helical trajectory. Because this helical motion depends on the frequency of the field, we can control both the speed and the direction of the skyrmion motion, which is a distinguishable characteristic compared with other methods.
Quantization of topological charges determines the various topological spin textures that are expected to play a key role in future spintronic devices. While the magnetic skyrmion with a unit topological charge Q has been extensively studied, spin textures with other integer valued have not been verified well so far. Here, we report the real-space image, creation, and manipulation of a type of multi Q three-dimensional skyrmionic texture, where a circular spin spiral ties a bunch of skyrmion tubes. We define these objects as skyrmion bundles, and show they have arbitrarily integer values Q from negative up to at least 55 in our experiment. These textures behave as quasiparticles in dynamics for the collective motions driven by electric pulses. Similar to the skyrmion, skyrmion bundles with non zero Q exhibit the skyrmion Hall effects with a Hall angle of 62 degree. Of particular interest, the skyrmion bundle with Q = 0 propagates collinearly with respect to the current flow without the skyrmion Hall effect. Our results open a new perspective for possible applications of multi Q magnetic objects in future spintronic devices.
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