Spin-Hall nano-oscillator with oblique magnetization and Dzyaloshinskii-Moriya interaction as generator of skyrmions and nonreciprocal spin-waves
A. GiordanoRoman VerbaRoberto ZivieriAntonino LaudaniVito PuliafitoG. GubbiottiRiccardo TomaselloGiulio SiracusanoB. AzzerboniMario CarpentieriA. N. SlavinGiovanni Finocchio
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Abstract Spin-Hall oscillators (SHO) are promising sources of spin-wave signals for magnonics applications, and can serve as building blocks for magnonic logic in ultralow power computation devices. Thin magnetic layers used as “free” layers in SHO are in contact with heavy metals having large spin-orbital interaction, and, therefore, could be subject to the spin-Hall effect (SHE) and the interfacial Dzyaloshinskii-Moriya interaction ( i -DMI), which may lead to the nonreciprocity of the excited spin waves and other unusual effects. Here, we analytically and micromagnetically study magnetization dynamics excited in an SHO with oblique magnetization when the SHE and i -DMI act simultaneously. Our key results are: (i) excitation of nonreciprocal spin-waves propagating perpendicularly to the in-plane projection of the static magnetization; (ii) skyrmions generation by pure spin-current; (iii) excitation of a new spin-wave mode with a spiral spatial profile originating from a gyrotropic rotation of a dynamical skyrmion. These results demonstrate that SHOs can be used as generators of magnetic skyrmions and different types of propagating spin-waves for magnetic data storage and signal processing applications.Keywords:
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Abstract Skyrmions are important in quantum field theory and information technology for being topological solitons and for their attractive applications. Magnetic skyrmions are believed to be circular and stripy spin textures accompanied skyrmion crystals (SkXs) termed spiral/helical/cycloid orders have zero skyrmion number. Here we show that those stripy spin textures are skyrmions, siblings of circular skyrmions in SkXs and cousins of isolated circular skyrmions. Various irregular morphologies are the nature structures of skyrmions in the ground states. At the extreme of one skyrmion in the whole sample, the skyrmion is a ramified stripe. As the skyrmion number density increases, skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to circular objects. At a high skyrmion number density, SkXs are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open an avenue for manipulating skyrmions.
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The novel physics and promising applications of magnetic skyrmions in helimagnets have attracted great attentions in the past years. Magnetic skyrmions are topologically protected spin textures in which the local moments on a two dimensional lattice point in all directions with a topologically nontrivial mapping to the unit sphere. The skyrmion radius, ranging from about 3 nm to 100 nm, is controlled by strength of the Dzyaloshinskii-Moriya interaction induced by inversion symmetry breaking. Furthermore, a skyrmion enjoys extra stability as a stable state under various temperatures, and can be driven by a tiny electric current or temperature gradient. These properties suggest future processing applications exploiting such topological spin texture as the information carrier. To this end, single bit operation must be achieved. However, up to now, most skyrmions are observed in the crystalline form, which forbids skyrmion-based applications. It is thus a challenge to realize individual skyrmion states. In this talk, I would present our recent theoretical and experimental efforts in achieving this goal.
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Abstract Size is a fundamental quantity of magnetic skyrmions. A magnetic skyrmion can be a local circular object and in an isolated form. A skyrmion can also coexist with a group of its siblings in a condensed phase. Each skyrmion in a condensed phase takes a stripe shape at low skyrmion density and a circular shape at high skyrmion density. Skyrmions at high density form a skyrmion crystal (SkX). So far, skyrmion size in an SkX has not been seriously studied. Here, by using a generic chiral magnetic film, it is found that skyrmion size in an SkX has a different parameter dependence as those for isolated skyrmions and stripes. A size formula and a good spin profile for skyrmions in SkXs are proposed. These findings have important implications in searching for stable smaller skyrmions at the room temperature.
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Abstract Magnetic textures known as skyrmions have captured the attention of the scientific community working on magnetism for a large part of the last decade due to their potential application in novel neuromorphic devices to carry information and perform computational operations [1, 2] . This is due to the ease of manipulation with electrical currents, and the stability of individual skyrmions against interactions with defects or other skyrmions. Now, while there are plenty of reports on skyrmion manipulation using electrical currents, there are very few studies of skyrmion-to-skyrmion interactions (i.e. skyrmion collisions). While there have recently been studies on skyrmion lattices to extract the interaction potential [3, 4] , a more direct approach is to manipulate individual skyrmions directly, which however has been challenging so far. The reason for that is that very few tools allow for manipulating skyrmions individually and with enough precision to cause collisions in a controllable and repeatable way. In here, we show how using magnetic force microscopy (MFM), and the field gradient produced by MFM probes, it is possible to visualize skyrmions, manipulate them, and create skyrmion collisions to study skyrmion-to-skyrmion interactions or investigate the role of pinning at material defects.
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Magnetic Skyrmions can be considered as localized vortexlike spin textures which are topologically protected in continuous systems. Because of their stability, their small size, and the possibility to move them by low electric currents, they are promising candidates for spintronic devices. Without changing the topological charge, it is possible to create Skyrmion-anti-Skyrmion pairs. We derive a Skyrmion equation of motion which reveals how spin-polarized charge currents create Skyrmion-anti-Skyrmion pairs. It allows us to identify general prerequisites for the pair creation process. We corroborate these general principles by numerical simulations. On a lattice, where the concept of topological protection has to be replaced by that of a finite energy barrier, the anti-Skyrmion partner of the pairs is annihilated and only the Skyrmion survives. This eventually changes the total Skyrmion number and yields a new way of creating and controlling Skyrmions.
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Abstract Skyrmions are important in topological quantum field theory for being soliton solutions of nonlinear sigma model and magnetics for their attractive applications in information technology. Either isolated skyrmions or skyrmion crystals may exist in a given chiral magnet, but not both at the same time. When skyrmion crystals, in which skyrmions often arrange themselves into triangular lattices, can be observed in a chiral magnet, stripy spin textures in various forms appear also and even mix with skyrmion crystals. People believe that skyrmions are circular objects and stripy spin textures have zero skyrmion number. Those stripy spin textures are called anything such as spiral, helical, and cycloid spin orders, but not skyrmions. Here we present convincing evidences showing that those stripy spin textures are skyrmions, ``siblings" of circular skyrmions in skyrmion crystals and ``cousins" of isolated circular skyrmions. Specifically, isolated skyrmions are excitations of chiral magnetic films whose ground states are ferromagnetic and skyrmion formation energy is positive. When the skyrmion formation energy is negative (relative to the single domain state), condensed skyrmions are the ground states and stripe skyrmions appear spontaneously. The density of skyrmion number determines the morphology of condensed skyrmion states. At the extreme of one skyrmion in the whole sample, the skyrmion has a ramified stripe structure that maximizes the skyrmion wall length in order to lower system energy. As the skyrmion number density increases, individual skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to disk-like objects due to the competition between negative formation energy and stripe-stripe or skyrmion-skyrmion repulsion. At a low skyrmion number density, the natural width of stripes is proportional to the ratio between the exchange stiffness constant and Dzyaloshinskii-Moriya interaction coefficient. At a high skyrmion number density, skyrmion crystals are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open a new avenue for manipulating skyrmions, especially condensed skyrmions such as skyrmion crystals.
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Skyrmions are important in topological quantum field theory for being soliton solutions of a nonlinear sigma model and in information technology for their attractive applications. Skyrmions are believed to be circular and stripy spin textures appeared in the vicinity of skyrmion crystals are termed spiral, helical, and cycloid spin orders, but not skyrmions. Here we present convincing evidences showing that those stripy spin textures are skyrmions, "siblings" of circular skyrmions in skyrmion crystals and "cousins" of isolated circular skyrmions. Specifically, isolated skyrmions are excitations when skyrmion formation energy is positive. The skyrmion morphologies are various stripy structures when the ground states of chiral magnetic films are skyrmions. The density of skyrmion number determines the morphology of condensed skyrmion states. At the extreme of one skyrmion in the whole sample, the skyrmion is a ramified stripe. As the skyrmion number density increases, individual skyrmion shapes gradually change from ramified stripes to rectangular stripes, and eventually to disk-like objects. At a low skyrmion number density, the natural width of stripes is proportional to the ratio between the exchange stiffness constant and Dzyaloshinskii-Moriya interaction coefficient. At a high skyrmion number density, skyrmion crystals are the preferred states. Our findings reveal the nature and properties of stripy spin texture, and open a new avenue for manipulating skyrmions, especially condensed skyrmions such as skyrmion crystals.
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