Hybridized magnon modes in the quenched skyrmion crystal
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Magnetic skyrmions have attracted attention as particlelike swirling spin textures with nontrivial topology, and their self-assembled periodic order i.e., the skyrmion crystal (SkX) is anticipated to host unique magnonic properties. In this paper, we investigate magnetic resonance in the quenched SkX state, which is obtained by the rapid cooling of the high-temperature equilibrium SkX phase in the chiral magnetic insulator ${\mathrm{Cu}}_{2}\mathrm{O}\mathrm{Se}{\mathrm{O}}_{3}$. At low temperatures, sextupole and octupole excitation modes of skyrmions are identified, which are usually inactive for oscillating magnetic fields ${B}^{\ensuremath{\nu}}$ with GHz-range frequency $\ensuremath{\nu}$ but turn out to be detectable through the hybridization with the ${B}^{\ensuremath{\nu}}$-active counterclockwise and breathing modes, respectively. The observed magnetic excitation spectra are well reproduced by theoretical calculations, which demonstrates that the effective magnetic anisotropy enhanced at low temperatures is the key for the observed hybridization between the ${B}^{\ensuremath{\nu}}$-active and ${B}^{\ensuremath{\nu}}$-inactive modes.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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Abstract A theoretical study on the interplay of frustrated skyrmion and magnons should reveal new physics and future experiment designs. In this study, we investigate the magnon-driven dynamics of frustrated skyrmion in synthetic antiferromagnets based on micromagnetic simulations, focusing on the effect of skyrmion helicity oscillation. The oscillation speed and Hall angle of the frustrated skyrmion depending on the magnon intensity and damping constant are simulated, which demonstrates that the skyrmion helicity oscillation effectively suppresses Hall motion. The elastic scattering theory reveals that the helicity oscillation affects the scattering cross-section of injected magnons, which in turn effectively modulates the skyrmion Hall motion. This study provides a comprehensive understanding of magnon-skyrmion scattering in frustrated magnets, thus benefiting future spintronic and magnonic applications.
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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 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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We study theoretically the dynamics of magnons in the presence of a single skyrmion in chiral magnets featuring Dzyaloshinskii-Moriya interaction. We show by micromagnetic simulations that the scattering process of magnons by a skyrmion can be clearly defined although both originate in the common spins. We find that (i) the magnons are deflected by a skyrmion, with the angle strongly dependent on the magnon wavenumber due to the effective magnetic field of the topological texture, and (ii) the skyrmion motion is driven by magnon scattering through exchange of the momenta between the magnons and a skyrmion: the total momentum is conserved. This demonstrates that the skyrmion has a well-defined, though highly non-Newtonian, momentum.
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Magnonics is now an attractive field which focuses on the dynamic characteristics of magnons, a kind of quasiparticles in magnetic media, and attempt to apply magnons for functional devices. In order to construct magnon based devices, it is necessary to fabricate materials with specific and tunable magnon bands and band gaps. Skyrmion based magnonic crystals is one of the most suitable materials which possess periodical skyrmion structure and show applicative magnon bands and band gaps. In this review, we provide an overview over recent theoretical and experimental research on skyrmion based magnonic crystals. We will firstly provide an introduction of magnonic crystals and magnetic skyrmion. And then we will show the theoretical and experimental progress on skyrmion based magnonic crystals and their magnon band characteristics. At the end, we will give an outlook and perspectives of new fascinating fields on topological nontrivial magnon modes, as well as hybrid and quantum magnonic phenomena of skyrmion based magnonic crystals.
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Chiral magnets support topological skyrmion textures due to the Dzyaloshinskii-Moriya spin-orbit interaction. In the presence of a sufficiently large applied magnetic field, such skyrmions are large amplitude excitations of the field-polarized magnetic state. We investigate analytically the interaction between such a skyrmion excitation and its small amplitude fluctuations, i.e., the magnons in a clean two-dimensional chiral magnet. The magnon spectrum is found to include two magnon-skyrmion bound states corresponding to a breathing mode and, for intermediate fields, a quadrupolar mode, which will give rise to subgap magnetic and electric resonances. Due to the skyrmion topology, the magnons scatter from a Aharonov-Bohm flux density that leads to skew and rainbow scattering, characterized by an asymmetric differential cross section with, in general, multiple peaks. As a consequence of the skew scattering, a finite density of skyrmions will generate a topological magnon Hall effect. Using the conservation law for the energy-momentum tensor, we demonstrate that the magnons also transfer momentum to the skyrmion. As a consequence, a magnon current leads to magnon pressure reflected in a momentum-transfer force in the Thiele equation of motion for the skyrmion. This force is reactive and governed by the scattering cross sections of the skyrmion; it causes not only a finite skyrmion velocity but also a large skyrmion Hall effect. Our results provide, in particular, the basis for a theory of skyrmion caloritronics for a dilute skyrmion gas in clean insulating chiral magnets.
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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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The excitation functions of the ~(23)Na(p,α_0)~(20)Ne_(g·s).and the ~(23)Na(p,α_1)~(20)Ne_(?) reae-tion have been measured from E_p=1 to 2.5 MeV at θ_L=30°,150° and 30°,respectively.Around the resonance at 2.171 MeV,the excitation functions of the(p,α_0)reactionhave been measured at 12 angles,then,some angular distributions have been obtainedfrom these excitation functions.In addition,the angular distribution of the(p,α_0)reaction for the resonance at 2.171 MeV has also been measured directly at energy ofthe resonance peak of the excitation function at 150°.For the resonance at 2.117MeV,the angular distribution have been measured at two energies,one at the energyof the resonance peak of the excitation function at 150°,another at the energy of thehalf maximum point of the resonance peak on the higher energy side.Around the re-sonance at 2.075 MeV,the excitation functions have been measured at 16 angles,andthe angular distribution has been obtained from three excitation functions.The an-gular distributions of the three resonances are not symmetric about 90°,and the posi-tions of the resonance peaks of these resonances varies with the angle of measurement.By means of the compound nucleus theory,discussions have been made for these non-solated resonances.
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