We report the direct evidence of field-dependent character of the interaction between individual magnetic skyrmions as well as between skyrmions and edges in B20-type FeGe nanostripes observed by means of high resolution Lorentz transmission electron microscopy. It is shown that above certain critical values of external magnetic field the character of such long-range skyrmion interactions change from attraction to repulsion. Experimentally measured equilibrium inter-skyrmion and skrymion-edge distances as function of applied magnetic field shows quantitative agreement with the results of micromagnetic simulations. Important role of demagnetizing fields and internal symmetry of three-dimensional magnetic skyrmions are discussed in details.
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…
The interplay of magnetic energies in a Kondo lattice is the underlying physics of a heavy fermion system. Creating an artificial Kondo lattice system by localizing the moments in an ordered metallic array provides a prototype system to tune and study the energetic interplay while avoiding the complications introduced by random alloying of the material. In this article, we create a Kondo lattice system by fabricating a hexagonally ordered nanostructured array using niobium as the host metal and cobalt as the magnetic constituent. Electrical transport measurements and magnetoresistivity measure…
Magnetic skyrmions in 2D chiral magnets are in general stabilized by a combination of Dzyaloshinskii-Moriya interaction and external magnetic field. Here, we show that skyrmions can also be stabilized in twisted moiré superlattices in the absence of an external magnetic field. Our setup consists of a 2D ferromagnetic layer twisted on top of an antiferromagnetic substrate. The coupling between the ferromagnetic layer and the substrate generates an effective alternating exchange field. We find a large region of skyrmion crystal phase when the length scales of the moiré periodicity and skyrmions …
We study the quantum mechanics of magnetic skyrmions in the vicinity of the skyrmion-crystal to ferromagnet phase boundary in two-dimensional magnets. We show that the skyrmion excitation has an energy dispersion that splits into multiple bands due to the combination of magnus force and the underlying lattice. Condensation of the skyrmions can give rise to an intermediate phase between the skyrmion crystal and ferromagnet: a quantum liquid, in which skyrmions are not spatially localized. We show that the critical behavior depends on the spin size $S$ and the topological number of the skyrmion.…
Magnetic skyrmions are particle-like textures in the magnetization, characterized by a topological winding number. Nanometer-scale skyrmions have been observed at room temperature in magnetic multilayer structures. The combination of small size, topological quantization, and their efficient electric manipulation makes them interesting candidates for information carriers in high-performance memory devices. A skyrmion racetrack memory has been suggested where information is encoded in the distance between skyrmions moving in a one-dimensional nanostrip. Here, we propose an alternative design whe…
Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh-Benard convection, Faraday waves, liquid crystals, domain patterns in ferromagnetic films and skyrmion crystals recently observed in chiral magnets. Here we study a simple model of an anisotropic frustrated magnet and show that its zero-temperature phase diagram contains numerous multi-q states including the skyrmion crystal. We clarify the mechanism for stabilization of these states, discuss their multiferroic properties and formulate rules for finding new skyrmion materials. In addition to skyrmion c…
A magnetic skyrmionium (also called 2$π$-skyrmion) can be understood as a skyrmion - a topologically non-trivial magnetic whirl - which is situated in the center of a second skyrmion with reversed magnetization. Here, we propose a new optoelectrical writing and deleting mechanism for skyrmioniums in thin films, as well as a reading mechanism based on the topological Hall voltage. Furthermore, we point out advantages for utilizing skyrmioniums as carriers of information in comparison to skyrmions with respect to the current-driven motion. We simulate all four constituents of an operating skyrmi…
To exploit nanometric magnetic skyrmions as information carriers in high-density storage devices, a method is needed that creates intended number of skyrmions at specified places in the device preferably at a low energy cost. We theoretically propose that using a system with a fabricated hole or notch, the controlled creation of individual skyrmions can be achieved even when using an external magnetic field applied to the entire specimen. The fabricated defect turns out to work like a catalyst to reduce the energy barrier for the skyrmion creation.
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 an…
In chiral magnets, localized topological magnetic whirls, magnetic skyrmions, can be moved by spin polarized electric currents. Upon increasing the current strength, with prospects for high-speed skyrmion motion for spintronics applications in mind, isolated skyrmions deform away from their typical circular shape. We analyze the influence of spin-transfer torques on the shape of a single skyrmion, including its stability upon adiabatically increasing the strength of the applied electric current. For rather compact skyrmions at uniaxial anisotropies well above the critical anisotropy for domain…
Skyrmions represent topologically stable field configurations with particle-like properties. We used neutron scattering to observe the spontaneous formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortices, in the chiral itinerant-electron magnet MnSi. The skyrmion lattice stabilizes at the border between paramagnetism and long-range helimagnetic order perpendicular to a small applied magnetic field regardless of the direction of the magnetic field relative to the atomic lattice. Our study experimentally establishes magnetic materials lacking inversion symmetry as an…
We study the quantum propagation of a Skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion to a finite-temperature path integral formalism, using field theoretic tools. Promoting the center of the Skyrmion to a dynamic quantity, the fluctuations around the Skyrmionic configuration give rise to a time-dependent damping of the Skyrmion motion. From the frequency dependence of the damping kernel, we are able to identify the Skyrmion mass, thus providing a microscopic description of the kinematic properties of Skyrmions. When defects are present or a magneti…
Nanostructured La0.67Ca0.33MnO3 (NS-LCMO) was formed by pulsed-laser deposition on the surface of porous Al2O3. The resistance peak temperature (Tp) of the NS-LCMO increases with increasing average thickness of the films, while their Curie temperatures (Tc) remain unchanged. The coercive field of the samples increases with decreasing film thickness and its temperature dependence can be well described by Hc(T) = Hc(0)[1-(T/TB)1/2]. A large magnetoresistance and strong memory effect were observed for the NS-LCMO. The results are discussed in terms of the size effect, Coulomb blockade and magneti…
Magnetic skyrmions, which are topological particle-like excitations in ferromagnets, have attracted a lot of attention recently. Skyrmionics is an attempt to use magnetic skyrmions as information carriers in next generation spintronic devices. Proposals of manipulations and operations of skyrmions are highly desired. Here, we show that the conversion, duplication and merging of isolated skyrmions with different chirality and topology are possible all in one system. We also demonstrate the conversion of a skyrmion into another form of a skyrmion, i.e., a bimeron. We design spin logic gates such…
The skyrmions generated by frustration in centrosymmetric structures host extra internal degrees of freedom: vorticity and helicity, resulting in distinctive properties and potential functionality, which are not shared by the skyrmions stemming from the Dzyaloshinskii-Moriya interaction in noncentrosymmetric structures. The present work indicates that the magnetism-driven electric polarization carried by skyrmions provides a direct handle for tuning helicity. Especially for the in-plane magnetized skyrmions, the helicity can be continuously rotated and exactly picked by applying an external el…
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…
Arising from emergent electromagnetic field of magnetic skyrmions due to their nontrivial topology, the skyrmion Hall effect might be a roadblock for practical applications since any longitudinal motions of skyrmions in nanotrack is accompanied by a transverse motion. A direct consequence of such an effect is easy destruction of skyrmions at the nanotrack edges during their fast motions along the nanotrack, despite their topological protection. Here we propose an entirely novel solution of completely inhibiting such skyrmion Hall effect without affecting its topological properties based on a a…
Skyrmions are vortex-like textures of magnetic moments found in some magnetically ordered materials. Here we describe the origin of the skyrmion and discuss the experimental realization of skyrmions in magnetic materials, the dynamic properties of the skyrmion and the potentially useful interaction of skyrmions with electrons. Our discussion is based on the physics of fields and allows us to touch on notions from field theory and topology that illustrate how skyrmions can be understood as part of a family of defects in an ordered field, and hint at other topological objects that await our disc…
Based on analytical estimation and lattice simulation, a proposal is made that magnetic skyrmions can be generated through the pinning effect in 2D chiral magnetic materials, in absence of an external magnetic field or magnetic anisotropy. In our simulation, stable magnetic skyrmions can be generated in the pinning areas. The properties of the skyrmions are studied for various values of ferromagnetic exchange strength and the Dzyaloshinskii-Moriya interaction strength.
Chiral magnetic textures with non-trivial topology are known as skyrmions, and due to their unique properties they are promising in novel magnetic storage applications. While the electric manipulation of either isolated skyrmions or a whole skyrmion lattice have been intensively reported, the electric effects on skyrmion clusters remain scarce. In magnetoelectric compound Cu$_2$OSeO$_3$, a skyrmion cluster can be created near the helical-skyrmion phase boundary. Here, we report the in situ electric field writing/erasing of skyrmions in such a skyrmion cluster. Our real space/time image data ob…
We report that in a $β$-Mn-type chiral magnet Co$_9$Zn$_9$Mn$_2$, skyrmions are realized as a metastable state over a wide temperature range, including room temperature, via field-cooling through the thermodynamic equilibrium skyrmion phase that exists below a transition temperature $T_\mathrm{c}$ $\sim$ 400 K. The once-created metastable skyrmions survive at zero magnetic field both at and above room temperature. Such robust skyrmions in a wide temperature and magnetic field region demonstrate the key role of topology, and provide a significant step toward technological applications of skyrmi…
Magnetic skyrmions have attracted considerable attention recently for their huge potential in spintronic applications. Generally skyrmions are big compared to the atomic lattice constant, which allows for the Ginzburg-Landau type description in the continuum limit. Such a description successfully captures the main experimental observations on skyrmions in B20 compound without inversion symmetry. Skyrmions can also exist in inversion-symmetric magnets with competing interactions. Here we derive a general Ginzburg-Landau theory for skyrmions in these magnets valid in the long wavelength limit. W…
Compared with the traditional magnetic bubble, skyrmion has smaller size, better stability therefore is considered as a very promising candidate for future memory devices. When skyrmions are manipulated, erased and created, the density of skyrmions can be varied, however the relationship between the radii and the densities of skyrmions needs more exploration. In this paper, we study this problem both theoretically and by using the lattice simulation. The average radius of skyrmions as a function of material parameters, the strength of external magnetic field and the density of skyrmions is obt…
Skyrmions are nanometric spin whirls that can be stabilized in magnets lacking inversion symmetry. The properties of isolated skyrmions embedded in a ferromagnetic background have been intensively studied. We show that single skyrmions and clusters of skyrmions can also form in the helical phase and investigate theoretically their energetics and dynamics. The helical background provides natural one-dimensional channels along which a skyrmion can move rapidly. In contrast to skyrmions in ferromagnets, the skymion-skyrmion interaction has a strong attractive component and thus skyrmions tend to …
Dielectric properties were investigated under various magnitudes and directions of magnetic field (H) for a chiral magnetic insulator Cu2OSeO3. We found that the skyrmion crystal induces electric polarization (P) along either in-plane or out-of-plane direction of the spin vortices depending on the applied H-direction. The observed H-dependence of P in ferrimagnetic, helimagnetic, and skyrmion crystal state can be consistently described by the d-p hybridization model, highlighting an important role of relativistic spin-orbit interaction in the magnetoelectric coupling in Cu2OSeO3. Our analysis …
Magnetic skyrmions are vortex-like topological spin textures often observed to form a triangular-lattice skyrmion crystal in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Recently $β$-Mn structure-type Co-Zn-Mn alloys were identified as a new class of chiral magnet to host such skyrmion crystal phases, while $β$-Mn itself is known as hosting an elemental geometrically frustrated spin liquid. Here we report the intermediate composition system Co$_7$Zn$_7$Mn$_6$ to be a unique host of two disconnected, thermal-equilibrium topological skyrmion phases; one is a conventional s…
Magnetic whirls in chiral magnets, so-called skyrmions, can be manipulated by ultrasmall current densities. Here we study both analytically and numerically the interactions of a single skyrmion in two dimensions with a small hole in the magnetic layer. Results from micromagnetic simulations are in good agreement with effective equations of motion obtained from a generalization of the Thiele approach. Skyrmion-defect interactions are described by an effective potential with both repulsive and attractive components. For small current densities a previously pinned skyrmion stays pinned whereas an…
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 …
Magnetic skyrmions are vortex-like topological spin textures often observed in structurally chiral magnets with Dzyaloshinskii-Moriya interaction. Among them, Co-Zn-Mn alloys with a $β$-Mn-type chiral structure host skyrmions above room temperature. In this system, it has recently been found that skyrmions persist over a wide temperature and magnetic field region as a long-lived metastable state, and that the skyrmion lattice transforms from a triangular lattice to a square one. To obtain perspective on chiral magnetism in Co-Zn-Mn alloys and clarify how various properties related to the skyrm…
Recent experiments have reported on controlled nucleation of individual skyrmions in chiral magnets. Here we show that in magnetic ultra-thin films with interfacial Dzyaloshinskii-Moriya interaction, single skyrmions of different radii can be nucleated by creating a local distortion in the magnetic field. In our study, we have considered zero temperature quantum nucleation of a single skyrmion from a ferromagnetic phase. The physical scenario we model is one where a uniform field stabilizes the ferromagnet, and an opposing local magnetic field over a circular spot, generated by the tip of a lo…
We discuss the scattering of high-energy magnons off a single magnetic skyrmion within the field-polarized ground state of a two-dimensional chiral magnet. For wavevectors larger than the inverse skyrmion radius, $k r_s \gg 1$, the magnon scattering is dominated by an emerging magnetic field whose flux density is essentially determined by the topological charge density of the skyrmion texture. This leads to skew and rainbow scattering characterized by an asymmetric and oscillating differential cross section. We demonstrate that the transversal momentum transfer to the skyrmion is universal due…
We study $\mathbb{C}P^2$ Skyrmion crystals in the ferromagnetic SU(3) Heisenberg model with a generalization of the Dzyaloshinskii-Moriya interaction and the Zeeman term. The model possesses two different types of Skyrmion crystals with unit-Skyrmions that can be interpreted as bound states of two half-Skyrmions or four quarter-Skyrmions. Our study on $\mathbb{C}P^2$ Skyrmion crystals opens up the possibility for useful future applications since $\mathbb{C}P^2$ Skyrmions have more degrees of freedom than the usual $\mathbb{C}P^1$ (magnetic) Skyrmions.
The experimental realization of magnetic skyrmions in centrosymmetric materials has been driven by theoretical understanding of how a delicate balance of anisotropy and frustration can stabilize topological spin structures in applied magnetic fields. Recently, the centrosymmetric material Gd$_{2}$PdSi$_{3}$ was shown to host a field-induced skyrmion phase, but the skyrmion stabilization mechanism remains unclear. Here, we employ neutron-scattering measurements on an isotopically-enriched polycrystalline Gd$_{2}$PdSi$_{3}$ sample to quantify the interactions that drive skyrmion formation. Our a…
We theoretically propose that magnetic skyrmion, nanometric spin vortex characterized by a quantized topological number, can be electrically created on a thin-film specimen of chiral-lattice magnetic insulator within a few nanoseconds by applying an electric field via an electrode tip taking advantage of coupling between noncollinear skyrmion spins and electric polarizations. This finding will pave a route to utilizing multiferroic skyrmions as information carriers for low-energy-consuming magnetic storage devices without Joule-heating energy losses.
Magnetic skyrmions, vortex-like swirling spin textures characterized by a quantized topological invariant, realized in chiral-lattice magnets are currently attracting intense research interest. In particular, their dynamics under external fields is an issue of vital importance both for fundamental science and for technical application. Whereas observations of magnetic skyrmions had been limited to metallic magnets so far, their realization was discovered also in a chiral-lattice insulating magnet Cu2OSeO3 in 2012. Skyrmions in the insulator turned out to exhibit multiferroic nature with spin-i…
We study the dynamics of skyrmions in a metallic chiral magnet. First we show that skyrmions can be created dynamically by destabilizing the ferromagnetic background state through a spin polarized current. We then treat skyrmions as rigid particles and derive the corresponding equation of motion. The dynamics of skyrmions is dominated by the Magnus force, which accounts for the weak pinning of skyrmions observed in experiments. Finally we discuss the quantum motion of skyrmions.
