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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. [ABSTRACT FROM AUTHOR]

We study the equilibrium and dynamical properties of skyrmions in thin films of chiral magnets with oblique magnetic field. The shape of an individual skyrmion is noncircular and the skyrmion density decreases with the tilt angle from the normal of films. As a result, the interaction between two skyrmions depends on the relative angle between them in addition to their separation. The triangular lattice of skyrmions under a perpendicular magnetic field is distorted into a centered rectangular lattice for a tilted magnetic field. For a low skyrmion density, skyrmions form a chainlike structure. The dynamical response of the noncircular skyrmions depends on the direction of external currents. [ABSTRACT FROM AUTHOR]

Skyrmions are topological spin defects which have been observed in chiral magnets and other materials including some multiferroics in recent years. The typical size of a skyrmion varies in the range 5–100 nm with thousands of spins in it and a characteristic energy scale of 1 meV per layer. They can also be viewed as emergent mesoscopic particles which can be moved or manipulated by electrical current, temperature gradient, electric and magnetic field, thus rendering them useful for a variety of applications including information storage. In particular, the current needed to move a skyrmion is five to six orders of magnitude smaller than that needed for moving magnetic domain walls and vortices, therefore making them promising candidates for spintronics. [ABSTRACT FROM PUBLISHER]

We study the equilibrium phase diagram of ultrathin chiral magnets with easy-plane anisotropy A. The vast triangular skyrmion lattice phase that is stabilized by an external magnetic Held evolves continuously as a function of increasing A into a regime in which nearest-neighbor skyrmions start overlapping with each other. This overlap leads to a continuous reduction of the skyrmion number from its quantized value Q = 1 and to the emergence of antivortices at the center of the triangles formed by nearest-neighbor skyrmions. The antivortices also carry a small "skyrmion number" QA ⪡ 1 that grows as a function of increasing A. The system undergoes a first order phase transition into a square vortex-antivortex lattice at a critical value of A. Finally, a canted ferromagnetic state becomes stable through another first order transition for a large enough anisotropy A. Interestingly enough, this first order transition is accompanied by metastable meron solutions. [ABSTRACT FROM AUTHOR]

We show that a temperature gradient induces an ac electric current in multiferroic insulators when the sample is embedded in a circuit. We also show that a thermal gradient can be used to move magnetic Skyrmions in insulating chiral magnets: the induced magnon flow from the hot to the cold region drives the Skyrmions in the opposite direction via a magnonic spin transfer torque. Both results are combined to compute the effect of Skyrmion motion on the ac current generation and demonstrate that Skyrmions in insulators are a promising route for spin caloritronics applications. [ABSTRACT FROM AUTHOR]

A topological excitation called skyrmion has been observed experimentally in chiral magnets without spatial inversion symmetry. The dynamics of a skyrmion is equivalent to an electron moving in a strong magnetic field. As a skyrmion involves large number of spins, it is not clear whether there exist observable quantum effects. In this work, we study the quantum dynamics of a skyrmion in a pinning potential. Without a pinning potential, the skyrmion performs cyclotron motion due to the strong emergent magnetic field originating from the Berry phase of spins, and all skyrmions occupy the lowest Landau level. Their wave functions are strongly localized in a region with radius less than 1 Å when no driving force is applied. Thus in most circumstances, the quantum effects of a skyrmion are weak. In the presence of a pinning potential, the lowest Landau level for skyrmions is split into quantized levels, characterized by the orbital moments. The transition between quantized levels can be observed experimentally by microwave absorption measurements in low temperature region. The quantum effects are more prominent for a skyrmion with a small size, which can be realized in magnets with a large Dzyaloshinskii-Moriya interaction. [ABSTRACT FROM AUTHOR]

A skyrmion in a nanosized disk of a chiral magnet can be used as a bit of information. To this end, it is desirable to control the creation and removal of a skyrmion only by currents without using external magnetic fields. Here, we propose to create a skyrmion by applying a current pulse to a nanodisk. The skyrmion can be removed from the disk by applying a dc current. We show that the dynamics of the created skyrmion can lead to a rectification effect, in which a dc voltage is generated by the motion of skyrmion in the presence of an ac current. [ABSTRACT FROM AUTHOR]

Recently spin textures called skyrmions have been discovered in certain chiral magnetic materials without spatial inversion symmetry, and they have attracted enormous attention due to their promising application in spintronics since only a low applied current is necessary to drive their motion. When a conduction electron moves around the skyrmion, its spin is fully polarized by the spin texture and acquires a quantized phase; thus, the skyrmion yields an emergent electrodynamics that in turn determines skyrmion motion and gives rise to a finite Hall angle. As topological excitations, skyrmions behave as particles. In this paper we derive the equation of motion for skyrmions as rigid point particles from a microscopic continuum model and obtain the short-range interaction between skyrmions and the interaction between skyrmions and defects. Skyrmions also experience a Magnus force perpendicular to their velocity due to the underlying emergent electromagnetic field. We validate the equation of motion by studying the depinning transition using both the particle and the continuum models. By using the particle description, we explain the recent experimental observations of the rotation of a skyrmion lattice in the presence of a temperature gradient. We also predict quantum and thermal creep motion of skyrmions in the pinning potential. [ABSTRACT FROM AUTHOR]

We study the dynamics of Skyrmions in chiral magnets in the presence of a spin polarized current. The motion of Skyrmions in the ferromagnetic background excites spin waves and contributes to additional damping. At a large current, the spin wave spectrum becomes gapless and Skyrmions are created dynamically from the ferromagnetic state. At an even higher current, these Skyrmions are strongly deformed due to the damping and become unstable at a threshold current, leading to a chiral liquid. We show how Skyrmions can be created by increasing the current in the magnetic spiral state. We then construct a dynamic phase diagram for a chiral magnet with a current. The instability transitions between different states can be observed as experimentally clear signatures in the transport measurements, such as jumps and hysteresis. [ABSTRACT FROM AUTHOR]

Skyrmions are disklike objects that typically form triangular crystals in two-dimensional systems. This situation is analogous to the so-called pancake vortices of quasi-two-dimensional superconductors. The way in which Skyrmion disks or "pancake Skyrmions" pile up in layered centrosymmetric materials is dictated by the interlayer exchange. Unbiased Monte Carlo simulations and simple stabilization arguments reveal face centered cubic and hexagonal close packed Skyrmion crystals for different choices of the interlayer exchange, in addition to the conventional triangular crystal of Skyrmion lines. Moreover, an inhomogeneous current induces a sliding motion of pancake Skyrmions, indicating that they behave as effective mesoscale particles. [ABSTRACT FROM AUTHOR]

Taking all the magnon modes into account, we derive the skyrmion dynamics in response to a weak external drive. A skyrmion has rotational symmetry, and the magnon modes can be characterized by an angular momentum. For a weak distortion of a skyrmion, only the magnon modes with an angular momentum |m|=1 govern the dynamics of skyrmion topological center. The skyrmion inertia is determined by the magnon modes in the continuum spectrum. For a skyrmion driven by a magnetic field gradient or by a spin transfer torque generated by a current, the dynamical response is practically instantaneous. This justifies the rigid skyrmion approximation used in Thiele's collective coordinate approach. For a skyrmion driven by a spin Hall torque, the torque couples to the skyrmion motion through the magnons in the continuum and damping; therefore the skyrmion dynamics shows sizable inertia in this case. The trajectory of a skyrmion is an ellipse for an ac drive of spin Hall torque. [ABSTRACT FROM AUTHOR]

Finite-Q magnetic instabilities are rather common in frustrated magnets. When the magnetic susceptibility is maximized at multiple-Q vectors related through lattice symmetry operations, exotic magnetic orderings such as vortex and skyrmion crystals may follow. Here, we show that a periodic array of nonmagnetic impurities, which can be realized through charge density wave ordering, leads to a rich phase diagram featuring a plethora of chiral magnetic phases, especially when there is a simple relation between the reciprocal vectors of the impurity superlattice and the magnetic Q vectors. We also investigate the effect of changing the impurity concentration or disturbing the impurity array with small quenched randomness. Alternative realizations of impurity superlattices are briefly discussed. [ABSTRACT FROM AUTHOR]

Motivated by the recent experimental observations on the skyrmion creation by cutting chiral stripe domains under a current drive [Jiang et al., Science 349, 283 (2015)], we study the mechanism of skyrmion generation by simulating the dynamics of stripe domains. Our theory for skyrmion generation is based on the fact that there are two half skyrmions attached to the ends of a stripe domain. These half skyrmions move due to the coupling between the skyrmion topological charge and current. As a consequence, the stripe domain is bent or stretched depending on the direction of motion of the half skyrmions. For a large current, skyrmions are created by chopping the stripe domains via strong bending or stretching. Our theory provides an explanation to the experiments and is supported by the new experiments. Furthermore, we predict that skyrmions can also be generated using a Bloch stripe domain under a spin transfer torque which can be realized in B20 compounds. [ABSTRACT FROM AUTHOR]

We clarify the conditions for the emergence of multiple-Q structures out of lattice and easy-axis spin anisotropy in frustrated magnets. By considering magnets whose exchange interaction has multiple global minima in momentum space, we find that both types of anisotropy stabilize triple-Q orderings. Moderate anisotropy leads to a magnetic-field-induced skyrmion crystal, which evolves into a bubble crystal for increasing spatial and spin anisotropy. The bubble crystal exhibits a quasicontinuous (devil's staircase) temperature-dependent ordering wave vector, characteristic of the competition between frustrated exchange and strong easy-axis anisotropy. [ABSTRACT FROM AUTHOR]

A magnetic skyrmion observed experimentally in chiral magnets is a topologically protected spin texture. For their unique properties, such as high mobility under current drive, skyrmions have a huge potential for applications in next-generation spintronic devices. Defects naturally occurring in magnets have profound effects on the static and dynamical properties of skyrmions. In this work we study the effect of an atomic defect on a skyrmion by performing the first-principles calculations within the density functional theory, taking MnSi as an example. By substituting one site of Mn or Si with different elements, we can tune the pinning energy. The effects of pinning by an atomic defect can be understood qualitatively within a phenomenological model. [ABSTRACT FROM AUTHOR]

Skyrmion lines in metallic chiral magnets carry an emergent magnetic field experienced by the conduction electrons. The inflow and outflow of this field across a closed surface is not necessarily equal, thus it allows for the existence of emergent monopoles. One example is a segment of skyrmion line inside a crystal, where a monopole and antimonopole pair is connected by the emergent magnetic flux line. This is a realization of Dirac stringlike excitations. Here we study the dynamics of monopoles in chiral magnets under an electric current. We show that in the process of creation of skyrmion lines, skyrmion line segments are first created via the proliferation of monopoles and antimonopoles. Then these line segments join and span the whole system through the annihilation of monopoles. The skyrmion lines are destroyed via the proliferation of monopoles and antimonopoles at high currents, resulting in a chiral liquid phase. We also propose to create the monopoles in a controlled way by applying an inhomogeneous current to a crystal. Remarkably, an electric field component in the magnetic field direction proportional to the current squared in the low current region is induced by the motion of distorted skyrmion lines, in addition to the Hall and longitudinal voltage. The existence of monopoles can be inferred from transport or imaging measurements. [ABSTRACT FROM AUTHOR]

A correction to the article "Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep" in the 2013 issue is presented.

We consider a C6 invariant lattice of magnetic moments coupled via a Kondo exchange J with a 2D electron gas (2DEG). The effective Ruderman-Kittel-Kasuya-Yosida interaction between the moments stabilizes a magnetic skyrmion crystal in the presence of magnetic field and easy-axis anisotropy. An attractive aspect of this mechanism is that the magnitude of the magnetic ordering wave vectors, Qν (ν=1, 2, 3), is dictated by the Fermi wave number kF: |Qν|=2kF. Consequently, the topological contribution to the Hall conductivity of the 2DEG becomes of the order of the quantized value, e²/h, when J is comparable to the Fermi energy εF. [ABSTRACT FROM AUTHOR]