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Skyrmions are topologically protected entities in magnetic materials which have the potential to be used in spintronics for information storage and processing. However, Skyrmions in ferromagnets have some intrinsic difficulties which must be overcome to use them for spintronic applications, such as the inability to move straight along current. We show that Skyrmions can also be stabilized and manipulated in antiferromagnetic materials. An antiferromagnetic Skyrmion is a compound topological object with a similar but of opposite sign spin texture on each sublattice, which e.g. results in a complete cancelation of the Magnus force. We find that the composite nature of antiferromagnetic Skyrmions gives rise to different dynamical behavior, both due to an applied current and temperature effects.

We express dynamics of domain walls in ferromagnetic nanowires in terms of collective coordinates generalizing Thiele's steady-state results. For weak external perturbations the dynamics is dominated by a few soft modes. The general approach is illustrated on the example of a vortex wall relevant to recent experiments with flat nanowires. A two-mode approximation gives a quantitatively accurate description of both the steady viscous motion of the wall in weak magnetic fields and its oscillatory behavior in moderately high fields above the Walker breakdown.Dynamics of domain walls in nanosized magnetic wires, strips, rings etc. is a subject of practical importance and fundamental interest [1,2]. Nanomagnets typically have two ground states related to each other by the symmetry of time reversal and thus can serve as a memory bit. Switching between these states proceeds via creation, propagation, and annihilation of domain walls with nontrivial internal structure and dynamics. Although domain-wall (DW) motion in macroscopic magnets has been studied for a long time [3], new phenomena arise on the submicron scale where the local (exchange) and long-range (dipolar) forces are of comparable strengths [4]. In this regime, domain walls are textures with a rich internal structure [2,5]. As a result, they have easily excitable internal degrees of freedom. Providing a description of the domain-wall motion in a nanostrip under an applied magnetic field is the main subject of this paper. We specialize to the experimentally relevant case of thin strips with a thickness-to-width ratio t/w ≪ 1.The dynamics of magnetization is described by the Landau-Lifshitz-Gilbert (LLG) equation [6] Here m = M/|M|, H eff (r) = −δU/δM(r) is an effective magnetic field derived from the free-energy functional U [M(r)], γ = g|e|/2mc is the gyromagnetic ratio, and α ≪ 1 is Gilbert's damping constant [7]. Equation (1) can be solved exactly only in a few simple cases. Walker [8] considered a one-dimensional domain wall m = m(x, t) in a uniform external magnetic field H||x.At a low applied field the wall exhibits steady motion, m = m(x − vt), with the velocity v ≈ γH∆/α, where ∆ is the wall width. Above a critical field H W = αM/2 magnetization starts to precess, the wall motion acquires an oscillatory component and the average speed of the wall drops sharply. Qualitatively similar behavior has been observed in magnetic nanostrips [1], however, numerical studies demonstrate that Walker's theory fails to provide a quantitative account of both the steady and oscillatory regimes [2].We formulate the dynamics of a magnetic texture in terms of collective coordinates ξ(t) = {ξ 0 , ξ 1 , . . .}, so that m(r, t) = m(r, {ξ(t)}). Although a magnetization field has infinitely many modes, its long-time dynamics-most relevant to the motion of domain walls-is dominated by a small subset of soft modes with long relaxation times. Focusing on soft modes and ignoring hard ones reduces complex field equations of magnetization dynamics to a much simpler problem. In Walke...

Antiferromagnets can be used to store and manipulate spin information, but the coupled dynamics of the staggered field and the magnetization are very complex. We present a theory which is conceptually much simpler and which uses collective coordinates to describe staggered field dynamics in antiferromagnetic textures. The theory includes effects from dissipation, external magnetic fields, as well as reactive and dissipative current-induced torques. We conclude that, at low frequencies and amplitudes, currents induce collective motion by means of dissipative rather than reactive torques. The dynamics of a one-dimensional domain wall, pinned at 90° at its ends, are described as a driven harmonic oscillator with a natural frequency inversely proportional to the length of the texture.

A magnetic bimeron is a pair of two merons and can be understood as the in-plane magnetized version of a skyrmion. Here we theoretically predict the existence of single magnetic bimerons as well as bimeron crystals, and compare the emergent electrodynamics of bimerons with their skyrmion analogues. We show that bimeron crystals can be stabilized in frustrated magnets and analyze what crystal structure can stabilize bimerons or bimeron crystals via the Dzyaloshinskii-Moriya interaction. We point out that bimeron crystals, in contrast to skyrmion crystals, allow for the detection of a pure topological Hall effect. By means of micromagnetic simulations, we show that bimerons can be used as bits of information in in-plane magnetized racetrack devices, where they allow for current-driven motion for torque orientations that leave skyrmions in out-of-plane magnets stationary.Over the last years magnetic skyrmions [ Fig. 1(a) top] [1-6] have attracted immense research interest, as these small spin textures m(r) possess strong stability, characterized by a topological charge N Sk = ±1. Skyrmions offer a topological contribution to the Hall effect [7][8][9][10][11][12][13][14][15][16][17][18], commonly measured in skyrmion crystals, and can be stabilized as individual quasiparticles in collinear ferromagnets. They can be driven by currents in thin films [6,[19][20][21][22][23][24][25][26] allowing for spintronics applicability. The stabilizing interaction in most systems is the Dzyaloshinskii-Moriya interaction (DMI) [27,28], while theoretical simulations also point to other stabilizing mechanisms, e. g. frustrated exchange interactions [29,30]. Textures with a half-integer topological charge, like merons and antimerons (or vortices and antivortices), have also been subject of intense research [31][32][33].Magnetic bimerons [34][35][36][37] [Fig.1(a) bottom] are the combination of two merons [red and blue] and can be understood as in-plane magnetized versions of magnetic skyrmions [38]. Instead of the out-of-plane component of the magnetization it is an in-plane component which is radial symmetric about the quasiparticle's center; being aligned with the saturation magnetization of the ferromagnet at the outer region of the bimeron and pointing into the opposite direction in the center. Recently, Kharkov et al. showed that isolated bimerons can be stabilized in an easy-plane magnet by frustrated exchange interactions [34]. In DMI dominated systems (as is the case for all experimentally known skyrmion-host materials) bimerons have only been shown to exist as unstable transition states [35,36].In this Rapid Communication, we show that bimerons in frustrated magnets can also be stabilized in an array, the bimeron crystal. Furthermore, we propose a structural configuration that allows for DMI stabilizing isolated bimerons and bimeron crystals. We compare fundamental properties of skyrmions and bimerons and find that both show the same topological Hall effect, whereas the bimeron allows for a pure detection, that is without supe...

We point out that a peculiar annihilation of a vortex-antovortex pair observed numerically by Hertel and Schneider [Phys. Rev. Lett. 97, 177202 (2006)] represents the formation and a subsequent decay of a skyrmion.PACS numbers: 75.40. Gb, 75.40.Mg, 75.75.+a Creation, annihilation, and fusion of topological solitons is constrained by conservation of related topological charges. For example, in a planar (XY) ferromagnet the destruction of a vortex always proceeds through its annihilation with an antivortex, a process that conserves the O(2) winding number. In this note we highlight the importance of another topological charge for vortex defects associated with the three-dimensional nature of the spin. Even in magnets with an easy-plane anisotropy the magnetization can and does point out of the plane at the core of a vortex.1 Even though the core region is exceedingly small, the direction of its out-of-plane magnetization p = sgnM z (0), henceforth referred to as polarization, is an important parameter. For instance, the gyrotropic force acting on a moving vortex depends on the polarization p but not on the size of the core, 2 indicating a topological nature of the effect.Recently Hertel and Schneider 3 performed numerical simulations of the vortex-antivortex pair annihilation in a thin magnetic film. They noted drastically different outcomes for pairs with parallel and antiparallel core magnetizations. In the former case the two defects dissipated quietly, while in the latter the annihilation was accompanied by a violent burst of spin waves. Below we show that the difference is due to the conservation of another topological charge, the skyrmion number. Hertel and Schneider observed the formation and decay of a skyrmion.In a thin film with no intrinsic anisotropy the magnetization is forced to stay mainly in the plane of the film by dipolar interactions. Therefore topological defects in the bulk of the film are characterized by an O(2) winding number, n = +1 for vortices and n = −1 for antivortices. At the core of these defects, the magnetization points out of the plane.1 As a result, there is a second topological invariant characterizing them, the skyrmion numberwheren(r) is the unit vector parallel to the local magnetization M(r). Skyrmions were introduced in the context of the two-dimensional Heisenberg model by Belavin and Polyakov. 4 However, similar topological defects were discussed earlier by Feldtkeller, 5 Kleman, 6 and Thiele. 2 A vortex with a winding number n and core polarization p has a half-integer skyrmion charge 7 q = np/2. A vortexantivortex pair with parallel polarizations p have opposite skyrmion numbers adding to zero and thus belongs to the same topological sector as uniform ground states. From the topological perspective, such a texture can be deformed continuously into a ground state and apparently this is exactly what happens: the energy decreases continuously until it reaches the ground-state value.In contrast, a vortex and an antivortex with antiparallel core polarizations have equal s...

We study current induced magnetization dynamics in a long thin ferromagnetic wire with Dzyaloshinskii-Moriya interaction (DMI). We find a spiral domain wall configuration of the magnetization and obtain an analytical expression for the width of the domain wall as a function of the interaction strengths. Our findings show that above a certain value of DMI a domain wall configuration cannot exist in the wire. Below this value we determine the domain wall dynamics for small currents, and calculate the drift velocity of the domain wall along the wire. We show that the DMI suppresses the minimum value of current required to move the domain wall. Depending on its sign, the DMI increases or decreases the domain wall drift velocity.

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