Erratum: Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep [Phys. Rev. B<b>87</b>, 214419 (2013)]

Lin, Shi-Zeng; Reichhardt, C.; Batista, Cristian D.; Saxena, Avadh

doi:10.1103/physrevb.88.019901

Cited by 67 publications

(120 citation statements)

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“…In the presence of quenched disorder, skyrmions exhibit pinningdepinning transitions 36 , as observed in experiments 20 and simulations [21][22][23][24][25] , and these are similar to the depinning transitions observed for vortices in type-II superconductors 17,37-39 . There are important differences between the two systems, particularly the dominant role that non-dissipative effects can take in skyrmion motion.…”

Section: Introductionsupporting

confidence: 71%

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

2015

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We examine the dynamics of a skyrmion moving over a two-dimensional periodic substrate utilizing simulations of a particle-based skyrmion model. We specifically examine the role of the non-dissipative Magnus term on the driven motion and the resulting skyrmion velocity-force curves. In the overdamped limit, there is a depinning transition into a sliding state in which the skyrmion moves in the same direction as the external drive. When there is a finite Magnus component in the equation of motion, a skyrmion in the absence of a substrate moves at an angle with respect to the direction of the external driving force. When a periodic substrate is added, the direction of motion or Hall angle of the skyrmion is dependent on the amplitude of the external drive, only approaching the substrate-free limit for higher drives. Due to the underlying symmetry of the substrate the direction of skyrmion motion does not change continuously as a function of drive, but rather forms a series of discrete steps corresponding to integer or rational ratios of the velocity components perpendicular ( V ⊥ ) and parallel ( V || ) to the external drive direction: V ⊥ / V || = n/m, where n and m are integers. The skyrmion passes through a series of directional locking phases in which the motion is locked to certain symmetry directions of the substrate for fixed intervals of the drive amplitude. Within a given directionally locked phase, the Hall angle remains constant and the skyrmion moves in an orderly fashion through the sample. Signatures of the transitions into and out of these locked phases take the form of pronounced cusps in the skyrmion velocity versus force curves, as well as regions of negative differential mobility in which the net skyrmion velocity decreases with increasing external driving force. The number of steps in the transport curve increases when the relative strength of the Magnus term is increased. We also observe an overshoot phenomena in the directional locking, where the skyrmion motion can lock to a Hall angle greater than the clean limit value and then jump back to the lower value at higher drives. The skyrmion-substrate interactions can also produce a skyrmion acceleration effect in which, due to the non-dissipative dynamics, the skyrmion velocity exceeds the value expected to be produced by the external drive. We find that these effects are robust for different types of periodic substrates. Using a simple model for a skyrmion interacting with a single pinning site, we can capture the behavior of the change in the Hall angle with increasing external drive. When the skyrmion moves through the pinning site, its trajectory exhibits a side step phenomenon since the Magnus term induces a curvature in the skyrmion orbit. As the drive increases, this curvature is reduced and the side step effect is also reduced. Increasing the strength of the Magnus term reduces the range of impact parameters over which the skyrmion can be captured by a pinning site, which is one of the reasons that strong Magnus force effects reduce the...

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Section: Introductionsupporting

confidence: 71%

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

2015

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“…[22], that skyrmions dynamics is activated when exposed to a thermal gradient and also displays a thermal creep motion in a pinning potential in Ref. [23].…”

Section: Introductionmentioning

confidence: 94%

Thermally assisted current-driven skyrmion motion

Troncoso

Núñez

2014

Phys. Rev. B

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We study the behavior of skyrmions in thin films under the action of stochastic torques arising from thermal fluctuations. We find that the Brownian motion of skyrmions is described by a stochastic Thiele's equation and its corresponding Fokker-Planck equation. The resulting FokkerPlanck equation is recognized as the one for a high-friction Brownian particle which has been studied extensively in different physical contexts. It is shown that thermal fluctuations favor the skyrmion motion allowing a finite mobility even in presence of pinning traps. We calculate explicitly the mobility tensor of skyrmions in linear response to an electric current finding that it increases with temperature.

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“…In the continuum, the lowest frequency mode of the skyrmion is the gapless Goldstone mode associated with invariance under the group of continuous translations. In recent derivations of the equation of motion [17][18][19][20][21][22][23] based on Thiele's collective coordinate approach 24 , only the translational mode was taken into account by assuming that the skyrmion is rigid. Knowledge of the internal modes can test the validity of this assumption.…”

Section: Introductionmentioning

confidence: 99%

Internal modes of a skyrmion in the ferromagnetic state of chiral magnets

2014

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A spin texture called skyrmion has been recently observed in certain chiral magnets without inversion symmetry. The observed skyrmions are extended objects with typical linear sizes of 10 nm to 100 nm that contain 10 3 to 10 5 spins and can be deformed in response to external perturbations. Weak deformations are characterized by internal modes, which are localized around the skyrmion center. Knowledge of internal modes is crucial to assess the stability and rigidity of these topological textures. Here we compute the internal modes of a skyrmion in a ferromagnetic background state by numerical diagonalization of the dynamical matrix. We find several internal modes below the magnon continuum, such as the mode corresponding to the translational motion and different kinds of breathing modes. The number of internal modes is larger for lower magnetic fields. Indeed, several modes become gapless in the low field region indicating that the single skyrmion solution becomes unstable, although a skyrmion lattice remains thermodynamically stable. On the other hand, only three internal modes exist at high fields and the skyrmion texture remains locally stable even when the ferromagnetic state becomes thermodynamically stable. We also show that the presence of out-of-plane easy-axis anisotropy stabilizes the single skyrmion solution. Finally, we discuss the effects of damping and possible experimental observations of these internal modes.

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Erratum: Particle model for skyrmions in metallic chiral magnets: Dynamics, pinning, and creep [Phys. Rev. B87, 214419 (2013)]

Cited by 67 publications

References 0 publications

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

Quantized transport for a skyrmion moving on a two-dimensional periodic substrate

Thermally assisted current-driven skyrmion motion

Internal modes of a skyrmion in the ferromagnetic state of chiral magnets

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