Transverse phase locking in fully frustrated Josephson junction arrays: A different type of fractional giant steps

Marconi, Veronica; Kolton, Alejandro B.; Domı́nguez, Daniel; Grønbech‐Jensen, Niels

doi:10.1103/physrevb.68.104521

Cited by 13 publications

(11 citation statements)

References 62 publications

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“…It can therefore be interesting to study the possibility of mode-locking when an ac force is applied in the direction perpendicular to the direction of the dc driving force. Recently, it has been found in rectangular periodic pin-ning arrays 17 and in Josephson junction arrays 18 that a transverse ac force leads to a new type of "transverse" phase-locking in these cases. In this paper we will investigate the possibility of transverse mode-locking in driven vortices with random pinning.…”

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Mode locking in driven vortex lattices with transverse ac drive and random pinning

2002

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We find mode-locking steps in simulated current-voltage characteristics of driven vortex lattices with random pinning when an applied ac-current is perpendicular to the dc-current. For low frequencies there is mode-locking only above a non-zero threshold ac force amplitude, while for large frequencies there is mode-locking for any small ac force. This is consistent with the nature of transverse temporal order in the different regimes in the absence of an applied ac-drive. For large frequencies the magnitude of the fundamental mode-locked step depends linearly with the ac force amplitude.

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Mode locking in driven vortex lattices with transverse ac drive and random pinning

2002

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“…Such steps have been studied for vortices moving over random disorder [21][22][23][24][25] or through confined channel geometries 26 . For particles confined to 2D and moving over a quasi-1D substrate, both the ac and dc drives must be applied in the same direction to produce Shapiro steps; however, for vortices moving over 2D periodic or egg-carton substrates, it is possible to obtain what are called transverse phase locking steps when the ac drive is perpendicular to the direction of the dc drive [27][28][29] . These phase locking steps are distinct from Shapiro steps, and their widths grow quadratically with increasing ac amplitude rather than showing the oscillatory behavior associated with Shapiro steps.…”

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confidence: 99%

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

Reichhardt

2015

Phys. Rev. B

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We numerically study the behavior of two-dimensional skyrmions in the presence of a quasi-onedimensional sinusoidal substrate under the influence of externally applied dc and ac drives. In the overdamped limit, when both dc and ac drives are aligned in the longitudinal direction parallel to the direction of the substrate modulation, the velocity-force curves exhibit classic Shapiro step features when the frequency of the ac drive matches the washboard frequency that is dynamically generated by the motion of the skyrmions over the substrate, similar to previous observations in superconducting vortex systems. In the case of skyrmions, the additional contribution to the skyrmion motion from a non-dissipative Magnus force shifts the location of the locking steps to higher dc drives, and we find that the skyrmions move at an angle with respect to the direction of the dc drive. For a longitudinal dc drive and a perpendicular or transverse ac drive, the overdamped system exhibits no Shapiro steps; however, when a finite Magnus force is present we find pronounced transverse Shapiro steps along with complex two-dimensional periodic orbits of the skyrmions in the phaselocked regimes. Both the longitudinal and transverse ac drives produce locking steps whose widths oscillate with increasing ac drive amplitude. We examine the role of collective skyrmion interactions and find that additional fractional locking steps occur for both longitudinal and transverse ac drives. At higher skyrmion densities, the system undergoes a series of dynamical order-disorder transitions, with the skyrmions forming a moving solid on the phase locking steps and a fluctuating dynamical liquid in regimes between the steps.

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“…On each step, the particle velocity remains fixed even though the dc drive is changing, so that the particle remains in resonance. If the ac drive is perpendicular to the dc drive, then for 2D periodic substrates it is possible to have another type of phase locking distinct from Shapiro steps which is known as transverse phase locking [28,29]. Multiple ac drives can also be applied in the form of multiple frequencies in the same direction or the same frequencies in different directions and out of phase by 90 • to create a circular drive [30,31,32,33,34,35].…”

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confidence: 99%

Skyrmion Dynamics and Transverse Mobility: Skyrmion Hall Angle Reversal on 2D Periodic Substrates with dc and Biharmonic ac Drives

Vizarim,

Reichhardt,

Venegas

et al. 2020

Preprint

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We numerically examine the dynamics of a skyrmion interacting with a two-dimensional periodic substrate under dc and biharmonic ac drives. We show that the Magnus force of the skyrmion produces circular orbits that can resonate with the ac drive and the periodicity of the substrate to create quantized motion both parallel and perpendicular to the dc drive. The skyrmion Hall angle exhibits a series of increasing and/or decreasing steps along with strongly fluctuating regimes. In the phase locked regimes, the skyrmion Hall angle is constant and the skyrmion motion consists of periodic orbits encircling an integer number of obstacles per every or every other ac drive cycle. We also observe phases in which the skyrmion moves at 90 • with respect to the driving direction even in the presence of damping, a phenomenon called absolute transverse mobility that can exhibit reentrance as a function of dc drive. When the biharmonic ac drives have different amplitudes, in the two directions we find regimes in which the skyrmion Hall angle shows a sign reversal from positive to negative, as well as a reentrant pinning effect in which the skyrmion is mobile at low drives but becomes pinned at higher drives. These behaviors arise due to the combination of the Magnus force with the periodic motion of the skyrmions, which produce Shapiro steps, directional locking, and ratchet effects.

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Transverse phase locking in fully frustrated Josephson junction arrays: A different type of fractional giant steps

Cited by 13 publications

References 62 publications

Mode locking in driven vortex lattices with transverse ac drive and random pinning

Mode locking in driven vortex lattices with transverse ac drive and random pinning

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

Skyrmion Dynamics and Transverse Mobility: Skyrmion Hall Angle Reversal on 2D Periodic Substrates with dc and Biharmonic ac Drives

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