Abstract
Paramagnetic colloidal particles move in the potential energy landscape of a magnetically modulated bubble lattice of a magnetic garnet film. The modulation causes the energy minima to alternate between positions above the centres of the bubbles and interstitial positions. The particles deterministically follow the time-dependent positions of the energy minima until the minima become unstable in one or several directions and allow the particles to hop to a new minimum. We control the time delay between instabilities of the minima in alternative directions by the angle of the external magnetic field with the crystallographic directions of the bubble lattice. When the time delay is large, the particles deterministically hop to the next minimum along the direction that becomes unstable first. When the time delay is short, diffusion of the particle in the marginal potential randomizes the choice of the hopping directions or the choice of the transport network. Gradual changes of the external field direction from 0° to 30° lead to a continuous crossover from a deterministic to a fully stochastic path of the colloids.
Highlights
Paramagnetic colloidal particles move in the potential energy landscape of a magnetically modulated bubble lattice of a magnetic garnet film
We describe the geometry of our bubble lattice within a Cartesian coordinate system with the x-axis aligned with one of the bubble lattice crystallographic axes in the plane of the garnet film, the y-axis along the −21 direction in the film and the z-axis normal to the film
We show a sequence of contour plots of the magnetic energy of a paramagnetic particle subject to an external field with azimuth φ = 210◦ and φ = 205◦ during a modulation t=0
Summary
Superposition of an external field modulation parallel to the film breaks the symmetry and this may be used to bias the hopping into a desired direction and to bias the use of the two networks. Both trajectories follow along a path passing from a bubble domain towards an interstitial position back to a bubble domain and so forth. A global dispersion of the transport direction occurs when the external magnetic field points from a bubble to an interstitial. These probabilities result from the probabilities of the individual hops occurring during each halfcycle by considering the hopping via the two interstitials that are common neighbours to the start and target bubbles.
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