Pinning, Ordering, and Dynamics of Vortices in Conformal Crystal and Gradient Pinning Arrays

TL;DR

This study uses numerical simulations to compare vortex pinning and dynamics in conformal crystal arrays with other gradient and quasiperiodic structures, revealing enhanced pinning and vortex guidance effects due to the arrays' local ordering and density gradients.

Contribution

It demonstrates that conformal crystal pinning arrays provide superior vortex pinning over a broad field range due to their unique density gradients and local order, introducing a new approach for optimizing vortex pinning.

Findings

Conformal arrays exhibit enhanced pinning compared to other structures.

Broad range of local commensuration effects due to conformal transformation.

Gradient arrays can induce strong vortex guidance and ordering.

Abstract

We numerically investigate magnetization, pinning, ordering, and dynamics of vortices interacting with pinning arrangements which have a density gradient. We focus on conformal crystal structures obtained by conformally transforming a spatially uniform periodic array, as well as non-conformal gradient structures and structures with quasiperiodic order. The conformal structures feature a density gradient and local ordering. Using magnetization simulations we find that conformal pinning arrays exhibit enhanced pinning compared to non-conformal gradient arrays as well as compared to random, periodic, and quasiperiodic arrays, for a broad range of fields. The effectiveness of conformal arrays arises from the continuum of length scales introduced into the arrays by the conformal transformation, allowing for a broad range of local commensuration effects. At higher vortex fillings above the range of conformal effectiveness, we show that a non-conformal rectangular gradient array exhibits strong pinning due to a novel commensuration effect and vortex ordering. Using transport simulations where vortices are driven along the gradient and at an angle to the gradient, we confirm the effectiveness of conformal pinning at increasing the critical current. For a rotated drive, the gradient arrays produce a strong vortex guidance effect in the direction perpendicular to the gradient.