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We measure the trajectories of macroscopic magnetic particles pulled againstgravity between twisted alternating magnetic square patterns in a superposedhomogeneous magnetic field normal to both patterns. The two patterns are builtfrom a set of magentic cubes having a distribution of magnetization. Themagnetic potential between the patterns is a sum of three contributions: twobeing periodic on two lattices with different magnitude and orientation, andthe third random contribution arising from the distribution of magnetization ofthe cubes. As one varies the twist angle between the two patterns each time thetwist angle coincides with a magic twist angle one of the two periodic latticesbecomes a sublattice of the other lattice. Simulations of particles movingthrough patterns with a precise cube magnetization produce pronounced mobilitypeaks near magic twist angles that are associated with flat channels. Weakrandom fluctuations of the cube magnetization in the experiment and thesimulations cause enhanced random disorder of the potential and reduce themobility by scattering particles into the interior of the twisted Wigner Seitzcells. The mobility undergoes an Anderson transition from magic to genericbehavior as the magnetization disorder increases beyond half of a percent ofthe cube magnetization.

Disorder scattering in classical flat channel transport of particles between twisted magnetic square patterns