  We theoretically study the motion of magnetic colloidal particles above a
magnetic pattern and compare the predictions with Brownian dynamics
simulations. The pattern consists of alternating square domains of positive and
negative magnetization. The colloidal motion is driven by periodic modulation
loops of an external magnetic field. There exist loops that induce
topologically protected colloidal transport between two different unit cells of
the pattern. The transport is very robust against internal and external
perturbations. Theory and simulations are in perfect agreement.
