Propagation of ferromagnetic domain walls on sub-atomic scale was measured in a thin uniaxial gamet film by using ballistic Hall magnetometry. Domain walls are found to move by equidistant steps, which correspond to the crystal lattice constant in this material. Our results are in good agreement with the theory of intrinsic pinning of a domain wall in the Peierls potential. We have also measured AC susceptibility of a domain wall moving inside a Peierls valley. The observed nonlinear behavior of the AC susceptibility can be understood within the framework of kinks and breathers nucleating and spreading along the domain wall. (C) 2003 Elsevier B.V. All rights reserved.