Analysis Of Measured Transport Properties Of Domain Walls In Magnetic   Nanowires And Films
  Existing data for soft magnetic materials of critical current for domain-wall motion, wall speed driven by a magnetic field, and wall electrical resistance, show that all three observable properties are related through a single parameter: the wall mobility $\mu$. The reciprocal of $\mu$ represents the strength of viscous friction between domain wall and conduction-electron gas. And $\mu$ is a function of the wall width, which depends in turn on the aspect ratio t/w, where t and w are the thickness and width of the sample. Over four orders of magnitude of $\mu$, the data for nanowires show $\mu\propto (t/w)^{-2.2}$. This dependence is in approximate agreement with the prediction of the 1984 Berger theory based on s-d exchange. On the other hand, it is inconsistent with the prediction of the 2004 Tatara and Kohno theory, and of the 2004 Zhang and Li theory. 
L. Berger