Geometric control over the motion of magnetic domain walls

We propose a method that enables a precise control of magnetic patterns and relies only on the fundamental properties of the wire as well as on the choice of the path in the controlled parameter space but not on the rate of motion along this path. Possible experimental realizations of this mechanism are discussed. In particular, we show that the domain walls in magnetic nanowires can be translated by rotation of the magnetic easy axis or by applying pulses of magnetic field directed transverse to the magnetic easy axis.