Figure 1
(a) The cartesian coordinate system and the spherical coordinate system used for the study of the TDW dynamics. The cross-sections indicate the position of the wall plane and the white arrows represent the orientation of the transverse magnetization. (b) The TDW moves linearly through the nanowire in the direction of electron flow (denoted with letter e) with a linear velocity proportional to \(\dot{\theta }\) and rotates around the axis of symmetry with velocity \(\dot{\varphi }\) in the absence of a magnetic field. (c) In the presence of a magnetic field \({H}_{z}={H}_{z}^{pin}\), the TDW stops its linear movement, however it keeps rotating with an angular velocity \({\dot{\varphi }}_{pin}\) in an equilibrium position z pin .
