Fig. 1. (a) The geometry and dimension of the trapezoid-cross-section nanostrip. The external magnetic field direction is denoted by the arrows on the top. A head-to-head transverse DW is initially positioned in the center of the nanostrip, and its direction is denoted by the arrows inside. The cross section of the nanostrip is shown at the bottom. (b) The schematic diagrams of the nanotube unrolled into a trapezoid-cross-section nanostrip when it is cut along the long axis.

Fig. 2. The absolute value of DW displacement varies with time driven by (a) ±10 Oe, (b) ± 35 Oe and (c) ± 50 Oe magnetic field in the case of a = 10, h = 5 nm. In (a), the red and black curves coincide. The symbols ↑, ↓, and ⊙, ⊗ represent the spin structure of transverse and anti-vortex DWs in xz-plane (top view), and the corresponding images is illustrated beside the symbols. The arrows inside the images as well as the color map represent the in-plane magnetization directions. The white/black dot in the images indicates an upward/downward anti-vortex core.

Fig. 3. The schematic diagrams of the directions of the local magnetization M. The magnetic torque τ on M and the demagnetizing field H_d (cross section view) is shown on the left panel of (a). The snapshots of the y-component demagnetizing field (H_d,y) distribution around the DW (cross section view) at t = 5 ns driving by ± 10 Oe fields are illustrated on the right panel of (a). The color bar indicates the H_d,y value. The nanostrip is artificially divided into 5 layers as shown in the inset of (c). The H_d,y for different layers is shown in (b) driven by +10 Oe field and (c) –10 Oe field in the case of a = 10 nm and h = 5 nm.

Fig. 4. (a) The E_demag and E_ex profiles versus time driven by 50 Oe magnetic field. (b) The sum of E_demag and E_ex versus time. The snapshots of anti-vortex walls and transverse walls in xz-plane (top view) are shown on the top and bottom of (b), respectively. The arrows inside the snapshots as well as the color map represent the in-plane magnetization directions.

Fig. 5. The DW average velocity v under different magnetic fields in the cases of (a) a = h = 5 nm, (b) a = h = 8 nm and (c) a = 10 nm, h = 5 nm.