368
X. S. Wang and X. R. Wang
(a)
(b)
(c)
(d)
(e)
Fig. 14.7 a–e Evolution of the DW structure during the propagation for smaller damping and
larger field. Figure redrawn using the results in [47]
edge. Together with two edge defects of winding number +1/2 at the bottom edge,
the antivortex detaches itself from the DW by creating an isolated defect region,
keeping the total winding number unchanged as shown in Fig. 14.7d. The isolated
defect eventually vanishes after dissipating its extra energy. As shown in in Fig. 14.7e,
a pure transverse DW appears again. This birth-death process of an antivortex repeats
itself periodically.
To manipulate DWs, one needs not only DW propagation but also DW pinning
and depinning [36]. The birth-death processes of (anti)vortices during the DW transformation are also closely related to the depinning of DWs from notches [48, 49].
A transverse DW can be depined from a notch assisted by the birth of a vortex [48].
For a strip with periodic notches, the DW motion can be even faster than that in a
perfect strip due to the vortex birth-death processes [49].
We have also studied DW models in higher dimensions. Consider R
3
→ M
2
model where the DW is a plane in 3D space. Due to the well-known bound states
inside the DW and the spin wave phase shift after crossing a DW [39, 50], the density
of states of spin waves in a DW and in a domain is different. In the presence of a
DW, there is an increase in number of low-energy states and a depletion in number
of high-energy states, keeping the total number of states equals the total degree of
X. S. Wang and X. R. Wang
(a)
(b)
(c)
(d)
(e)
Fig. 14.7 a–e Evolution of the DW structure during the propagation for smaller damping and
larger field. Figure redrawn using the results in [47]
edge. Together with two edge defects of winding number +1/2 at the bottom edge,
the antivortex detaches itself from the DW by creating an isolated defect region,
keeping the total winding number unchanged as shown in Fig. 14.7d. The isolated
defect eventually vanishes after dissipating its extra energy. As shown in in Fig. 14.7e,
a pure transverse DW appears again. This birth-death process of an antivortex repeats
itself periodically.
To manipulate DWs, one needs not only DW propagation but also DW pinning
and depinning [36]. The birth-death processes of (anti)vortices during the DW transformation are also closely related to the depinning of DWs from notches [48, 49].
A transverse DW can be depined from a notch assisted by the birth of a vortex [48].
For a strip with periodic notches, the DW motion can be even faster than that in a
perfect strip due to the vortex birth-death processes [49].
We have also studied DW models in higher dimensions. Consider R
3
→ M
2
model where the DW is a plane in 3D space. Due to the well-known bound states
inside the DW and the spin wave phase shift after crossing a DW [39, 50], the density
of states of spin waves in a DW and in a domain is different. In the presence of a
DW, there is an increase in number of low-energy states and a depletion in number
of high-energy states, keeping the total number of states equals the total degree of