Domain Wall Programmable Magnetic Logic
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micromagnetic simulation, are shown in Fig. 2. The DW motion from the bifurcation
to the lower branch is completed via a complex DW transformation.
Besides chirality, the DW can also be represented as the composite of topological edge defects [30]. For instance, a vortex wall is a combination of two −½ edge
defects (vertices) and a +1 bulk defect (core). A transverse DW is a composite of two
half integer edge defects with their positions dependent on its chirality. The magnetization switching in the bifurcated nanowire is governed by the conservation of these
topological edge defects. Schematic representations of the elementary defects with
+½ and −½ winding numbers are shown in Fig. 1. A defect in which all the spins
are diverging is assigned a +½ winding number. Defect with two spins diverging and
one spin converging is assigned with −½ winding number. A TT-U TDW has a, −½
~ +½, winding number at the top and bottom edge of the DW respectively as seen in
Fig. 1. At the bifurcation, there is vertex, which is characterized by a −1/2 winding
number. When the DW reaches the bifurcation, it gets pinned before interacting with
the vertex state. The TTU TDW has a CW spin orientation. When the DW reaches
the bifurcation, the spins adopt a CW orientation which in turn pushes the vertex
core towards the upper branch. The DW has higher energy at the +½ edge defect
as compared to the −½ edge defect due to the transverse variation of the DW width
[32]. With the increase of magnetic field strength, the bottom part of the DW depins
and collides with the vertex at the bifurcation. The collision between the TDW and
the edge defect at the vertex leads to the formation of a VDW with a CW orientation. Conservation of topological charge dictates that the total winding numbers
of edge defects should be conserved during DW interaction or transformation [30].
The VDW is characterized by a +1 bulk defect at the core and two −½ defects at
the edges. In this system, the transformation of the +½ defect from the TT-U TDW
to a +1 defect leads to formation of the vortex configuration. To conserve the total
winding number of the system, a −½ defect is nucleated along the same edge of the
transformed +½ defect, as shown in the bottom inset of Fig. 2. Further increasing
the magnetic field strength causes the core of the VDW to move towards point A,
where the core eventually annihilates. To maintain the total topological charge at the
bifurcation, the annihilation of the vortex core (+1 defect) leaves behind −½ edge
defect from the TT-U TDW at the bifurcation and a new TDW is nucleated within the
lower branch as shown in Fig. 2. The motion of the TDW through the lower branch
changes the magnetization orientation of the branch. The DW motion through the
network structure displaces the position of the edge defect from position A to B. It
shows that the total topological winding number is always −½ before and after DW
motion through the dual branch structure.
To investigate the effect of the DW chirality on the reversal process, a TT TDW
with “DOWN” chirality (TT-D TDW) is relaxed in the nanowire as shown in Fig. 3.
The magnetization switching of the TT-D TDW follows the same process as the
TT-U TDW. However, when the DW is driven through the Y-shaped structure, the
TT-D selectively travels through the upper branch and switches its magnetization,
as shown in Fig. 3. A TT-D is composed of a +½ defect at the top edge and a −½
defect at the bottom edge, as shown in Fig. 2. Similar TDW pinning at the bifurcation
occurs when a magnetic field is applied. The spins in the TT-D TDW always rotates
229
micromagnetic simulation, are shown in Fig. 2. The DW motion from the bifurcation
to the lower branch is completed via a complex DW transformation.
Besides chirality, the DW can also be represented as the composite of topological edge defects [30]. For instance, a vortex wall is a combination of two −½ edge
defects (vertices) and a +1 bulk defect (core). A transverse DW is a composite of two
half integer edge defects with their positions dependent on its chirality. The magnetization switching in the bifurcated nanowire is governed by the conservation of these
topological edge defects. Schematic representations of the elementary defects with
+½ and −½ winding numbers are shown in Fig. 1. A defect in which all the spins
are diverging is assigned a +½ winding number. Defect with two spins diverging and
one spin converging is assigned with −½ winding number. A TT-U TDW has a, −½
~ +½, winding number at the top and bottom edge of the DW respectively as seen in
Fig. 1. At the bifurcation, there is vertex, which is characterized by a −1/2 winding
number. When the DW reaches the bifurcation, it gets pinned before interacting with
the vertex state. The TTU TDW has a CW spin orientation. When the DW reaches
the bifurcation, the spins adopt a CW orientation which in turn pushes the vertex
core towards the upper branch. The DW has higher energy at the +½ edge defect
as compared to the −½ edge defect due to the transverse variation of the DW width
[32]. With the increase of magnetic field strength, the bottom part of the DW depins
and collides with the vertex at the bifurcation. The collision between the TDW and
the edge defect at the vertex leads to the formation of a VDW with a CW orientation. Conservation of topological charge dictates that the total winding numbers
of edge defects should be conserved during DW interaction or transformation [30].
The VDW is characterized by a +1 bulk defect at the core and two −½ defects at
the edges. In this system, the transformation of the +½ defect from the TT-U TDW
to a +1 defect leads to formation of the vortex configuration. To conserve the total
winding number of the system, a −½ defect is nucleated along the same edge of the
transformed +½ defect, as shown in the bottom inset of Fig. 2. Further increasing
the magnetic field strength causes the core of the VDW to move towards point A,
where the core eventually annihilates. To maintain the total topological charge at the
bifurcation, the annihilation of the vortex core (+1 defect) leaves behind −½ edge
defect from the TT-U TDW at the bifurcation and a new TDW is nucleated within the
lower branch as shown in Fig. 2. The motion of the TDW through the lower branch
changes the magnetization orientation of the branch. The DW motion through the
network structure displaces the position of the edge defect from position A to B. It
shows that the total topological winding number is always −½ before and after DW
motion through the dual branch structure.
To investigate the effect of the DW chirality on the reversal process, a TT TDW
with “DOWN” chirality (TT-D TDW) is relaxed in the nanowire as shown in Fig. 3.
The magnetization switching of the TT-D TDW follows the same process as the
TT-U TDW. However, when the DW is driven through the Y-shaped structure, the
TT-D selectively travels through the upper branch and switches its magnetization,
as shown in Fig. 3. A TT-D is composed of a +½ defect at the top edge and a −½
defect at the bottom edge, as shown in Fig. 2. Similar TDW pinning at the bifurcation
occurs when a magnetic field is applied. The spins in the TT-D TDW always rotates