Domain-wall dynamics in multisegmented Ni/Co nanowires

The current-induced motion of transverse magnetic domain walls (DWs) in a multisegmented Co/Ni nanowire is investigated numerically. We find that the phase diagram current pulse length magnitude presents a rare diversity of behaviors depending on the segment's length and material parameters. We show that by changing only the pulse shape, in a range of parameters we obtain the controlled motion of the DW with or without polarity change. The polarity change arises in the simplest case from the birth and propagation of an antivortex along the width of the nanowire. The antivortex can be displaced over long distances depending on the pulse characteristics and boundary conditions. The systematic motion of the DW with polarity flip is found to be stable at room temperature. Moreover, by modifying the material parameters through alloying, the phase diagram can be engineered, decreasing the depinning current and paving the way for storage or logic applications.

Figure 1

(a) Multisegmented Co/Ni nanowire with an in-plane transverse DW. The Ni regions (40 nm length) are shaded and the Co regions (80 nm length) have a magnetocrystalline anisotropy along the $z$ axis. The arrows indicate the direction of the magnetization. The enlarged section shows the central regions with the transverse domain wall. (b) Expanded part of the multisegmented nanowire when the Co regions have a magnetocrystalline anisotropy along the $y$ axis. The length of the regions have been inverted: Co regions of 40 nm and Ni regions of 80 nm. The nanowire is 1300 nm long, 60 nm wide, and 5 nm thick.

Figure 2

Micromagnetic phase diagrams (pulse stable time—pulse amplitude) of DW motion under a periodic current pulse in a multisegmented Ni/Co nanowire at $T=0$ K. The periodic pulse is formed of two identical current pulses of opposite amplitude (forward-backward motion) separated by a waiting time of 5 ns. The length of the Ni and Co regions is varied as—from the top row to the bottom row—the Ni region's length increases from 20 nm (top row) to 40 nm (bottom row) in steps of 10 nm, while the Co region's length increases from left column to right column from 50 nm (left column) to 90 nm (right column) in steps of 10 nm. The thickness of the nanowire is 5 nm and its total length is around 1300 nm (varies slightly to always have Co regions at the ends). The observed DW motion is classified in bands numbered as follows: positive bands correspond to the DW moving in the direction of the electron flow, negative numbers to the DW moving contrary to the electron flow, zero state correspond to the DW staying pinned at initial position, and u to the unintended states in which the DW does not come back to the initial state after the periodic pulse.

Figure 3

DW displacement in a 40-nm Ni/80-nm Co segmented nanowire under a current pulse when ${\mathrm{t}}_s=400\mathrm{ps}, {\mathrm{j}}_e=5.5\mathrm{A}/\mu {\mathrm{m}}^2$ (a) or ${\mathrm{t}}_s=1050\mathrm{ps}, {\mathrm{j}}_e=6.4\mathrm{A}/\mu {\mathrm{m}}^2$ (b) was applied. Both cases correspond to a state $+1$. The Ni regions are indicated by darker colors. In panel (a), an antivortex is observed crossing the nanowire width (first row, blue circle) while the TDW changes polarity when moving to the nearest Ni region. In panel (b), the antivortex does not cross the nanowire width and is expelled on the same edge it entered. The TDW does not change its polarity when moving to the nearest Ni region. The second row in panel (a) shows the $m_x$ component of magnetization, illustrating the DW deformation in the process.

Figure 4

Time variation of the DW upper (dotted line) and lower (full line) center position (first row) and azimuthal angle (second row) in a 40-nm Ni/80-nm Co multisegmented nanowire. The first column corresponds to a forward followed by a backward pulse with characteristics ${\mathrm{t}}_s=400\mathrm{ps}, {\mathrm{j}}_e=5.5\mathrm{A}/\mu {\mathrm{m}}^2$ separated by ${\mathrm{t}}_z=5$ ns, the second column to forward-backward pulses with characteristics ${\mathrm{t}}_s=1050\mathrm{ps}, {\mathrm{j}}_e=6.4\mathrm{A}/\mu {\mathrm{m}}^2, {\mathrm{t}}_z=5$ ns, the third column to forward-backward pulses with characteristics ${\mathrm{t}}_s=250\mathrm{ps}, {\mathrm{j}}_e=8.5\mathrm{A}/\mu {\mathrm{m}}^2, {\mathrm{t}}_z=5$ ns, and the last column to to forward-backward pulses with characteristics ${\mathrm{t}}_s=800\mathrm{ps}, {\mathrm{j}}_e=6.4\mathrm{A}/\mu {\mathrm{m}}^2, {\mathrm{t}}_z=5$ ns. The last row shows the temporal antivortex trajectory (time variation from dark to lighter colors) with the arrows indicating the current pulse end. The horizontal dotted lines in the first row and the vertical dotted lines in the last row illustrate the Ni regions edges. The vertical dotted lines in the first row pinpoint the current pulse end.

Figure 5

Temporal antivortex trajectory (time variation from dark to lighter colors) in a 40-nm Ni/80-nm Co multisegmented nanowire for a 5-ns current pulse with magnitude ${\mathrm{j}}_e$ of 5.5 $\mathrm{A}/\mu {\mathrm{m}}^2$ in (a) and 6.4 $\mathrm{A}/\mu {\mathrm{m}}^2$ in (d). The temporal evolution of the demagnetizing (full line) and exchange (dashed line) energies and the antivortex $y$ position corresponding to panel (a) are shown in (b) and (c), respectively. The vertical dotted lines in (a) and (d) illustrate the Ni regions edges. The nanowire is 1300 nm long.

Figure 6

Micromagnetic phase diagrams of DW motion under a periodic current pulse in a multisegmented 40-nm Ni/80-nm Co nanowire at $T=0$ K. Only exchange stiffness constant $A$ is varied for the Co regions from 15 pJ/m (a) to 20 pJ/m (b), 28.1 pJ/m (c), 35 pJ/m (d), 40 pJ/m (e), and 50 pJ/m (f). The observed DW motion is classified in bands numbered as follows: positive bands correspond to the DW moving in the direction of the electron flow, negative numbers to the DW moving contrary to the electron flow, zero state correspond to the DW staying pinned at initial position, and u to the unintended states in which the DW does not come back to the initial state after the periodic pulse.

Figure 7

Micromagnetic phase diagrams of DW motion under a periodic current pulse in a multisegmented $\mathrm{Ni}/{\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$ nanowire at $T=0$ K. The length of the regions varies as (a), 30-nm Ni/50-nm ${\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$; (b), 20-nm Ni/60-nm ${\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$; (c), (d) 40-nm Ni/80-nm ${\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$. From (a)–(c), $\alpha =0.05$ and $\beta =2\alpha$ for both region types, while in (d) ${\alpha }_{{\text{Co}}_{50}{\text{Ni}}_{50}}=0.005$. The observed DW motion is classified in bands numbered as follows: positive bands correspond to the DW moving in the direction of the electron flow, negative numbers to the DW moving contrary to the electron flow, zero state correspond to the DW staying pinned at initial position, and u to the unintended states in which the DW does not come back to the initial state after the periodic pulse.

Figure 8

Probability of DW motion in $+1$ bands at $T=293$ K for a multisegmented nanowire of Ni and Co or ${\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$ regions: (a) 30-nm Ni/50-nm Co, (b) 20-nm Ni/60-nm Co, (c) 40-nm Ni/80-nm Co, (d) 30-nm Ni/50-nm ${\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$, (e) 20-nm Ni/60-nm ${\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$, and (f) 40-nm Ni/80-nm ${\mathrm{Co}}_{50}{\mathrm{Ni}}_{50}$.