Spin-Transfer-Torque-Assisted Domain-Wall Creep in a $\mathrm{Co}/\mathrm{Pt}$ Multilayer Wire

We have studied field- and current-driven domain-wall (DW) creep motion in a perpendicularly magnetized $\mathrm{Co}/\mathrm{Pt}$ multilayer wire by real-time Kerr microscopy. The application of a dc current of density of $\lesssim {10}^7\mathrm{A}/{\mathrm{cm}}^2$ assisted only the DW creeping under field in the same direction as the electron flow, a signature of spin-transfer torque effects. We develop a model dealing with both bidirectional spin-transfer effects and Joule heating, with the same dynamical exponent $\mu =1/4$ for both field- and current-driven creep, and use it to quantify the spin-transfer efficiency as $3.6\pm 0.6\mathrm{Oe}{\mathrm{cm}}^2/\mathrm{MA}$ in our wires, confirming the significant nonadiabatic contribution to the spin torque.

Figure 1

Room-temperature polar Kerr effect hysteresis loop of an unpatterned $\mathrm{Co}/\mathrm{Pt}$ multilayer.

Figure 2

Kerr microscope snapshots at different times of a device at constant field ($H=136\mathrm{Oe}$). The positions of DWB and DWC are marked with vertical solid lines. Wall propagation is observed under no current (a), positive current of $+3\mathrm{mA}$ (b), and negative current of $-3\mathrm{mA}$ (c). The current-assisted creep motion is marked with a dotted line.

Figure 3

Velocities of both DWs (DWC, open symbols; DWB, solid symbols) as a function of current density for fields of 122 Oe (▽, ▼), 136 Oe (□, ■), and 148 Oe (○, ●). The solid and dashed lines show the fits to the spin-transfer assisted creep model described by Eq. (2) in the text. The inset shows the wire temperature as a function of current density, with a solid line showing the quadratic fit.