Dependence of Domain-Wall Depinning Threshold Current on Pinning Profile

We have investigated the threshold current density required for depinning a domain wall from constrictions in NiFe nanowires, which give rise to pinning potentials of fixed amplitude but variable profile. We observed it to vary linearly with the angle of the triangular constriction. These results are reproduced using micromagnetic simulations including the adiabatic and nonadiabatic spin-torque terms. By curve-fitting the calculated variations to the experimental results, we obtain the nonadiabaticity parameter $\beta =0.04(\pm 0.005)$ and current spin polarization $P=0.51(\pm 0.02)$.

Figure 1

(a) SEM image (uncontacted), and (b) longitudinal MR measurement (large circles and squares) and focused MOKE measurement (small circles) of a structure with a 43.1° notch angle. The inset shows a wire with the contact pads used for measurements.

Figure 2

(a) Longitudinal MR response as a function of dc offset for a notch angle of 43°, where the positive field data are MR sweeps following saturation in the $-2\mathrm{kOe}$ field and the negative field data are MR sweeps following saturation in the $+2\mathrm{kOe}$ field. (b) Mean threshold current density at a longitudinal field of 10 Oe versus notch angle where the solid circles are the experimental points, together with the associated error bars due to uncertainties in device dimensions, and the line is a straight line fit. In the inset, the probability of DW depinning as a function of dc offset is shown for the notch angle of 43°, where the solid circles are the experimental points and the solid curve is an error function fit.

Figure 3

DW pinning position at zero magnetic field, after reversal from saturation, as a function of notch angle determined using micromagnetic simulations (top) and spin-SEM imaging (bottom). The spin-SEM images show the magnetization direction along the length of the wire.

Figure 4

(a) Summary of experimental results showing variation of threshold current with notch angle. (b) Calculated threshold current as a function of notch angle at 0 Oe for nonadiabaticity parameter $\beta$ of 0.03, 0.04, and 0.05 and best fit current spin polarization $P$ of 0.51. The solid circles are the threshold current values measured at 0 Oe using pc measurements.