Time-Domain Observation of the Spinmotive Force in Permalloy Nanowires

The spinmotive force associated with a moving domain wall is observed directly in Permalloy nanowires using real time voltage measurements with proper subtraction of the electromotive force. Whereas the wall velocity exhibits nonlinear dependence on magnetic field, the generated voltage increases linearly with the field. We show that the sign of the voltage reverses when the wall propagation direction is altered. Numerical simulations explain quantitatively these features of spinmotive force and indicate that it scales with the field even in a field range where the wall motion is no longer associated with periodic angular rotation of the wall magnetization.

Figure 1

(a) Schematic of the experimental setup. (b) Time dependence of the nanowire resistance when TT and HH walls are injected from line A and a sense current of $100\mu \mathrm{A}$ is applied from the current source. The drop in the resistance indicates the presence of a domain wall in section B–C. (c) Time dependence of the voltage measured with the current source turned off. Wire width ($w$) is 600 nm, and the length of section B–C ($L$) is $2\mu \mathrm{m}$.

Figure 2

(a) Temporal evolution of the scope voltage when TT and HH walls are injected from line A. No sense current is applied. (b) Subtraction of the waveforms shown in (a). The waveform associated with the HH wall is subtracted from that corresponding to the TT wall. (c) Mean of the two waveforms shown in (a). (d)–(f) The same as in (a)–(c) but the wall motion is reversed; i.e., the wall is injected from line D here. Wire width ($w$) is 600 nm, and the length of section B–C ($L$) is $2\mu \mathrm{m}$.

Figure 3

(a)–(d) Time dependence of the nanowire resistance or scope voltage when TT and HH walls are injected from line A. The sense current is set to $100\mu \mathrm{A}$ for (a) and (c), whereas it is turned off for (b) and (d). Wire width ($w$) is 600 nm for (a) and (b) and 300 nm for (c) and (d). The length of section B–C ($L$) is $4\mu \mathrm{m}$. (e),(f) Calculated spinmotive force of a (e) 600- and (f) 300-nm-wide wire. The wall is launched $3\mu \mathrm{m}$ away from the voltage probe.

Figure 4

(a),(b) Field dependence of the wall velocity and (c),(d) generated voltage. Results from wires with different lengths $L$ of section B–C are shown. Solid lines in (c) and (d) are a linear fit to the data with zero crossing. Wire width ($w$) is 600 nm for (a) and (c) and 300 nm for (b) and (d).

Figure 5

(a) Time dependence of a calculated spinmotive force for 200-nm-wide, 10-nm-thick Permalloy nanowire. The field is varied as indicated by the legend. (b),(c) Field dependence of the wall velocity (b) and spinmotive force (c) for the same wire. The arrows indicate the field where the corresponding voltage traces are shown in (a).