Experimental determination of spin-transfer torque nonadiabaticity parameter and spin polarization in permalloy

The domain-wall depinning boundary, showing the variation in critical current density with magnetic field, is measured for notched permalloy wires using pulsed-current measurements. The structure of domain walls trapped at the pinning potential provided by the notch is imaged using photoemission electron microscopy. The experimental depinning boundary is compared with those obtained by micromagnetic simulations including the adiabatic and nonadiabatic spin-torque terms. This method allows for the determination of both the nonadiabaticity parameter $\beta$ and spin current polarization $P$, which we obtain as $\beta =0.040\pm 0.005$ and $P=0.40\pm 0.02$ at room temperature.

Figure 1

(Color online) (a) SEM image of notched wire. [(b) and (c)] PEEM images of notched wire with $3\mu \text{m}$ notch length showing a domain wall pinned at the notch. (d) in-plane PEEM vector map obtained from the two PEEM images in (b) and (c) taken with the x-ray beam at orthogonal angles. (e) Micromagnetic simulation of notched wire with $3\mu \text{m}$ notch length showing a domain wall pinned at the notch.

Figure 2

(Color online) (a) Pulse from generator and resulting pulse across the sample. (b) Domain-wall depinning probability map, showing variation in critical current density as a function of pulse width for an applied longitudinal magnetic field of 14 Oe. (c) Temperature change in the sample as a result of Joule heating by current pulses of varying pulse width and fixed pulse amplitude resulting in a current density of $8.9\times {10}^{11}\text{A}/{\text{m}}^2$. The data points are acquired using an internal storage buffer on the lock-in amplifier.

Figure 3

(Color online) Domain-wall depinning boundary as a function of pulse width for different magnetic field values.

Figure 4

(Color online) Experimental domain-wall depinning boundary, together with associated error bars, as a function of magnetic field for fixed pulse width of 380 ns, and simulated depinning boundaries for different values of nonadiabaticity parameter and spin polarization 0.4. In the inset, the fitting coefficient (solid circles) and best fit spin polarization (open circles) are plotted as a function of nonadiabaticity parameter.

Figure 5

(Color online) Experimental domain-wall depinning boundary and calculated boundaries for $\beta =0.02$ and 0.06 showing the best fit for $P$.