Nonlocal electrical detection of spin accumulation generated by anomalous Hall effect in mesoscopic $\mathrm{N}{\mathrm{i}}_{81}\mathrm{F}{\mathrm{e}}_{19}$ films

Spin accumulation generated by the anomalous Hall effect (AHE) in mesoscopic ferromagnetic $\mathrm{N}{\mathrm{i}}_{81}\mathrm{F}{\mathrm{e}}_{19}$ (permalloy, Py) films is detected electrically by a nonlocal method. The reciprocal phenomenon, the inverse spin Hall effect (ISHE), can also be generated and detected all electrically in the same structure. For accurate quantitative analysis, a series of nonlocal AHE/ISHE structures and supplementary structures are fabricated on each sample substrate to account for statistical variations and to accurately determine all essential physical parameters in situ. By exploring Py thicknesses of 4, 8, and 12 nm, the Py spin diffusion length ${\lambda }_{\mathrm{Py}}$ is found to be much shorter than the film thicknesses. The product of ${\lambda }_{\mathrm{Py}}$ and the Py spin Hall angle ${\alpha }_{\mathrm{SH}}$ is determined to be independent of thickness and resistivity: ${\alpha }_{\mathrm{SH}}{\lambda }_{\mathrm{Py}}=(0.066\pm 0.009)\mathrm{nm}$ at 5 K and $(0.041\pm 0.010)\mathrm{nm}$ at 295 K. These values are comparable to those obtained from mesoscopic Pt films.

Figure 1

(a) Angle evaporation through a mesoscopic suspended shadow mask designed for the AHE/ISHE structures. SEM images for (b) an AHE/ISHE structure, (c) a NLSV, and (d) a Py resistivity measurement structure. All structures are fabricated on the same substrate.

Figure 2

$R_s$ versus $B_x$ curves at 5 K for (a) an ISHE measurement and (b) an AHE measurement from the same AHE/ISHE structure with 8-nm-thick Py2. The insets of (a) and (b) show the measurement configurations. The magnetic field is applied parallel to the Cu channel ($\pm x$ direction). (c) Illustration of the symmetrical nonlocal spin signal (top), the asymmetrical SHE/ISHE signal (middle), and their superposition (bottom).

Figure 3

(a) $R_s$ versus $B_y$ curve at 5 K for a NLSV with magnetic field $B_y$ applied along the $\pm y$ direction (shown in the inset). The blue arrows indicate the magnetization states of the injector and the detector. (b) $\mathrm{\Delta }{R}_s$ versus $L^{\prime }$ and a fit (solid red line) for NLSVs on the substrate with 8-nm-thick Py2.

Figure 4

The apparent spin Hall ${\alpha }_{\mathrm{SH}}^{\prime }$ as a function of Py thickness (a) at 5 K and (b) at 295 K and fits (solid lines). The insets show the Py resistivity ${\rho }_{\mathrm{Py}}$ as a function of Py thickness. (c) The obtained values of ${\alpha }_{\mathrm{SH}}{\lambda }_{\mathrm{Py}}$ as a function of $t_{\mathrm{Py}}$ at 5 K (red squares) and 295 K (black dots). The dash-dotted line is a guide for the eyes.

Figure 5

Comparison of ${\alpha }_{\mathrm{SH}}\lambda$ between mesoscopic Py and Pt films as a function of film thickness at 5 K.