Noncollinear spin transport in magnetic multilayers

We study giant magnetoresistance at $4.2\mathrm{K}$ in magnetic multilayers with noncollinear magnetizations, and various thicknesses of one of the layers. We show that these measurements are extremely sensitive to the transverse spin currents in ferromagnets, and measure the transverse spin-current penetration length into a ferromagnet. The implications of our results for the spin-torque effect are discussed.

Figure 1

(a), (b) Schematics of samples $A$ (a) and $B$ (b), with layer compositions as labeled (thicknesses not to scale). Different sections of the samples are labeled 1–3, as described in the text. (c) $R$ vs $H$ in sample $A12$.

Figure 2

AGMR for $H=100\mathrm{Oe}$ in samples $A12$ (a) and $A1.5$ (b). The solid lines are fits with $\chi =1.96\pm 0.05$ and $\chi =7.7\pm 0.6$, respectively, as described in the text. The measurement error bars $\pm 0.02\mathrm{n}\Omega$ are shown.

Figure 3

(a) Measured (symbols) and calculated (line) $A\Delta R$ vs $t_{Py}$ for samples $A$. (b) The same as (a), for samples $B$. (c) $\chi$ from the fits of measured (symbols) and calculated (lines) AGMR with Eq. (1) for samples $A$. The solid line is calculated with correction for a finite $l_t=0.8\mathrm{nm}$; the dashed line, with $l_t=0$. (d) The same as (c), for samples $B$. All the lines are $B$-spline fits of the calculated points for $t_{Py}=1.5,3,6,12\mathrm{nm}$.

Figure 4

(a), (b) Calculations of $\mathrm{AR}\left(\theta \right)–{\mathrm{AR}}_P$ (a) and normalized STT (b) for samples $A12$. The solid (dashed) curves are calculated assuming $l_t=0.8\mathrm{nm}$ $(l_t=0)$. (c), (d) The same as (a) and (b), for $A1.5$, and $l_t=0.8\mathrm{nm}$. In (d), the solid (dotted) line is the STT acting on the bottom (top) Py layer.