Effect of anisotropic spin absorption on the Hanle effect in lateral spin valves

We have succeeded in fully describing dynamic properties of spin current including the different spin absorption mechanisms for longitudinal and transverse spins in lateral spin valves, which enable one to elucidate intrinsic spin transport and relaxation mechanisms in the nonmagnet. The deduced spin lifetimes are found independent of the contact type. From the transit-time distribution of spin current extracted from the Fourier transform in Hanle measurement data, the velocity of the spin current in Ag with Py/Ag Ohmic contact turns out much faster than that expected from the widely used model.

Figure 1

Hanle signal in LSVs with Py/Ag junctions and Py/MgO/Ag junctions with various separations $L$. Black and red circles show nonlocal resistance $V$/$I$ of parallel and antiparallel magnetic configurations of the injector and detector electrodes, respectively, at $T=10$ K. Curves are obtained by the formula of Hanle effect (see Supplemental Material [22]) with adjusting parameters shown in Table 1. Arrows ($B_{\mathrm{z}}^{\pi /2}$ and $B_{\mathrm{z}}^{-\pi /2}$) show the first cross points of the Hanle signal for the parallel and antiparallel configurations corresponding to the collective ±π/2 rotation of diffusive spins.

Figure 2

(a),(b) Derived transit-time distribution of pure spin current $P$($t$) (red circle) by performing Fourier transform on the Hanle signal shown in Figs. 1 and 1. Dashed curves are derived by the empirical model, i.e., diffusion distribution with spin flip expressed by Eq. (2), with the values of $D_{\mathrm{N}}$ and ${\tau }_{\mathrm{sf}}$ listed in Table 1. Solid curve shows the distribution including the effect of spin absorption (see Supplemental Material [22]). All $P$($t$) is normalized by $P\left(t_{\max }\right)$, where $t_{\max }$ gives the maximum of $P$($t$). (c) Velocity and full width at half maximum (FWHM) for the spin absorption model normalized by those for the empirical model. Lines are guides to the eyes.

Figure 3

(a) Absorbed longitudinal spin current $I_{\mathrm{S}\parallel }$ is proportional to longitudinal spin accumulation $\delta {\mu }_{\parallel }$ and inversely proportional to the spin resistance of ferromagnet $R_{\mathrm{F}}$. (b) Absorbed transverse spin current $I_{\mathrm{S}\perp }$ is proportional to transverse spin accumulation $\delta {\mu }_{\perp }$ and the real part of spin mixing conductance $G_{\uparrow \downarrow }$. (c), (d) Schematic of $\delta {\mu }_{\parallel }$ and $\delta {\mu }_{\perp }$ in the vicinity of the detector junction. In ferromagnet, $\delta {\mu }_{\perp }$ is decaying with precessing along the magnetization direction, which results in damping with oscillation [29]. The red and blue curves are calculated by the spin diffusion equation with using the equation (48) in [29].