Contact-Induced Spin Relaxation in Graphene Nonlocal Spin Valves

We report on a systematic study of contact-induced spin relaxation in gated graphene nonlocal spin valves. We demonstrate the enhancement of the nonlocal magnetoresistance ($\mathrm{\Delta }{R}_{\mathrm{NL}}$) as the $\mathrm{Co}/\mathrm{Al}{\mathrm{O}}_x/\text{graphene}$ interface resistance increases relative to the graphene spin resistance. We measure Hanle precession at many gate voltages on 14 separate spin-valve devices fabricated from graphene grown by chemical vapor deposition (CVD). These measurements are compared by normalizing $\mathrm{\Delta }{R}_{\mathrm{NL}}$ to the ideal limit of large contact resistance, and the result is shown to be consistent with isotropic contact-induced spin relaxation caused by spin current flowing from the graphene into the Co contacts. After accounting for this source of spin relaxation, we extract spin lifetimes of up to 600 ps in CVD graphene with a gate-voltage dependence which can be described by a combination of both Elliott-Yafet and D’yakonov-Perel’ spin-relaxation mechanisms.

Figure 1

(a) SEM image of a CVD graphene nonlocal spin-valve device on a 300-nm ${\mathrm{SiO}}_2/p\text{−}\mathrm{Si}$ substrate. As indicated, $d$ refers to the separation between the ferromagnetic contacts. (b) Three-terminal geometry and injector-contact $I\text{−}V$ measurements of devices 1–3 taken at $V_g=0\mathrm{V}$. (c) Spin-valve (SV) and nonlocal-Hanle (NLH) measurement configurations. (d)–(f) Spin-valve and nonlocal Hanle measurements for devices 1–3. The spin signal $\mathrm{\Delta }{R}_{\mathrm{NL}}$ from the spin-valve measurement is indicated in (d). Nonlocal Hanle measurements are taken with contact magnetizations oriented parallel (P) and antiparallel (AP). A quadratic background is subtracted for clarity.

Figure 2

Gate-voltage dependence of the spin signal $\mathrm{\Delta }{R}_{\mathrm{NL}}$ extracted from spin-valve measurements and the four-terminal graphene resistance per square $R_{\mathrm{sq}}$ for devices 1–3. The range of $R_C/R_N$ for each device is listed.

Figure 3

(a)–(c) Representative Hanle measurements and fits for devices 1–3, according to Eq. (2). The fits account for contact-induced spin relaxation using the measured values of $R_{\mathrm{inj}}$ and $R_{\det }$ at each gate voltage. In each case, the bottom curve is taken at a gate voltage closer to the Dirac point than the top curve and is offset for clarity. The gate-voltage dependence of the parameters extracted from the fits can be found in Fig. 4.

Figure 4

Gate-voltage dependence of the spin lifetime ${\tau }_s$ and the diffusion constant $D$ resulting from fitting the nonlocal Hanle curves, and the spin-diffusion length $\lambda =\sqrt{D{\tau }_s}$, for devices 1–3. The Dirac point $V_D$ and the best-fit value for $\alpha$ are indicated for each device.

Figure 5

Scaling of the normalized spin signal with $S^{*}$, given by Eq. (6), with respect to $R_C/R_N$, which is the ratio of the average contact resistance to the graphene spin resistance. Each data point represents one device at a particular gate voltage. Data from each device are shown in a different color, and the symbol type indicates the number of graphene layers. Devices 1, 2, and 3 are represented by black squares, red triangles, and blue squares, respectively. The full data set consists of 14 devices with various numbers of layers, tunnel-barrier growth methods, and measurement temperatures. The theoretical curve is from Eq. (9).

Figure 6

Analysis of the Elliott-Yafet and D’yakonov-Perel’-type spin-relaxation spin-orbit coupling strengths following Ref. [59]. Extracted spin-orbit coupling strengths are shown in Table 1. Linear fits are shown as solid lines. (Inset) The region near the origin.