Long-distance spin transport in high-mobility graphene on hexagonal boron nitride

We performed spin transport measurements on boron nitride based single layer graphene devices with mobilities up to 40 000 cm${}^2$ V${}^{-1}$ s${}^{-1}$. We could observe spin transport over lengths up to 20 $\mu$m at room temperature, the largest distance measured so far for graphene. Due to enhanced charge-carrier diffusion, spin relaxation lengths are measured up to 4.5 $\mu$m. The relaxation times are similar to values for lower quality SiO${}_2$-based devices, around 200 ps. We find that the relaxation rate is determined in almost equal measures by the Elliott-Yafet and D'Yakonov-Perel mechanisms.

Figure 1

(a) Optical micrograph of device 2, partly on SiO${}_2$ (right side) and partly on h-BN (left side). (b) Square resistance versus charge-carrier density measured on both SiO${}_2$- and h-BN-based parts of the same graphene flake. The inset shows the respective field effect mobilities.

Figure 2

(a) Schematic showing the nonlocal four-terminal geometry for device 3. Contacts not used in the measurement are represented by dashed lines. (b) Spin valve measurement showing the nonlocal resistance versus magnetic field, parallel to the electrodes, at $n=1.5\times {10}^{12}$ ${\text{cm}}^{-2}$. Switching of electrodes A to C shows up in the measurement. (c) Hanle spin precession measurement ($R_{nl}$ versus perpendicular magnetic field) averaged between measurements at levels I–III (original data in inset). The solid line shows the fit from which ${\tau }_s$ and $D_s$ are extracted with an error of 16$\%$.

Figure 3

Room temperature data extracted from precession measurements for devices 1, 2, and 3 as a function of charge-carrier density, with respective injector detector spacings of 3.5, 3.5, and 2 $\mu$m. The standard fitting error lies in general within the size of data points. The barriers are made of Al${}_2$O${}_3$ for devices 1 and 2 and of TiO${}_2$ for device 3. (a) Spin- and charge-diffusion constants, symbols, and lines, respectively. The latter are extracted from charge transport. (b) Spin-relaxation times. (c) Spin-relaxation lengths.

Figure 4

Room temperature data obtained from devices 1, 2, and 3. All error bars fall within the data point size. Linear relations allow for extraction of the spin-orbit coupling assuming (a) the DP mechanism or (b) the EY mechanism. The solid lines reflect the theoretical relation for several spin-orbit couplings. For both mechanisms the data deviates from theoretical expectations. (c) The combination of both the DP and EY mechanisms allows for extraction of the respective spin-orbit couplings using Eq. (1). The solid lines are linear fits; the error margins result from the standard error in the linear fits.