Separating spin and charge transport in single-wall carbon nanotubes

We demonstrate spin injection and detection in single wall carbon nanotubes using a four-terminal nonlocal geometry. This measurement geometry completely separates the charge and spin circuits. Hence all spurious magnetoresistance effects are eliminated and the measured signal is due to spin accumulation only. Combining our results with a theoretical model, we deduce a spin polarization at the contacts ${\alpha }_F$ of approximately $25\%$. We show that the magnetoresistance changes measured in the conventional two-terminal geometry are only partly due to spin accumulation.

Figure 1

A single wall carbon nanotube ($d=3.4\pm 0.4\mathrm{nm}$; possibly it is a bundle containing a few nanotubes) contacted by four ferromagnetic (cobalt) electrodes. (a) An AFM picture of the device. Note that imperfect lift off resulted in some PMMA residue on top of the cobalt electrodes, this partially obscures the well defined Co electrodes underneath (Ref. 31). (b) Geometry of a conventional spin valve (or “local”) measurement, in which contacts ${\mathrm{F}}_2$ and ${\mathrm{F}}_3$ are used both to inject current and to measure voltage. (c) The “nonlocal” geometry. In this case the voltage circuit $\left({\mathrm{F}}_1\text{−}\mathrm{SWNT}\text{−}{\mathrm{F}}_2\right)$ is completely separated from the current circuit $\left({\mathrm{F}}_3\text{−}\mathrm{SWNT}\text{−}{\mathrm{F}}_4\right)$.

Figure 2

Two-terminal spin valve measurements (${\mathrm{F}}_2\text{−}\mathrm{SWNT}\text{−}{\mathrm{F}}_3$, $I=10\mathrm{nA}$) at $4.2\mathrm{K}$ [see Fig. 1b]. (a) Upon sweeping the $B$ field, the “local” resistance increases when $\mid B\mid$ reaches $\approx 80\mathrm{mT}$. It falls back to its original value when $\mid B\mid$ increases further. $\mathrm{\Delta }R∕R$ has a maximum value of $\approx 6\%$. We observe significant substructure on top of the resistance peaks. (b) A similar measurement on the same sample (also at $4.2\mathrm{K}$, but with a thermal cycling step in between). The magnetoresistance trace is completely different from the traces in a) and shows both positive and negative values for $\mathrm{\Delta }R∕R$.

Figure 3

(Color online) Nonlocal measurements at $T=4.2\mathrm{K}$. The current path (from ${\mathrm{F}}_3$ to ${\mathrm{F}}_4$) is separated from the voltage probes [${\mathrm{F}}_2$ to ${\mathrm{F}}_1$, see Fig. 1c]. The observed resistance switching is due to spin accumulation and spin transport in the single wall carbon nanotube. (a) Full magnetic field scan with an ac current of $30\mathrm{nA}$. $R_{\mathrm{nonloc}}$ is negative when the spin injector ${\mathrm{F}}_3$ is magnetized antiparallel to the spin detector ${\mathrm{F}}_2$. In this situation the detector measures mainly the negative chemical potential of the minority spin species. (b) The memory effect $(I=30\mathrm{nA})$, in which only the magnetization of ${\mathrm{F}}_3$ is switched. (c) Similar measurement to (a), but now with an ac current of $60\mathrm{nA}$, resulting in a reduction of the resistance noise level. (d) Nonlocal measurement similar to (a), with $I=30\mathrm{nA}$. Between (a)–(c) and (d), respectively, the sample was annealed to room temperature.

Figure 4

A resistor model of our system (here, all four electrodes are assumed magnetized in the “up” direction). The upper half of the resistor network corresponds to the spin up $(\uparrow )$ transport channel in the nanotube. The lower half to the spin down $(\downarrow )$ channel. The resistance of the carbon nanotube between the cobalt contacts ${\mathrm{F}}_1\text{−}{\mathrm{F}}_2$, ${\mathrm{F}}_2\text{−}{\mathrm{F}}_3$, and ${\mathrm{F}}_3\text{−}{\mathrm{F}}_4$ is equal to $R_{12}∕2$, $R_{23}∕2$, and $R_{34}∕2$, respectively. The contact between the carbon nanotube and ferromagnet ${\mathrm{F}}_i$ $(i=1,2,3,4)$ can be represented by a number of spin-dependent resistances $R_{i,\eta }$ and $r_{i,\eta }$, where $\eta =\uparrow ,\downarrow$ denotes spin. Assuming spin up to be the majority species, we have $R_{i,\uparrow }<R_{i,\downarrow }$ and $r_{i,\uparrow }<r_{i,\downarrow }$. Due to the spin-dependent resistances in the current circuit (${\mathrm{F}}_3$ and ${\mathrm{F}}_4$), the charge current $I$ produces a finite spin current $I_S$. Due to the spin-dependent resistances in the voltage circuit (${\mathrm{F}}_1$ and ${\mathrm{F}}_2$), a nonzero voltage difference $V^{+}-V^{-}$ consequently develops, leading to a finite nonlocal resistance $R_{\mathrm{nonloc}}\equiv (V^{+}-V^{-})∕I$.