Spin-dependent quantum interference in single-wall carbon nanotubes with ferromagnetic contacts

We report the experimental observation of spin-induced magnetoresistance in single-wall carbon nanotubes contacted with high-transparency ferromagnetic electrodes. In the linear regime the spin-induced magnetoresistance oscillates with gate voltage in quantitative agreement with calculations based on a Landauer-Büttiker model for independent electrons. Consistent with this interpretation, we find evidence for bias-induced oscillation in the spin-induced magnetoresistance signal on the scale of the level spacing in the nanotube. At higher bias, the spin-induced magnetoresistance disappears because of a sharp decrease in the effective spin polarization injected from the ferromagnetic electrodes.

Figure 1

(a) Gate and bias dependence of the conductance measured at $4.2\mathrm{K}$, exhibiting a characteristic (Fabry-Pérot) pattern due to quantum interference of the electron waves (Ref. 10) (b) Atomic force microscope picture of the sample on which the data shown in this paper were measured. The obtained level spacing is approximately $6\mathrm{mV}$, in reasonable agreement with the length of the nanotube between the contacts $\left(350\mathrm{nm}\right)$.

Figure 2

(Color online) (a) Magnetoresistance traces measured at different gate voltages (black dots correspond to magnetic-field upsweeps; gray (red) dots to downsweeps). The reversal of the magnetization in the electrodes produces an increase in magnetoresistance; in a few cases a decrease is observed (e.g., $V_{\mathrm{G}}=6.30\mathrm{V}$). (b) Difference between the magnetoresistance signal measured in the up- and downsweeps, normalized to $R_{\mathrm{P}}=R\left(700\mathrm{mT}\right)$, as a function of magnetic field and gate voltage. The periodicity with gate voltage is apparent.

Figure 3

(Color online) Comparison of theoretical predictions based on Eqs. (1, 2) (lines) and experimental data (symbols) for the gate-voltage-dependent conductance (top) and amplitude of the spin-induced magnetoresistance (bottom).

Figure 4

(Color online) (a) and (b) Magnetoresistance traces for different values of the applied bias $V_{\mathrm{B}}$, at $V_{\mathrm{G}}=8.0$ and $7.6\mathrm{V}$ (curves offset for clarity). At $V_{\mathrm{G}}=8.0\mathrm{V}$ the SIMR signal at $V_{\mathrm{B}}=0\mathrm{mV}$ is larger than at $V_{\mathrm{B}}=5\mathrm{mV}$; at $V_{\mathrm{G}}=7.6\mathrm{V}$ the situation is reversed. This indicates that the amplitude of the SIMR signal oscillates with bias. The full $V_{\mathrm{G}}$ dependence is shown in (c). (a)–(c) also clearly show that the SIMR signal at $V_{\mathrm{B}}=20\mathrm{mV}$ is fully suppressed. (d) Bias dependence of the gate-voltage-averaged SIMR and of its standard deviation (as a measure of the oscillating component).