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Spin Relaxation Times of Single-Wall Carbon Nanotubes

We have measured temperature ($T$)- and power-dependent electron spin resonance in bulk single-wall carbon nanotubes to determine both the spin-lattice and spin-spin relaxation times, $T_1$ and $T_2$. We observe that $T_1^{-1}$ increases linearly with $T$ from 4 to 100 K, whereas $T_2^{-1}$ {\em decreases} by over a factor of two when $T$ is increased from 3 to 300 K. We interpret the $T_1^{-1} \propto T$ trend as spin-lattice relaxation via interaction with conduction electrons (Korringa law) and the decreasing $T$ dependence of $T_2^{-1}$ as motional narrowing. By analyzing the latter, we find the spin hopping frequency to be 285 GHz. Last, we show that the Dysonian lineshape asymmetry follows a three-dimensional variable-range hopping behavior from 3 to 20 K; from this scaling relation, we extract a localization length of the hopping spins to be $\sim$100 nm.