Electron Spin Relaxation Dynamics in Single-Walled Carbon Nanotubes*

We have measured temperature-dependent electron spin resonance (ESR) in an ensemble of single-walled carbon nanotubes. From the linewidths of these traces, we clearly observe that the spin-spin dephasing time, $T_{2}$, decreases by over a factor of two when temperature, $T$, is lowered from 300 K to 3 K, a phenomenon we attribute to motional narrowing. We fit the temperature dependence of $T_{2}$ with a hopping model and obtain a spin hopping frequency of 285 GHz. At selected temperatures below 100 K, we performed microwave power-dependent scans to investigate the saturation behavior of the ESR signal. A homogenously broadened two-level model fit the saturation data well, which allowed us to extract the spin-lattice relaxation times, $T_{1}$, for the investigated temperature range. We observed that the spin-lattice relaxation rate,1/$T_{1}$, is proportional to $T$ from 100 K to 3 K, suggesting that the relaxation occurs via phonon emission. Last, we show that the Dysonian lineshape asymmetry, which is roughly proportional to the conductivity, follows a three-dimensional variable-range hopping behavior from 3 K to 20 K, from which we estimate a spin hopping localization length of 100 nm.