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 the spin-spin relaxation times, T₁ and T₂. We observe that T₁^-1 increases linearly with T from 4 K to 100 K, whereas T₂^-1 decreases by over a factor of two when T is increased from 3 K to 300 K. We interpret the T₁^-1∝T trend as spin-lattice relaxation via interaction with conduction electrons (Korringa law) and the decreasing T dependence of T₂^-1 as motional narrowing. By analyzing the latter, we find the spin hopping frequency to be 285 GHz. Last, we show that the Dysonian line shape asymmetry follows a three-dimensional variable-range hopping behavior from 3 K to 20 K; from this scaling relation, we extract a localization length of the hopping spins to be ∼100 nm.