Low-temperature theory of proton NMR in the molecular antiferromagnetic ring Fe10

The proton nuclear spin-lattice relaxation rate $1/T_1$ in the molecular “ferric wheel” $\ab{Fe}_{10}\ab{(OCH}_3)_{20}(\ab{C}_2\ab{H}_2\ab{O}_2\ab{Cl})_{10}$ (Fe10) is calculated in the framework of the linear response theory, starting from the unperturbed eigenvalues and eigenstates of the magnetic ring. The dipole-dipole superhyperfine interaction between the proton nuclear spins and the electronic spins of the magnetic ions is shown to induce transitions between states $|S,M\rangle$ which differ by 1 both in the quantum number S (the total spin of the ring) and in M (the projection of the total spin along the quantization axis). The theory predicts that level crossing between the states $|S+1,-(S+1)\rangle$ and $|S,-S\rangle$ induced by an applied magnetic field should be accompanied by a strong enhancement of $T_1^{-1}$, in good agreement with recent low-temperature NMR experimental data on Fe10