Relaxation dynamics in the frustrated Cr 9 antiferromagnetic ring probed by NMR

We investigate the magnetic properties and the phonon-induced relaxation dynamics of the first regular ${\mathrm{Cr}}_{9}$ antiferromagnetic (AF) ring, which represents a prototype frustrated AF ring. Geometrical frustration in ${\mathrm{Cr}}_{9}$ yields an energy spectrum with twofold degenerate low-lying levels and a low-spin ground state. The electronic relaxation dynamics is probed by ${}^{1}\mathrm{H}$-NMR through the temperature dependence of the spin-lattice relaxation rate $1/{T}_{1}$. We develop a microscopic model that reproduces $1/{T}_{1}(T)$ curves, taking also into account the wipeout effect. By interpreting these measurements we determine the spin-phonon coupling strength and we investigate the decay of the cluster magnetization due to the spin-phonon interaction. We find that at very low temperatures, the relaxation is characterized by a single dominating Arrhenius-type relaxation process, whereas several relevant processes emerge at higher temperatures. In addition, we calculate the temperature and magnetic field dependence of level lifetimes.