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 $1/T_1\left(T\right)$ 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.

• Received 5 October 2015
• Revised 11 December 2015

DOI:https://doi.org/10.1103/PhysRevB.93.024424