In this work we present a detailed NMR and ${\mu }^{+}\mathrm{SR}$ investigation of the spin dynamics in the new hydrated sodium salt containing the single-ion magnet ${\left[\mathrm{Er}{\left({\mathrm{W}}_5{\mathrm{O}}_{18}\right)}_2\right]}^{9-}$. The ${}^1\mathrm{H}\mathrm{NMR}$ absorption spectra at various applied magnetic fields present a line broadening on decreasing temperature which indicates a progressive spin freezing of the single-molecule magnetic moments. The onset of quasistatic local magnetic fields, due to spin freezing, is observed also in the muon relaxation curves at low temperature. Both techniques yield a local field distribution of the order of 0.1–0.2 T, which appears to be of dipolar origin. On decreasing the temperature, a gradual loss of the ${}^1\mathrm{H}\mathrm{NMR}$ signal intensity is observed, a phenomenon known as wipe-out effect. The effect is analyzed quantitatively on the basis of a simple model which relies on the enhancement of the NMR spin-spin, $T_2^{-1}$, relaxation rate due to the slowing down of the magnetic fluctuations. Measurements of spin-lattice relaxation rate $T_1^{-1}$ for ${}^1\mathrm{H}\mathrm{NMR}$ and of the muon longitudinal relaxation rate λ show an increase as the temperature is lowered. However, while for the NMR case the signal is lost before reaching the very slow fluctuation region, the muon spin-lattice relaxation λ can be followed until very low temperatures and the characteristic maximum, reached when the electronic spin fluctuation frequency becomes of the order of the muon Larmor frequency, can be observed. At high temperatures, the data can be well reproduced with a simple model based on a single correlation time $\tau ={\tau }_0\exp \left(\mathrm{\Delta }/\mathrm{T}\right)$ for the magnetic fluctuations. However, to fit the relaxation data for both NMR and ${\mu }^{+}\mathrm{SR}$ over the whole temperature and magnetic field range, one has to use a more detailed model that takes into account spin-phonon transitions among the $\mathrm{E}{\mathrm{r}}^{3+}$ magnetic sublevels. A good agreement for both proton NMR and ${\mu }^{+}\mathrm{SR}$ relaxation is obtained, which confirms the validity of the energy level scheme previously calculated from an effective crystal field Hamiltonian.

• Received 8 December 2017
• Revised 15 March 2018

DOI:https://doi.org/10.1103/PhysRevB.97.144414