Enhancement of spin relaxation times by dilution and by an avoided crossing in the molecular nanomagnet Cr$_7$Mn*

We report an increase in the spin relaxation times of dilute samples of the spin $S=1$ molecular nanomagnet [(CH$_3$)$_2$NH$_2$][Cr$_7$MnF$_8$((CH$_3$)$_3$CCOO)$_{16}$] (``Cr$_7$Mn") in the vicinity of an avoided crossing. We study both 100\% and dilute samples, with the dilution achieved by co-crystallizing Cr$_7$Mn with Ga$_7$Zn, a diamagnetic isostructural analogue. We perform parallel-mode electron-spin resonance (ESR) spectroscopy using a loop-gap resonator (LGR), allowing us to probe the zero-field avoided crossing. With the resonant frequency of the LGR tuned to the tunnel splitting of Cr$_7$Mn, $\sim4$ GHz, we observe an ESR peak centered at zero field. We measure the saturation of that peak with pulsed ESR experiments in a pump-probe configuration, and find that $T_1$ increases from $\sim450$ ns for a non-dilute sample to $\sim15$ $\mu$s for a 10\% dilute sample. The dramatic effect that dilution has on the measured $T_1$ value indicates that there is substantial spin diffusion taking place. We can estimate $T_2^*$ from the saturation data and $T_1$ values and find it to be $\sim20$ ns and largely independent of dilution. The results of spin-echo experiments to measure $T_2$, currently in progress, will also be discussed.