Relaxation of muon spins in molecular nanomagnets

We address the cause of the unusual muon spin-relaxation $\left({\mu }^{+}\text{SR}\right)$ results on molecular nanomagnets (MNMs). Through measurements on protonated and deuterated samples of the MNMs ${\text{Cr}}_7\text{Mn}$ $\left(S=1\right)$ and ${\text{Cr}}_8$ $\left(S=0\right)$, we show that the muon spin for $S\ne 0$ MNMs is relaxed via dynamic fluctuations of the electronic spins. A freezing out of dynamic processes occurs on cooling and at low temperatures the muon spins are relaxed by the electronic spins which themselves are dephased by incoherent nuclear-field fluctuations. We observe a transition to a state of static magnetic order of the MNM electronic spins in ${\text{Cr}}_7\text{Mn}$ below 2 K.

Figure 1

(Color online) ${\mu }^{+}\text{SR}$ spectra for protonated and deuterated (a) ${\text{Cr}}_7\text{Mn}$ and (b) ${\text{Cr}}_8$ materials, measured at $T=4.5\text{K}$. Inset: structures of the molecules.

Figure 2

(Color online) (a) Temperature evolution of the relaxation rates $\lambda$ for ${\text{Cr}}_7\text{Mn}$ and ${\Delta }_0$ for ${\text{Cr}}_8$. The lines are fits to a phenomenological equation (see main text). (b) Ratio of the ${\text{Cr}}_7\text{Mn}\text{−}h$ and $\text{−}d$ relaxation rates. The line is a guide to the eye.

Figure 3

(Color online) Example spectrum measured at 0.5 K for ${\text{Cr}}_7\text{Mn}\text{−}h$ (at $\text{S}\mu \text{S}$) showing heavily damped oscillations with a frequency of ${\gamma }_{\mu }B/\left(2\pi \right)\sim 30\text{MHz}$. Inset: spectra from ISIS show a discontinuous change upon cooling below 2 K.