Muon spin relaxation investigation of tetranuclear iron(III) ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ molecular cluster

We present a study of the spin dynamics of ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ single molecule magnet by means of SQUID magnetization and muon relaxation $\left({\mu }^{+}SR\right)$ measurements. In longitudinal field ${\mu }^{+}SR$ experiments performed at magnetic fields $H=200$, 1000 Oe, the muon asymmetry $P\left(t\right)$ could be fitted by means of three components, the first constant, the second fast relaxing through a quasiexponential decay, and the third, the slowest relaxing, showing an exponential decay. The slowest muon relaxation rate $\lambda$ studied as a function of temperature $T$ displayed two structures, a broad peak at $T\sim 15/20\text{K}$ and a shoulder at $T<5\text{K}$, both decreasing in amplitude and displacing toward higher temperatures as the field is increased. To mimic qualitatively the temperature behavior $\lambda \left(T\right)$ at the investigated fields, we used a function expressed as the sum of two Bloembergen-Purcell-Pound (BPP)-like laws, reproducing the mechanism of relaxation. The exponential data resulted well fitted by means of a heuristic model which takes into account two correlation times ${\tau }^{\prime }$ and $\tau$, related to the ground-state multiplet barrier $\left({\Delta }^{\prime }/k_B=7.25\text{K}\right)$ and to the intermultiplet separation $\left(\Delta /k_B=86.4\text{K}\right)$ between $\text{S}=5$ and $\text{S}=4$.

Figure 1

Molecular structure of ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$. The four iron(III) ions are represented as dark-gray spheres while the oxygen and carbon atoms are drawn as light gray and medium-gray spheres, respectively. Hydrogen atoms are omitted for clarity. The arrows provide the spin configuration in the ground $S_T=5$ state.

Figure 2

$\left(M/H\right)\cdot T$ versus $T$ plot for a powder sample of ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ at three different fields.

Figure 3

Temperature dependence of the ${\mu }^{+}$ polarization decay in $\text{LF}=200$ and 1000 Oe. Solid lines represent the fits to Eq. (1) in the main text.

Figure 4

Temperature dependence of the muon longitudinal relaxation rates $\lambda$ on ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ powder in $\text{LF}=200$ and 1000 Oe.

Figure 5

Fits (solid lines) of the muon longitudinal relaxation rates $\lambda$ on ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ powder in (a) $\text{LF}=200$ and (b) 1000 Oe by means of Eq. (3); contributions at muon Larmor frequency ${\omega }_L$ (dashed lines) and at electronic Larmor frequency (dotted lines) are also shown.

Figure 6

Fits (solid lines) of the muon longitudinal relaxation rates $\lambda$ on ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ powder in $\text{LF}=200$ and 1000 Oe by means of the Eq. (4).

Figure 7

Fits (solid lines) of the muon longitudinal relaxation rates $\lambda$ on ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ powder in $\text{LF}=200$ and 1000 Oe by means of Eq. (5) with five free parameters. The rectangular distribution width for the energy barrier $\Delta$ of the intermultiplet transition is $\delta =34.5\text{K}$.

Figure 8

Fits (solid lines) of the muon longitudinal relaxation rates $\lambda$ on ${\text{Fe}}_4{\left({\text{OCH}}_3\right)}_6{\left(\text{dpm}\right)}_6$ powder in $\text{LF}=200$ and 1000 Oe by means of the heuristic model, Eq. (5), with ${\Delta }^{\prime }/k_B=7.25\text{K}$, $\Delta /k_B=86.4\text{K}$, and $\delta =43\text{K}$.