Alignment of magnetic anisotropy axes in crystals of ${\text{Mn}}_{12}$ acetate and ${\text{Mn}}_{12}$-tBuAc molecular nanomagnets: Angle-dependent ac susceptibility study

We report the results of angular-dependent ac susceptibility experiments performed on two derivatives of ${\text{Mn}}_{12}$ single-molecular magnets: the well-known ${\text{Mn}}_{12}$ acetate, which contains disordered acetic acid molecules in interstitial sites of the crystal structure and ${\text{Mn}}_{12}$-tBuAc, for which solvent molecules are very well ordered in the structure. Our results show (a) that the angular variation is very similar in the two compounds investigated and compatible with a maximum misalignment of the anisotropy axes of less than $3°$ and (b) that the tunneling rate is faster for the better ordered ${\text{Mn}}_{12}$-tBuAc compound. These experiments question interstitial disorder as the dominant origin of the thermally activated tunneling phenomenon.

Figure 1

(Color online) ac susceptibility data of a single crystal of ${\text{Mn}}_{12}$-tBuAc measured along and perpendicular to the crystallographic $c$ axis. The inset shows the angular dependence of the susceptibility measured at $T=4.8\text{K}$ and for a frequency $\omega /2\pi =1\text{Hz}$ (equilibrium).

Figure 2

(Color online) Frequency-dependent ac susceptibility of single crystals of (a) ${\text{Mn}}_{12}$-tBuAc and [(b) and (c)] ${\text{Mn}}_{12}$ acetate. Solid lines are least-square fits of a Cole-Cole function [Eq. (2)] to the data, from which the relaxation time $\tau$ and the susceptibility drop $\Delta \chi$ between the low- and high-frequency limits are estimated.

Figure 3

(Color online) Angular dependence of $\Delta \chi$ (normalized by its value at $\psi =0$) for the slow and fast-relaxing species in the two ${\text{Mn}}_{12}$ derivatives. The solid line represents the prediction for perfectly oriented anisotropy axes. The inset shows a magnification of the data measured for the standard ${\text{Mn}}_{12}$ acetate clusters in the proximity of $\psi =90°$. These data are compared with predictions for two configurations of the anisotropy axes.

Figure 4

(Color online) Top: magnetic relaxation time of ${\text{Mn}}_{12}$-tBuAc and ${\text{Mn}}_{12}$ acetate. Solid lines are least-square Arrhenius fits giving activation energies $U=65\left(1\right)\text{K}$ for the former compound and $U=66\left(1\right)\text{K}$ for the latter. Bottom: relaxation time calculated with the model described in Ref. 20 and the Hamiltonian parameters given in the text. Results obtained for two values of the dipolar bias field are shown. The activation energies are $U=65.1\text{K}$ for $H_{\text{dip},z}=150\text{Oe}$ and $U=66.1\text{K}$ for $H_{\text{dip},z}=300\text{Oe}$. The inset shows the dependence of $U$, calculated for $H_{\text{dip},z}=300\text{Oe}$, on the orthorhombic parameter $E$. The shadowed area represents experimentally acceptable values for ${\text{Mn}}_{12}$ acetate.