Experimental determination of the Weiss temperature of ${\text{Mn}}_{12}\text{-ac}$ and ${\text{Mn}}_{12}\text{-ac-MeOH}$

We report measurements of the susceptibility in the temperature range from 3.5 to 6.0 K of a series of ${\text{Mn}}_{12}\text{-ac}$ and ${\text{Mn}}_{12}\text{-ac-MeOH}$ samples in the shape of rectangular prisms of length $l_c$ and square cross section of side $l_a$. The susceptibility obeys a Curie-Weiss law, $\chi =C/\left(T-\theta \right)$, where $\theta$ varies systematically with sample aspect ratio. Using published demagnetization factors, we obtain $\theta$ for an infinitely long sample corresponding to intrinsic ordering temperatures $T_c\approx 0.85\text{K}$ and $\approx 0.74\text{K}$ for ${\text{Mn}}_{12}\text{-ac}$ and ${\text{Mn}}_{12}\text{-ac-MeOH}$, respectively. The difference in $T_c$ for two materials that have nearly identical unit cell volumes and lattice constant ratios suggests that, in addition to dipolar interactions, there is a nondipolar (exchange) contribution to the Weiss temperature that differs in the two materials because of the difference in ligand molecules.

Figure 1

(Color online) Magnetization of ${\text{Mn}}_{12}\text{-ac}$ as a function of longitudinal magnetic field for different temperatures above the blocking temperature $T_B$. Sufficiently slow sweep rates are chosen to ensure that the system is in equilibrium. Inset: open hysteresis loops displaying the familiar steps associated with spin tunneling in molecular magnets are obtained at lower temperature and higher sweep rates.

Figure 2

(Color online) The inverse susceptibility of ${\text{Mn}}_{12}\text{-ac}$ as a function of temperature for two samples each of ${\text{Mn}}_{12}\text{-ac}$ and ${\text{Mn}}_{12}\text{-ac-MeOH}$ with different (matched) aspect ratios, as indicated. The dotted-dashed and solid lines are for aspect ratios $\approx 3.3$ and $\approx 1.5$, respectively. Extension of the straight lines yield temperature intercepts, $\theta$, that vary with aspect ratio and are different for the two materials.

Figure 3

(Color online) Temperature intercept $\theta$ as a function of aspect ratio for ${\text{Mn}}_{12}\text{-ac}$ (triangles) and ${\text{Mn}}_{12}\text{-ac-MeOH}$ (circles). The lines denote fits obtained as described in the text.

Figure 4

(Color online) Temperature intercept $\theta$ as a function of demagnetization factor $N_m$ (in cgs units) for ${\text{Mn}}_{12}\text{-ac}$ (triangles) and ${\text{Mn}}_{12}\text{-ac-MeOH}$ (circles). Approximate fits are denoted by the solid lines with (negative) slopes constrained to be equal to the Curie constant $C=0.138$ [see Eq. (1)]. Inset: magnetometric demagnetization factor $N_m$ as a function of aspect ratio; values of $N_m$ are obtained by interpolation from the tables published by Chen, Pardo and Sanchez (Refs. 3, 4).