The effect of sample aspect ratio on Curie temperature of Mn$_{12}$-ac

The inverse magnetic susceptibility measured in a SQUID-based Quantum Design MPMS magnetometer was investigated for different samples of Mn$_{12}$-ac as a function of the aspect ratio $(c/a$) of the crystal, where $c$ is the length and $a$ is the width of the sample. The Curie temperature $T_c$ inferred from the positive intercepts of the Curie-Weiss law increases from $0.3$ K for a sample of aspect ratio around $1$, and approaches saturation to a value $\sim 0.75$ K for crystals with aspect ratio above $5$. Our results can be explained by taking into account the effect of demagnetization field.