Local magnetic susceptibility study of long-range order in Mn$_{12}$-ac*

The magnetic susceptibility of single crystals of Mn$_{12}$-ac obeys a Curie-Weiss law, indicating a transition to a ferromagnetic phase below 1 K [1]. Measurements by Hall magnetometry have yielded different temperature intercepts ranging from 0.4 K to 0.9 K. Moreover, these values differ from those obtained for the same crystals in a SQUID-based MPMS. We have proposed two possible origins: (1) the effect of crystal's aspect ratio, reported in [2]; (2) the possibility that the local ordering temperature differs from the global average value. Here we report an ongoing study of the longitudinal magnetic susceptibility at different locations of a single crystal, performed on a Hall sensor array in both zero and finite transverse magnetic field. Preliminary results yield temperature intercepts that are lower near the end of the crystal than in the middle. \\[4pt] [1] Bo WEN et al., PRB 82, 014406 (2010). \\[0pt] [2] Shiqi LI et al., PRB 82, 174405 (2010).