Susceptibility of single molecule magnet Mn$_{12}$-acetate single crystals as a function of temperature and transverse field*

The longitudinal susceptibility of Mn$_{12}$-acetate single crystals has been measured in a magnetic field applied transverse to the Ising axis using micro-Hall effect magnetometry in a He$^3$ cryostat with a 3D vector superconducting magnet. We have investigated the blocking temperature as a function of longitudinal-field-sweep-rate and as a function of the magnitude of the transverse field. We find that the transverse field accelerates the relaxation to equilibrium and lowers the blocking temperature, as expected based on the Mn$_{12}$-ac spin-Hamiltonian and a classical model of single domain uniaxial nanomagnets. The susceptibility is found to obey a Curie-Weiss law, indicating a low temperature transition to a ferromagnetic phase due to dipolar interactions. We discuss these experiments as well as experiments in which an array of Hall-bars is used to spatially resolve the longitudinal susceptibility above the blocking temperature.