  Decoherence processes in crystals of molecular magnets are prototypical for
interacting electronic spin systems. We analyze the Landau-Zener dynamics of
the archetypical TbPc$_2$ complex diluted in a diamagnetic monocrystal. The
dependence of the tunneling probability on the field sweep rate is evaluated in
the framework of the recently proposed master equation in which the decoherence
processes are described through a phenomenological Lindblad operator. Thus, we
showcase low temperature magnetic measurements that complement resonant
techniques in determining small tunnel splittings and dephasing times.
