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We study electronic transport through a magnetic molecule with an intrinsicspin $S$ coupled to two magnetic electrodes, in the incoherent regime. Themolecule is modeled as a single resonant level with large Coulomb repulsion (nodouble occupancy). The molecular spin is isotropic and it interacts with theelectronic spin through an exchange interaction. Using an alternative method tothe usual master equation approach, we are able to obtain analytical formulasfor various physical quantities of interest, such as the mean current and thecurrent fluctuations, but also the mean value of $J_z$ -the $z$ component ofthe total spin on the molecule- and its fluctuations. This allows us tounderstand how the electronic current between the magnetized electrodes cancontrol the polarization of the molecular spin. We observe in particular thatthe fluctuations of $J_z$ reach unexpectedly high values.

Colossal spin fluctuations in a molecular quantum dot magnet with ferromagnetic electrodes