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

We study electronic transport through a magnetic molecule with an intrinsic spin $S$ coupled to two magnetic electrodes, in the incoherent regime. The molecule is modeled as a single resonant level with large Coulomb repulsion (no double occupancy). The molecular spin is isotropic and it interacts with the electronic spin through an exchange interaction. Using an alternative method to the usual master equation approach, we are able to obtain analytical formulas for various physical quantities of interest, such as the mean current and the current fluctuations, but also the mean value of $J_z$ -the $z$ component of the total spin on the molecule- and its fluctuations. This allows us to understand how the electronic current between the magnetized electrodes can control the polarization of the molecular spin. We observe in particular that the fluctuations of $J_z$ reach unexpectedly high values.