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We study the electron transport through a magnetic molecular transistor inthe Kondo limit using the slave boson technique. We include the electron-phononcoupling and analyze the cases where the spin of the molecule is either S=1/2or S=1. We use the Schrieffer-Wolff transformation to write down a low energyHamiltonian for the system. In the presence of electron-phonon coupling, andfor $S\smeq1$, the resulting Kondo Hamiltonian has two active channels. At lowtemperature, these two channels interfere destructively, leading to a zeroconductance.

Slave boson theory for transport through magnetic molecules with vibronic states