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We investigate the time-dependent Kondo effect in a single-molecule magnet(SMM) strongly coupled to metallic electrodes. Describing the SMM by a Kondomodel with large spin S > 1/2, we analyze the underscreening of the localmoment and the effect of anisotropy terms on the relaxation dynamics of themagnetization. Underscreening by single-channel Kondo processes leads to alogarithmically slow relaxation, while finite uniaxial anisotropy causes asaturation of the SMM's magnetization. Additional transverse anisotropy termsinduce quantum spin tunneling and a pseudospin-1/2 Kondo effect sensitive tothe spin parity.

Nonequilibrium Dynamics of Anisotropic Large Spins in the Kondo Regime: Time-Dependent Numerical Renormalization Group Analysis