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Recent experimental advances in scanning tunneling microscopy make themeasurement of the conductance spectra of isolated and magnetically coupledatoms on nonmagnetic substrates possible. Notably these spectra arecharacterized by a competition between the Kondo effect and spin-flip inelasticelectron tunneling. In particular they include Kondo resonances and alogarithmic enhancement of the conductance at voltages corresponding tomagnetic excitations, two features that cannot be captured by second orderperturbation theory in the electron-spin coupling. We have now derived a thirdorder analytic expression for the electron-spin self-energy, which can bereadily used in combination with the non-equilibrium Green's function schemefor electron transport at finite bias. We demonstrate that our method iscapable of quantitative description the competition between Kondo resonancesand spin-flip inelastic electron tunneling at a computational costsignificantly lower than that of other approaches. The examples of Co and Fe onCuN are discussed in detail.

A pertubative approach to the Kondo effect in magnetic atoms on nonmagnetic substrates