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Magnetic transitions induced by tunnelling electrons in individual adsorbed M-Phthalocyanine molecules (M $\equiv$ Fe, Co)

We report on a theoretical study of magnetic transitions induced by tunnelling electrons in individual adsorbed M-Phthalocyanine (M-Pc) molecules where M is a metal atom: Fe-Pc on a Cu(110)(2$\times$1)-O surface and Co-Pc layers on Pb(111) islands. The magnetic transitions correspond to the change of orientation of the spin angular momentum of the metal ion with respect to the surroundings and possibly an applied magnetic field. The adsorbed Fe-Pc system is studied with a Density Functional Theory (DFT) transport approach showing that i) the magnetic structure of the Fe atom in the adsorbed Fe-Pc is quite different from that of the free Fe atom or of other adsorbed Fe systems and ii) that injection of electrons (holes) into the Fe atom in the adsorbed Fe-Pc molecule dominantly involves the Fe $3d_{z^2}$ orbital. These results fully specify the magnetic structure of the system and the process responsible for magnetic transitions. The dynamics of the magnetic transitions induced by tunnelling electrons is treated in a strong-coupling approach. The Fe-Pc treatment is extended to the Co-Pc case. The present calculations accurately reproduce the strength of the magnetic transitions as observed by magnetic IETS (Inelastic Electron Tunnelling Spectroscopy) experiments; in particular, the dominance of the inelastic current in the conduction of the adsorbed M-Pc molecule is accounted for.