  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.
