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The system of an iron phthalocyanine molecule on the Au(111) surface, hasbeen studied recently due to its peculiar properties. In particular, severalsurprising results of scanning tunneling spectroscopy changing the position ofthe molecule and applying magnetic field can be explained by the {\itnon-Landau} Fermi liquid state of a 2-channel spin-1 Kondo model withanisotropy. The localized orbitals near the Fermi level are three, one ofsymmetry $z^2$ and two (nearly) degenerate $\pi$ orbitals of symmetry $xz$ and$yz$. Previous studies using the numerical renormalization group neglected oneof these orbitals to render the problem tractable. Here we investigate, using aslave-boson mean-field approximation, if the splitting $S$ between $\pi$orbitals caused by spin-orbit coupling (SOC) justifies this approximation. Weobtain an abrupt transition from a 3-band regime to a 2-band one at a value of$S$ which is about 1/3 of the atomic SOC for Fe, justifying the 2-band modelfor the system.

Low-energy physics for an iron phthalocyanine molecule on Au(111)