Simple model of the ground state and spin-orbital excitations of free and adsorbed Fe(II) phthalocyanine molecules

Abstract

We investigate the ground state and low-energy spin-orbital excitations of a single iron(II) phthalocyanine molecule in isolation and on an oxidized Cu(110) surface. Considering the subspace spanned by the three lowest spin-triplet states of $^{3}A_{2g}$ and $^{3}E_{g}$ symmetry, we diagonalize the Hamiltonian made of the anisotropic spin-orbit interaction and the ligand field splitting $\mathrm{\ensuremath{\Delta}}$, defined as the energy difference between $^{3}E_{g}$ and $^{3}A_{2g}$. We find that the ground state switches from a $^{3}E_{g}$-like state with large orbital moment and out-of-plane easy axis for $\mathrm{\ensuremath{\Delta}}l\ensuremath{-}60$ meV to a $^{3}A_{2g}$-like singlet state with in-plane easy axis for $\mathrm{\ensuremath{\Delta}}g\ensuremath{-}60$ meV. The analysis of the first excited states in the two regimes explains the zero-field splitting data reported for $\ensuremath{\beta}$-FePc as well as for FePc molecules adsorbed on an oxidized Cu(110) surface [N. Tsukahara et al., Phys. Rev. Lett. 102, 167203 (2009)]. Importantly, the calculated magnetic susceptibility obtained with the ab initio value $\mathrm{\ensuremath{\Delta}}=93$ meV compares remarkably well with the experimental data of $\ensuremath{\beta}$-FePc in the whole available temperature range of 1--300 K.