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 $\mathrm{\Delta }$, 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 $\mathrm{\Delta }<-60$ meV to a ${}^{3}A_{2g}$-like singlet state with in-plane easy axis for $\mathrm{\Delta }>-60$ meV. The analysis of the first excited states in the two regimes explains the zero-field splitting data reported for $\beta$-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 $\mathrm{\Delta }=93$ meV compares remarkably well with the experimental data of $\beta$-FePc in the whole available temperature range of 1–300 K.

• Received 15 July 2018
• Revised 13 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.195108