Importance of the fourth-rank zero field splitting parameters for Fe2+(S=2) adatoms on the CuN/Cu(100) surface evidenced by their determination based on DFT and experimental data

Due to their potential applications, single atoms on surfaces (adatoms) have been extensively studied using STM, IETS, INS, and EPR techniques or using DFT andab initiomethods. Especially interesting are Fe2+(S= 2) adatoms on CuN/Cu(100) and Cu2N/Cu(100) surfaces due to their non-Kramers features described by the zero field splitting (ZFS) Hamiltonian. The 4th-rank ZFS parameters (ZFSPs), allowed for spinS= 2, are commonly disregarded. By extracting 4th-rank ZFSPs from DFT predicted spin energy levels for the Fe2+@CuN/Cu(100) system, we show that including only 2nd-rank ZFSPs yield incomplete description of magnetic and spectroscopic properties. The algebraic method developed by us is used to extract 2nd- and 4th-rank ZFSPs utilizing knowledge of energy levels without a magnetic field, which may be obtained experimentally or theoretically. Reasonable constraints on particular 4th-rank ZFSPs are considered based on comparison of data on ZFSPs and energies for Fe2+@CuN/Cu(100) and other Fe2+(S= 2) systems. Influence on energies due to 2nd-rank ZFSPs aloneversusthat of both 2nd- and 4th-rank ZFSPs is analyzed. A series of simulations of ZFS energies for different ZFSP variants is carried out. The results prove the importance of 4th-rank ZFS parameters. Our method enables a more accurate description of 3d(4)and 3d(6)(S= 2) ions in various systems, includingS= 2 adatoms.