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

Abstract

Due to their potential applications, single atoms on surfaces (adatoms) have been extensively studied using STM, IETS, INS, and EPR techniques or using DFT and ab initio methods. 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 spin S = 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 alone versus that 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 3d⁴ and 3d⁶ (S = 2) ions in various systems, including S = 2 adatoms.