Modeling Spin Hamiltonian Parameters for Fe²⁺ (S = 2) Adatoms on Cu₂N/Cu(100) Surface Using Semiempirical and Density Functional Theory Approaches

Transition metal atoms adsorbed on surfaces (adatoms) behaving like magnets are important for potential applications in quantum computing and memory storage. Better insight into their magnetic properties, described by spin Hamiltonian (SH) parameters, is essential. Comprehensive modeling of SH parameters for Fe²⁺ with spin S = 2 adatoms on various surfaces is carried out using two approaches: (1) semiempirical CF/MSH [based on crystal field (CF) and microscopic spin Hamiltonian (MSH) theory], and (2) density functional theory (DFT). Here preliminary results of modeling of zero-field splitting parameters (ZFSPs) for Fe²⁺ on Cu₂N/Cu(100) surface [for short Fe²⁺@Cu₂N/Cu(100)] are presented. We focus on the orthorhombic second-rank ZFSPs in the conventional notation (D, E) measured for Fe²⁺@Cu₂N/Cu(100). The fourth-rank ZFSP in the Stevens notation ($B_k^q$, k = 2, 4) measured for Fe²⁺ on CuN/Cu(100) surface are considered elsewhere. Using the CF/MSH approach within ⁵D approximation, the ZFSPs (k = 2, 4) and Zeeman g-factors are calculated for wide range of the microscopic parameters: spin–orbit (λ), spin–spin (ρ) coupling constants, and the crystal field energy levels (∆_i). The ρ-contributions and the fourth-rank ZFSPs are found important. Computations of the ZFSPs (D, E) are done using the SIESTA code by mapping of the physical energy levels to those of effective ZFS Hamiltonian. Comparison of the results enables bridging the gap between DFT methods and CF/MSH ones. The present results will also be utilized in ongoing studies of adatoms on other surfaces, single molecule magnets and single-ion magnets.