Probing spin excitations in two-dimensional arrays of Eu(3+) ions on Au(111) substrates

This study investigates the role of nearest-neighbor exchange interactions within a rectangular finite-size array of Eu(3+) ions on a Au(111) substrate. We employ density functional theory to evaluate the energetics of a four-site chain for different spin-projection configurations. The effective nearest and next-nearest neighbor coupling strengths can be extracted for a one-dimensional chain in a Heisenberg model, J1 and J2, respectively [1]. Next, using the energetics for a system with periodicity along both in-plane directions allows us to determine a diagonal exchange, J3. The ground state and complete magnetic excitation spectra are obtained using these parameters for clusters of experimentally realizable sizes. We employ direct diagonalization of the spin Hamiltonian, including the role of magnetic anisotropy in the system. Different cluster sizes and their spin-flip excitations are studied to derive differential conductance profiles akin to those acquired through scanning tunneling microscopy techniques. By engineering the arrangement of such rare-earth ion clusters, we gain unprecedented insights into the subtle interplay of magnetic moments at the atomic scale in 2D arrays.