First-Principles Insights into the Effect of Spin-Insulating Substrates on Molecular Kondo States

Surface magnetic molecular systems have attracted increasing attention because of their potential applications in spintronic devices. Recent experiments have shown that bis(phthalocyaninato)terbium(III) molecules adsorbed on a bare Cu substrate exhibit a Kondo state, whereas introducing an insulating NaCl layer on the Cu surface significantly suppresses this spin response around the zero bias voltage. The microscopic mechanism underlying this transition remains unclear. To address this issue, we employed a combined approach of the density functional theory and hierarchical equations of motion method (DFT + HEOM) to examine how spin-insulating layers affect the molecular Kondo state. We first developed a novel algorithm to evaluate the hybridization functions that allows quantitative assessments of the molecule-substrate interactions in different configurations at the DFT level. Subsequently, we combined the HEOM method to simulate the differential conductance (dI/dV) spectra of the molecule adsorbed on different substrates. The obtained dI/dV spectra via the present combined approach agree well with the experimental observations. Our results indicate that the strength of the molecule-substrate hybridization critically determines the magnetic properties of the adsorbed molecule. Our work elucidates the important role of spin-insulating layers in tuning the Kondo effect and provides valuable insights for the rational design of surface magnetic molecular systems.