Size-dependent energy splitting of unoccupied electronic states in antiferromagnetic monolayer Mn nanoislands

Quantum size effect (QSE) on the electronic structures of nanoscale antiferromagnets with a monolayer (ML) thickness is of fundamental importance in antiferromagnetic (AFM) spintronics. Here, we have carried out systematic studies on the size-dependent unoccupied electronic states of ML Mn nanoislands on Ag (111) by employing scanning tunneling microscopy/spectroscopy (STM/STS) together with density-functional theory (DFT). According to bias-dependent height profiles, a lower apparent height has been found on the larger Mn island within a bias voltage range of 1. 00. 16em{0ex}eV, suggesting a smaller Mn--Ag interlayer distance. Additionally, a single broad dI/dU peak from small Mn islands gradually evolves into two distinct peaks at approximately 1. 34pt{0ex}eV (peak 1) and 1. 54pt{0ex}eV (peak 2) as the island size increases. On top of that, peaks 1 and 2 move about 0. 370. 050. 16em{0ex}eV and 0. 300. 030. 16em{0ex}eV toward lower energy positions when the area size of the ML Mn island increases. Given the projected density of states (PDOS) deduced from orbital-dependent electronic band structures of ML Mn/Ag (111), two unoccupied dI/dU peaks originate from the contributions of out-of-plane Mn-3d orbitals. Further PDOS comparison analyses reveal that the Mn--Ag interlayer coupling develops a stronger energy shift in unoccupied states than the Mn--Mn atomic bonding, yielding the two-peak feature in dI/dU spectra resolved experimentally.