Exchange interaction between magnetic adatoms on surfaces of noble metals

TL;DR

This study uses first principles calculations to analyze how magnetic impurities interact on noble metal surfaces, revealing oscillatory behaviors linked to surface states and Fermi vectors, with variations depending on surface orientation and impurity depth.

Contribution

It provides detailed insights into the surface-state mediated exchange interactions between magnetic adatoms on Cu and Au surfaces, highlighting the effects of surface orientation and electronic structure.

Findings

Oscillatory exchange interactions decay as 1/R^2 on certain surfaces.

Surface state properties influence oscillation frequency and symmetry.

Bulk states mediate interactions when impurities are buried.

Abstract

We present first principles calculations of the exchange interactions between magnetic impurities deposited on (001), (110) and (111) surfaces of Cu and Au and analyze them, in particular, in the asymptotic regime. For the (110) and the (111) surfaces we demonstrate that the interaction shows an oscillatory behavior as a function of the distance, R, of the impurities and that the amplitude of the oscillations decays as 1/R^2. Furthermore, the frequency of the oscillations is closely related to the length of the Fermi vector of the surface states existing on these surfaces. Due to the asymmetry of the the surface states' dispersion, the frequency of the oscillations becomes also asymmetric on the (110) surfaces, while on the Au(111) surface two distinct frequencies are found in the oscillations as a consequence of the Bychkov-Rashba splitting of the surface states. Remarkably, no long range oscillations of the exchange interaction are observed for the (001) surfaces where the surface states are unoccupied. When burying the impurities beneath the surface layer, oscillations mediated by the bulk states become visible.