Anisotropic surface-state-mediated RKKY interaction between adatoms

Paul N. Patrone, T. L. Einstein

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Motivated by recent numerical studies of Ag on Pt(111), we derive an expression for the RKKY interaction mediated by surface states, considering the effect of anisotropy in the Fermi edge. Our analysis is based on a stationary phase approximation. The main contribution to the interaction comes from electrons whose Fermi velocity v F is parallel to the vector R connecting the interacting adatoms; we show that, in general, the corresponding Fermi wave vector k F is not parallel to R. The interaction is oscillatory; the amplitude and wavelength of oscillations have angular dependence arising from the anisotropy of the surface-state band structure. The wavelength, in particular, is determined by the projection of this k F (corresponding to v F) onto the direction of R. Our analysis is easily generalized to other systems. For Ag on Pt(111), our results indicate that the RKKY interaction between pairs of adatoms should be nearly isotropic and so cannot account for the anisotropy found in the studies motivating our work. However, for metals with surface-state dispersions similar to Be(101̄0), we show that the RKKY interaction should have considerable anisotropy.

Original languageEnglish (US)
Article number045429
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number4
StatePublished - Jan 18 2012
Externally publishedYes


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