Multisite lateral interactions and their consequences

Einstein, T. L.

doi:10.1021/la00059a021

Cited by 50 publications

(29 citation statements)

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“…29 Preliminary results for Cu(001) suggest that ⑀ 2 is indeed attractive, and that ⑀ 2 / ⑀ 1 is about 1 / 8; there are also indications of an attractive right-triangle trio interaction ⑀ RT with sizable magnitude (perhaps comparable to ͉⑀ 2 ͉, consistent with a priori expectations 25,30 ), but there is also a sizeable colinear trio interaction which is repulsive.…”

Section: Discussionsupporting

confidence: 60%

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

et al. 2004

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Within the solid-on-solid (SOS) approximation, we carry out a calculation of the orientational dependence of the step stiffness on a square lattice with nearest-and next-nearest-neighbor interactions. At low temperature our result reduces to a simple, transparent expression. The effect of the strongest trio (three-site, nonpairwise) interaction can easily be incorporated by modifying the interpretation of the two pairwise energies. The work is motivated by a calculation based on nearest neighbors that underestimates the stiffness by a factor of 4 in directions away from close-packed directions, and a subsequent estimate of the stiffness in the two highsymmetry directions alone that suggested that inclusion of next-nearest-neighbor attractions could fully explain the discrepancy. As in these earlier papers, the discussion focuses on Cu(001).

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Section: Discussionsupporting

confidence: 60%

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

et al. 2004

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“…5͒. In contrast to the ones considered heretofore, 23,24 these trio interactions must be orientation dependent: If the triangle points in one direction ͑say up͒, the interaction energy has a different value than if it points in the opposite ͑down͒ direction. Alternatively, one can separate out the average of these two values as an ordinary trio energy with full 6-fold symmetry ͑the main effect of which presumably is to renormalize the NN interaction 9 ͒; then we can write the new contribution as an antisymmetric term which changes sign with each rotation of the triangle by / 3.…”

Section: Orientation-dependent Three-atom Interactionmentioning

confidence: 85%

Low-temperature orientation dependence of step stiffness on {111} surfaces

et al. 2005

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For hexagonal nets, descriptive of ͕111͖ fcc surfaces, we derive from combinatoric arguments a simple, low-temperature formula for the orientation dependence of the surface step line tension and stiffness, as well as the leading correction, based on the Ising model with nearest-neighbor ͑NN͒ interactions. Our formula agrees well with experimental data for both Ag and Cu͕111͖ surfaces, indicating that NN interactions alone can account for the data in these cases ͑in contrast to results for Cu͕001͖͒. Experimentally significant corollaries of the low-temperature derivation show that the step line tension cannot be extracted from the stiffness and that with plausible assumptions the low-temperature stiffness should have six-fold symmetry, in contrast to the three fold symmetry of the crystal shape. We examine Zia's exact implicit solution in detail, using numerical methods for general orientations and deriving many analytic results including explicit solutions in the two high-symmetry directions. From these exact results we rederive our simple result and explore subtle behavior near close-packed directions. To account for the three-fold symmetry in a lattice gas model, we invoke an orientation-dependent trio interaction and examine its consequences.

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“…24,80 Such interactions typically decay asymptotically as d 5/2 , where d is the perimeter of the triangle made by the three interacting adatoms. 81 While any particular trio interaction is expected to be weaker than the three associated pair interactions, the difference in the decay envelope is just a half power (5/2 vs. 2) for SS mediation.…”

Section: G Open Directionsmentioning

confidence: 99%

Anisotropic surface-state-mediated RKKY interaction between adatoms

Patrone

Einstein

2012

Phys. Rev. B

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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 vF is parallel to the vector R connecting the interacting adatoms; we show that in general, the corresponding Fermi wave-vector kF 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 kF (corresponding to vF) 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(1010), we show that the RKKY interaction should have considerable anisotropy.

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Multisite lateral interactions and their consequences

Cited by 50 publications

References 1 publication

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

Effects of next-nearest-neighbor interactions on the orientation dependence of step stiffness: Reconciling theory with experiment for Cu(001)

Low-temperature orientation dependence of step stiffness on {111} surfaces

Anisotropic surface-state-mediated RKKY interaction between adatoms

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