Ruderman-Kittel-Kasuya-Yosida interactions on a bipartite lattice

Bunder, J. E.; Lin, Hsiu‐Hau

doi:10.1103/physrevb.80.153414

Cited by 53 publications

(58 citation statements)

References 20 publications

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“…This interaction determines the relative orientation of magnetic moments embedded in graphene and has been the subject of many recent papers, [14][15][16][17][18][19][20] as an understanding of this interaction is a major step in the implementation of graphene devices in the field of spintronics. When the linear dispersion approximation is used, a cutoff function is required to prevent the result diverging due to high-energy contributions.…”

Section: A Application To Rkky Interactionmentioning

confidence: 99%

Electronic structure of graphene beyond the linear dispersion regime

Power

Ferreira

2011

Phys. Rev. B

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Among the many interesting features displayed by graphene, one of the most attractive is the simplicity with which its electronic structure can be described. The study of its physical properties is significantly simplified by the linear dispersion relation of electrons in a narrow range around the Fermi level. Unfortunately, the mathematical simplicity of graphene electrons is limited only to this narrow energy region and is not very practical when dealing with problems that involve energies outside the linear dispersion part of the spectrum. In this communication we remedy this limitation by deriving a set of closed-form analytical expressions for the real-space single-electron Green function of graphene which is valid across a large fraction of the energy spectrum. By extending to a wider energy range the simplicity with which graphene electrons are described, it is now possible to derive more mathematically transparent and insightful expressions for a number of physical properties that involve higher energy scales. The power of this new formalism is illustrated in the case of the magnetic (RKKY) interaction in graphene.

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Section: A Application To Rkky Interactionmentioning

confidence: 99%

Electronic structure of graphene beyond the linear dispersion regime

Power

Ferreira

2011

Phys. Rev. B

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“…Therefore, for describing the RKKY interaction in graphene, these two unique features must be correctly taken into account. The RKKY interaction in graphene has already been studied by many authors both for the doped and the undoped case [5][6][7][8][9][10][11][12][13] . However, the results differ from one another, either in the power-law decay, or in the oscillatory behavior in the long-distance limit, or sometimes even in the sign of the interaction, viz., ferromagnetic (FM) or anti-ferromagnetic (AFM).…”

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confidence: 99%

Analytical expression for the RKKY interaction in doped graphene

2011

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We obtain an analytical expression for the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction J in electron or hole doped graphene for linear Dirac bands, extending our earlier results for the undoped case.1 The results agree very well with the numerical calculations for the full tight-binding band structure in the regime where the linear band structure is valid. The analytical result, expressed in terms of the Meijer G-function, consists of the product of two oscillatory terms, one coming from the interference between the two Dirac cones and the second coming from the finite size of the Fermi surface. For large distances, the Meijer G-function behaves as a sinusoidal term, leading to the result J ∼ R −2 kF sin(2kF R){1 + cos [( K − K ′ ). R]} for moments located on the same sublattice. The R −2 dependence, which is the same for the standard two-dimensional electron gas, is universal irrespective of the sublattice location and the distance direction of the two moments except when kF = 0 (undoped case), where it reverts to the R −3 dependence. These results correct several inconsistencies found in the literature.

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“…Not surprisingly, then, many theory groups have recently devoted attention to the prospect of RKKY interactions. [63][64][65][66][67][68][69][70][71][72][73][74] They and others pointed out a variety of complicating issues and idiosyncrasies of mono-layer graphene, such as the bipartite nature of the lattice (leading to ferromagnetic or repulsive coupling for impurities on the same hexagonal, Bravais sublattice of the honeycomb graphene lattice 63,64 and antiferromagnetic or attractive coupling when on opposite Bravais sublattices, 64,65,68,69 ), the vanishing density of states at the Fermi level in undoped and ungated lattices, the suppression of backscattering (leading to R −3 rather than R −2 decay 75 ), 63,64 the role of electron-electron interactions, 70 etc. Usually the adsorbates are taken in atop sites but sometimes in bridge sites above bonds or hollow sites at the center of the hexagon.…”

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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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Ruderman-Kittel-Kasuya-Yosida interactions on a bipartite lattice

Cited by 53 publications

References 20 publications

Electronic structure of graphene beyond the linear dispersion regime

Electronic structure of graphene beyond the linear dispersion regime

Analytical expression for the RKKY interaction in doped graphene

Anisotropic surface-state-mediated RKKY interaction between adatoms

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