We study the exchange interaction J between two magnetic impurities in graphene (the RKKY interaction) by directly computing the lattice Green's function for the tight-binding band structure for the honeycomb lattice. The method allows us to compute J numerically for much larger distances than can be handled by finite-lattice calculations as well as for small distances. In addition, we rederive the analytical long-distance behavior of J for linearly dispersive bands and find corrections to the oscillatory factor that were previously missed in the literature. The main features of the RKKY interaction in graphene are that unlike the J ∝ (2kF R) −2 sin(2kF R) behavior of an ordinary 2D metal in the long-distance limit, J in graphene falls off as 1/R 3 , shows the 1 + cos((K − K ′ ).R)-type oscillations with additional phase factors depending on the direction, and exhibits a ferromagnetic interaction for moments on the same sublattice and an antiferromagnetic interaction for moments on the opposite sublattices as required by particle-hole symmetry. The computed J with the full band structure agrees with our analytical results in the long-distance limit including the oscillatory factors with the additional phases.

In the original paper, figure 12(b) was incorrect and the caption of figure 12 was also erroneous. The correct figure and caption are shown below. E/t Figure 12. LDOS at the impurity site ρ 0A (top), the NN site ρ 0B (middle) and the next-NN site ρ 1A (bottom) obtained from equations (13) and (14) for different strengths of the impurity potential U 0 /t = 0, 2 and 5, denoted by black dashed, black solid and red dashed lines, respectively. As U 0 → ∞, the top LDOS goes to zero (except for the bound state beyond the top of the band whose energy goes to ∞), and the zero-mode state lives only on the B sublattice, as indicated from the middle and the bottom panels. The prominent zero-mode peak in the middle panel for U 0 /t = 5 will develop into a δ-function peak at E = 0 as the impurity potential U 0 → ∞.Abstract. We study the electronic structure of graphene with a single substitutional vacancy using a combination of the density-functional, tight-binding and impurity Green's function approaches. Density-functional studies are performed with the all-electron spin-polarized linear augmented plane wave (LAPW) method. The three sp 2 σ dangling bonds adjacent to the vacancy introduce localized states (Vσ ) in the mid-gap region, which split due to the crystal field and a Jahn-Teller distortion, while the p z π states introduce a sharp resonance state (Vπ ) in the band structure. For a planar structure, symmetry strictly forbids hybridization between the σ and the π states, so that these bands are clearly identifiable in the calculated band structure. As to the magnetic moment of the vacancy, the Hund's rule coupling aligns the spins of the four localized Vσ 1 ↑↓, Vσ 2 ↑ and Vπ ↑ electrons, resulting in an S = 1 state, with a magnetic moment of 2µ B , which is reduced by about 0.3µ B due to the anti-ferromagnetic spin polarization of the π band itinerant states in the vicinity of the vacancy. This results in the net magnetic moment of 1.7µ B . Using the Lippmann-Schwinger equation, we reproduce the well-known ∼1/r decay of the localized Vπ wave function with distance, and in addition, find an

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.

Phase separation is a crucial ingredient of the physics of manganites; however, the role of mixed phases in the development of the colossal magnetoresistance (CMR) phenomenon still needs to be clarified. We report the realization of CMR in a single-valent LaMnO 3 manganite. We found that the insulator-to-metal transition at 32 GPa is well described using the percolation theory. Pressure induces phase separation, and the CMR takes place at the percolation threshold. A large memory effect is observed together with the CMR, suggesting the presence of magnetic clusters. The phase separation scenario is well reproduced, solving a model Hamiltonian. Our results demonstrate in a clean way that phase separation is at the origin of CMR in LaMnO 3 .colossal magnetoresistance | strongly correlated materials | phase separation | high pressure | transport measurements I n hole-doped rare earth manganite compounds, the colossal magnetoresistance (CMR) peaks at a transition from a hightemperature (T) insulating paramagnetic phase to a low-T conducting ferromagnetic phase. The presence of Mn 3+ and Mn 4+ ions together with the site-site double-exchange (DE) mechanism (1) appear to capture the essence of this phenomenon. A plethora of experimental and theoretical investigations have recently suggested that the ground states of manganites are intrinsically inhomogeneous and characterized by the presence of competing phases (2-8) extending over domains at nanoscale/mesoscale. High pressure (P) has a triggering effect for phase separation because either magnetic or structural domains have been observed in compressed manganites (9-12). The role of the nanostructuring and of the interdomain interactions in the CMR phenomenon is still far from being completely understood, and to design materials that incorporate CMR at room temperature (RT) remains a challenge because of the strong interplay among electronic, structural, and magnetic interactions at both atomic and interdomain scales.As an archetypal cooperative Jahn-Teller (JT) system (13) and the parent compound of several important mixed-valence CMR manganite families, LaMnO 3 (LMO) is at the focus of intense investigations. Up to now, the CMR effect has been observed in hole-doped LMO, but not in single-valent LMO. At RT, LMO enters a high conductive phase above 32 GPa showing a "badmetal" behavior (14). Previous Raman spectroscopy study (9) shows the emergence, in compressed LMO, of a phase-separated (PS) state consisting of domains of JT-distorted and undistorted MnO 6 octahedra. The simultaneous presence of an inherent phase separation as well as of a metallization process resembles the conditions under which CMR is observed in doped compounds, and suggests the onset of CMR in compressed LMO. To verify this hypothesis, we have carried out an extensive study of the transport properties of LMO over a wide P-T region (12 < P < 54 GPa and 10 < T < 300 K) and applied magnetic field H, varying from 0 to 8 T. Here, we report the realization of CMR in a narrow pressure range between 3...