## Yildirim, Taner

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Publication Orientational Phases for M3C60(1993-10-15) Yildirim, Taner; Harris, A. Brooks; Mele, Eugene J; Hong, SuklyunThe mechanism of the orientational ordering of C60 in alkali-metal-doped fullerenes M3C60 is studied. Since the M-C60 (M=K,Rb) interactions cause the C60 molecules to assume one of two standard orientations, this model is equivalent to a generalized Ising model on a fcc lattice. The Ising interactions depend on two type of energies: (1) the direct interaction, i.e., the orientationally dependent part of interactions between nearest-neighboring C60 molecules (each carrying charge -3e), and (2) the band energy of the electrons transferred from M+ ions to the C603- ions. It is shown that the contribution to the pairwise interaction from the direct orientational interaction is ferromagnetic and dominantly nearest neighbor. However, contributions from the band (kinetic) energy of the conduction electrons are found to be antiferromagnetic for first- and third-nearest neighbors, ferromagnetic for second- and fourth-nearest neighbors, and negligible for further neighbors. The total first-neighbor interaction is probably antiferromagnetic. a non-negligible four-spin interaction is also obtained. The implication of these results for the orientational structure is discussed.Publication Spin Structures of Tetragonal Lamellar Copper Oxides(1994-06-06) Yildirim, Taner; Harris, A. Brooks; Entin-Wohlman, Ora; Aharony, AmnonThe spin Hamiltonian of tetragonal lamellar antiferromagnets is shown to contain several novel anisotropies. Symmetry allows bond-dependent anisotropic exchange interactions, which lead to (a) interplane mean-field coupling and (b) an in-plane anisotropy which vanishes classically but arises from quantum zero point energy (QZPE). A similar QZPE involving the interplane isotropic interaction prefers collinear spins. Adding also diploar anisotropy, the competition between all these effects explains for the first time the spin structures of many cuprates.Publication Lattice Dynamics of Solid C60(1992-09-15) Yildirim, Taner; Harris, A. BrooksThe lattice dynamics of C60 has been studied first by means of group theory and then by diagonalizing the dynamical matrix for two recently proposed intermolecular potentials. The libron and phonon energies are calculated as a function of momentum along various symmetry directions with and without phononâ€“libron interactions. The effects of these interactions on the density of states are also discussed. Explicit expressions for the energies of these modes at zero wave vector are given. It is found that both potential models have nearly the same phonon but a somewhat different libron spectrum. The calculated libron energies agree reasonably well with currently available experimental results.Publication Symmetry Analysis of the 2a Phase of C60(1994-07-15) Harris, A. Brooks; Yildirim, Taner; Sachidanandam, RaviA symmetry analysis of the 2a phase recently observed in some samples of C60 is presented. This phase is described by a unit cell with eight molecules in inequivalent orientations. We first show that if this structure is assumed to be exactly cubic, there are only three allowed space groups, none of which corresponds to the Pa3Â¯ arrangement of threefold axes previously established for C60 by several groups. Our calculated powder diffraction spectra for these space groups are not consistent with existing experimental data. Second, if the symmetry of the Pa3Â¯ structure is lowered by a doubling of the unit cell, we show that the resulting structure is trigonal, space group R3Â¯. We calculate powder diffraction spectra for this scenario and thereby place upper limits on both the angular distortion and the trigonal lattice distortion. Third, since the microscopic origin of this distortion probably involves defects of some presently unknown type, we consider a phenomenological scenario for the origin of this trigonal distortion. Within this scenario, we study the symmetry of the interactions needed to explain this structure. We start by giving an analysis of the structural distortion within harmonic lattice dynamics. However, to obtain the correct (R3Â¯) symmetry structure we were forced to study the cubic coupling between zone-corner librons and macroscopic strains. In this way we relate the development of R3Â¯ symmetry from the Pa3Â¯ structure in terms of a phenomenological model of lattice dynamics. Fourth, we extend the above arguments to construct a Landau theory for the hypothesized Pa3Â¯â†’R3Â¯ phase transition, which occurs as a function of the concentration of the presumed defects. The resulting free energy has no cubic terms (so the transition can be continuous) but has five fourth-order invariants.Publication Anisotropic Spin Hamiltonians Due to Spin-Orbit and Coulomb Exchange Interactions(1995-10-01) Yildirim, Taner; Harris, A. Brooks; Aharony, Amnon; Entin-Wohlman, OraHere we correct, extend, and clarify results concerning the spin Hamiltonian â„‹S used to describe the ground manifold of Hubbard models for magnetic insulators in the presence of spin-orbit interactions. Most of our explicit results are for a tetragonal lattice as applied to some of the copper oxide lamellar systems and are obtained within the approximation that â„‹S consists of a sum of nearest-neighbor bond Hamiltonians. We consider both a "generic" model in which hopping takes place from one copper ion to another and a "real" model in which holes can hop from a copper ion to an intervening oxygen 2p band. Both models include orbitally dependent direct and exchange Coulomb interactions involving two orbitals. Our analytic results have been confirmed by numerical diagonalizations for two holes occupying any of the 3d states and, if applicable, the oxygen 2p states. An extension of the perturbative scheme used by Moriya is used to obtain analytic results for â„‹S up to order t2 (t is the matrix of hopping coefficients) for arbitrary crystal symmetry for both the "generic" and "real" models. With only direct orbitally independent Coulomb interactions, our results reduce to Moriyaâ€™s apart from some minor modifications. For the tetragonal case, we show to all orders in t and Î», the spin-orbit coupling constant, that â„‹S is isotropic in the absence of Coulomb exchange terms and assuming only nearest-neighbor hopping. In the presence of Coulomb exchange, scaled by K, the anisotropy in â„‹S is biaxial and is shown to be of order Kt2Î»2. Even when K=0, for systems of sufficiently low symmetry, the anisotropy in â„‹S is proportional to t6Î»2 when the direct on-site Coulomb interaction U is independent of the orbitals involved and of order t2Î»2 otherwise. These latter results apply to the orthorhombic phase of La2CuO4.Publication Yildirim et al. Reply(1995-04-03) Yildirim, Taner; Harris, A. Brooks; Entin-Wohlman, Ora; Aharony, AmnonA Reply to the Comment by S. Skanthakumar, J. W. Lynn, and I. W. Sumarlin, Phys. Rev. Lett. 74, 2842 (1995).Publication Spin Dynamics of Trimers on a Distorted Kagome Lattice(2013-07-11) Harris, A. Brooks; Yildirim, TanerWe treat the ground state, elementary excitations, and neutron scattering cross section for a system of trimers consisting of three tightly bound spins 1/2 on a distorted kagome lattice, subject to isotropic nearest-neighbor (usually antiferromagnetic) Heisenberg interactions. The interactions between trimers are assumed to be weak compared to the intratrimer interactions. We compare the spin-wave excitation spectrum of trimers with that obtained from standard spin-wave theory and attribute the differences at low energy to the fact that the trimer formulation includes exactly the effects of intratrimer zero-point motion.Publication Multipole Approach to Orientational Interactions in Solid C60(1993-07-15) Yildirim, Taner; Harris, A. Brooks; Erwin, Steven C; Pederson, Mark RWe calculate electrostatic multipole moments of C60 up to l=18 using the quantum-mechanical charge distribution with icosahedral symmetry obtained from ab initio calculations. It is found that the second nonzero moment (l=10) is comparable to the first nonzero moment (l=6). The values of several low-order multipole moments are almost 10 times smaller than those found from the charge distribution of recently proposed potential models and thus the actual Coulomb interaction between C60 molecules is much smaller than previously predicted. Much better agreement with calculated multipoles is obtained from a model which introduces point charges at the center of hexagonal and pentagonal plaquettes, following the physical arguments of David et al. [Nature 353, 147 (1991)]. We show that a multipole expansion including only l=6 and 10 moments can predict the potential due to a C60 molecule at distances Râ‰¥2R0 within an error of about 5%, where R0 is the radius of the C60 molecule. At distances less than R<3/2R0 the multipole expansion is qualitatively incorrect even if one includes the terms up to l=18, indicating the importance of short-range quantum effects at these distances. The Coulomb interaction we obtain predicts two nearly degenerate, locally stable configurations for solid C60: (1) a metastable structure with Pa3 symmetry and setting angle Ï†=23.3Â°, close to experimentally observed value, and (2) a global minimum with the Pa3 structure but a setting angle Ï†=93.6Â°. We give physical arguments for expecting two such configurations and give a qualitative explanation for their near degeneracy. We conclude that a satisfactory intermolecular potential requires a first-principles calculation of the quantum-mechanical short-range repulsive interactions.Publication Symmetry, Spin-Orbit Interactions, and Spin Anisotropies(1994-11-21) Yildirim, Taner; Harris, A. Brooks; Entin-Wohlman, Ora; Aharony, AmnonThe origins of anisotropy in the effective spin Hamiltonian, describing the ground manifold of Hubbard models with spin-orbit interactions, are critically discussed. For tetragonal symmetry, we show exactly that spin anisotropy can arise only if one includes both spin-orbit and Coulomb exchange interactions. For lower symmetries, additional anisotropies arise from terms which were hitherto neglected. Our analytic results are supported by numerical solutions for single bond clusters. These results can explain the easy plane anisotropy in the antiferromagnetic cuprates.Publication Towards a Microscopic Approach to the Intermolecular Interaction in Solid C60(1997-06-01) Savin, Sergei; Harris, A. Brooks; Yildirim, TanerAlthough the calculation of the ground-state and thermodynamic properties of solid C60 have been the subject of intense research, our understanding is still based on ad hoc models that treat phenomenologically both the Coulomb and short-range part of the interaction potential between C60 molecules. These potentials do not predict well those properties not fitted to fix the free parameters of the model, and they also do not properly represent the Coulomb interaction between molecules. To remedy this situation, here we introduce a semiempirical model in which the Coulomb interaction is treated microscopically using the local-density approximation C60 molecular charge densities, and the short-range part of the potential is modeled phenomenologically via Lennard-Jones (LJ) 12-6 interactions between the centers, delocalized over the surfaces of C60 molecules. The regular LJ parameters Ïƒ and Îµ as well as multipole moments of the interaction centers distribution were taken to reproduce the details of the observed low-temperature structure. We found that the Coulomb interaction is dominated by the charge overlap between the neighboring C60 molecules, and is much larger than the interaction calculated using the multipole expansion of the charge densities. Contrary to common belief, this Coulomb interaction by itself does not lead to the observed low-temperature structure. However, combined with the proposed short-range interaction, it stabilizes Pa3 spatial structure with the correct setting angle. We make a comprehensive comparison between the wide range of experimental results and predictions of our, as well as previously proposed models. Our results show that the proposed model has the best overall agreement with the experimental observations in both the low- and high-temperature phases.