Yildirim, Taner
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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 phonon–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 Pa3¯ 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 Pa3¯ structure is lowered by a doubling of the unit cell, we show that the resulting structure is trigonal, space group R3¯. 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 (R3¯) 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 R3¯ symmetry from the Pa3¯ structure in terms of a phenomenological model of lattice dynamics. Fourth, we extend the above arguments to construct a Landau theory for the hypothesized Pa3¯→R3¯ 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 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 Frustration and Quantum Fluctuations in Heisenberg fcc Antiferromagnets(1998-08-01) Yildirim, Taner; Harris, A. Brooks; Shender, Eugene FWe consider the quantum Heisenberg antiferromagnet on a face-centered-cubic lattice in which J, the second-neighbor (intrasublattice) exchange constant, dominates J′, the first-neighbor (intersublattice) exchange constant. It is shown that the continuous degeneracy of the classical ground state with four decoupled (in a mean-field sense) simple cubic antiferromagnetic sublattices is removed so that at second order in J′/J the spins are collinear. Here we study the degeneracy between the two inequivalent collinear structures by analyzing the contribution to the spin-wave zero-point energy which is of the form Heff/J=C0+C4σ1σ2σ3σ4(J′/J)4+O(J′/J)5, where σi specifies the phase of the ith collinear sublattice, C0 depends on J′/J but not on the σ’s, and C4 is a positive constant. Thus the ground state is one in which the product of the σ’s is −1. This state, known as the second kind of type A, is stable in the range |J′|<2|J| for large S. Using interacting spin-wave theory, it is shown that the main effect of the zero-point fluctuations is at small wave vector and can be well modeled by an effective biquadratic interaction of the form ΔEQeff=−1/2Q∑i,j[S(i)⋅S(j)]2/S3. This interaction opens a spin gap by causing the extra classical zero-energy modes to have a nonzero energy of order J′√S. We also study the dependence of the zero-point spin reduction on J′/J and the sublattice magnetization on temperature. The resulting experimental consequences are discussed.Publication Charge and Spin Ordering in the Mixed-Valence Compound LuFe2O4(2010-04-15) Harris, A. Brooks; Yildirim, TanerLandau theory and symmetry considerations lead us to propose an explanation for several seemingly paradoxical behaviors of charge ordering (CO) and spin ordering (SO) in the mixed valence compound LuFe2O4. Both SO and CO are highly frustrated. We analyze a lattice gas model of CO within mean-field theory and determine the magnitude of several of the phenomenological interactions. We show that the assumption of a continuous phase transitions at which CO or SO develops implies that both CO and SO are incommensurate. To explain how ferroelectric fluctuations in the charge-disordered phase can be consistent with an antiferroelectric-ordered phase, we invoke an electron-phonon interaction in which a low-energy (20 meV) zone-center transverse phonon plays a key role. The energies of all the zone center phonons are calculated from first principles. We give a Landau analysis which explains SO and we discuss a model of interactions which stabilizes the SO state, if it is assumed commensurate. However, we suggest a high-resolution experimental determination to see whether this phase is really commensurate, as believed up to now. The applicability of representation analysis is discussed. A tentative explanation for the sensitivity of the CO state to an applied magnetic field in field-cooled experiments is given.Publication Quantum Dynamics of a Hydrogen Molecule Confined in a Cylindrical Potential(2003-06-27) Yildirim, Taner; Harris, A. BrooksWe study the coupled rotation-vibration levels of a hydrogen molecule in a confining potential with cylindrical symmetry. We include the coupling between rotations and translations and show how this interaction is essential to obtain the correct degeneracies of the energy level scheme. We applied our formalism to study the dynamics of H2 molecules inside a “smooth” carbon nanotube as a function of tube radius. The results are obtained both by numerical solution of the (2J+1)-component radial Schrödinger equation and by developing an effective Hamiltonian to describe the splitting of a manifold of states of fixed angular momentum J and number of phonons N. For nanotube radius smaller than ≈3.5Å, the confining potential has a parabolic shape and the results can be understood in terms of a simple toy model. For larger radius, the potential has the “Mexican hat” shape and therefore the H2 molecule is off centered, yielding radial and tangential translational dynamics in addition to rotational dynamics of H2 molecule which we also describe by a simple model. Finally, we make several predictions for the the neutron scattering observation of various transitions between these levels.Publication Unusual Symmetries in the Kugel-Khomskii Hamiltonian(2003-08-22) Harris, A. Brooks; Yildirim, Taner; Aharony, Amnon; Entin-Wohlman, Ora; Korenblit, I. YaThe Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between d1 ions having threefold degenerate t2g orbitals. Since orbitals do not couple along “inactive” axes, perpendicular to the orbital planes, the total number of electrons in |α⟩ orbitals in any such plane and the corresponding total spin are both conserved. A Mermin-Wagner construction shows that there is no long-range spin ordering at nonzero temperatures. Inclusion of spin-orbit coupling allows such ordering, but even then the excitation spectrum is gapless due to a continuous symmetry. Thus, the observed order and gap require more symmetry breaking terms.Publication Spin Waves in the Frustrated Kagomé Lattice Antiferromagnet KFe3(OH)6(SO4)2(2006-06-23) Matan, Kittiwit; Grohol, Daniel; Yildirim, Taner; Nocera, Daniel G.; Harris, A. Brooks; Lee, Seunghun; Nagler, Stephen E.; Lee, YoungsuThe spin wave excitations of the S=5/2 kagomé lattice antiferromagnet KFe3(OH)6(SO4)2 have been measured using high-resolution inelastic neutron scattering. We directly observe a flat mode which corresponds to a lifted “zero energy mode,” verifying a fundamental prediction for the kagomé lattice. A simple Heisenberg spin Hamiltonian provides an excellent fit to our spin wave data. The antisymmetric Dzyaloshinskii-Moriya interaction is the primary source of anisotropy and explains the low-temperature magnetization and spin structure.Publication Rotational and Vibrational Dynamics of Interstitial Molecular Hydrogen(2002-12-06) Yildirim, Taner; Harris, A. BrooksThe calculation of the hindered roton-phonon energy levels of a hydrogen molecule in a confining potential with different symmetries is systematized for the case when the rotational angular momentum J is a good quantum number. One goal of this program is to interpret the energy-resolved neutron time-of-flight spectrum previously obtained for H2C60. This spectrum gives direct information on the energy-level spectrum of H2 molecules confined to the octahedral interstitial sites of solid C60. We treat this problem of coupled translational and orientational degrees of freedom (i) by construction of an effective Hamiltonian to describe the splitting of the manifold of states characterized by a given value of J and having a fixed total number of phonon excitations, (ii) by numerical solutions of the coupled translation-rotation problem on a discrete mesh of points in position space, and (iii) by a group theoretical symmetry analysis. Results obtained from these three different approaches are mutually consistent. The results of our calculations explain several aspects of the experimental observations, but show that a truly satisfactory orientational potential for the interaction of an H2 molecule with a surrounding array of C atoms has not yet been developed.