A Reply to the Comment by S. Skanthakumar, J. W. Lynn, and I. W. Sumarlin, Phys. Rev. Lett. 74, 2842 (1995)
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The five-band Hubbard model for a d band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e.g., cubic) symmetry. In that case, if the crystal-field... more
The five-band Hubbard model for a d band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e.g., cubic) symmetry. In that case, if the crystal-field splitting is large, one may consider excitations confined to the lowest threefold-degenerate t2g orbital states. When the electron hopping matrix element (t) is much smaller than the on-site Coulomb interaction energy (U), the Hubbard model can be mapped onto the well-known effective Hamiltonian (at order t2/U) derived by Kugel and Khomskii (KK). Recently we have shown that the KK Hamiltonian does not support long-range spin order at any nonzero temperature due to several novel hidden symmetries that it possesses. Here we extend our theory to show that these symmetries also apply to the underlying three-band Hubbard model. Using these symmetries we develop a rigorous Mermin-Wagner construction, which shows that the three-band Hubbard model does not support ...
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The number of absorption and Raman optical modes for each Wyckoff orbit in the high-temperature tetragonal (I4/mmm) parent lattice of the Ruddlesden-Popper compounds Ca3X2O7, with X=Mn or X=Ti is given. We analyze the effect of sequential... more
The number of absorption and Raman optical modes for each Wyckoff orbit in the high-temperature tetragonal (I4/mmm) parent lattice of the Ruddlesden-Popper compounds Ca3X2O7, with X=Mn or X=Ti is given. We analyze the effect of sequential perturbations which lower the symmetry to Cmcm and Cmc21 and finally include magnetic ordering. We determine the power law behavior (within mean field theory) for the cross section for photon absorption and Raman scattering of modes which appear as the symmetry is successively lowered. In the Cmc21 phase we give a symmetry analysis to discuss the magnon-phonon coupling which in other systems gives rise to electromagnons. From our results we suggest several experiments to clarify the phase diagram and other properties of these systems
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We present an analytical calculation of the spin-wave spectrum of the Jahn-Teller system LaTiO3. The calculation includes all superexchange couplings between nearest-neighbor Ti ions allowed by the space-group symmetries: The isotropic... more
We present an analytical calculation of the spin-wave spectrum of the Jahn-Teller system LaTiO3. The calculation includes all superexchange couplings between nearest-neighbor Ti ions allowed by the space-group symmetries: The isotropic Heisenberg couplings and the antisymmetric (Dzyaloshinskii-Moriya) and symmetric anisotropies. The calculated spin-wave dispersion has four branches, two nearly degenerate branches with small zone-center gaps and two practically indistinguishable high-energy branches having large zone-center gaps. The two lower-energy modes are found to be in satisfying agreement with neutron-scattering experiments. In particular, the experimentally detected approximate isotropy in the Brillouin zone and the small zone-center gap are well reproduced by the calculations. The higher-energy branches have not been detected yet by neutron scattering but their zone-center gaps are in satisfying agreement with recent Raman data
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The 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... more
The 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-ne...
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A phenomenological explanation of the magnetoelectric behavior of Co3TeO6 is developed. We explain the second harmonic generation data and the magnetic field induced spontaneous electric polarization in the magnetically ordered phase... more
A phenomenological explanation of the magnetoelectric behavior of Co3TeO6 is developed. We explain the second harmonic generation data and the magnetic field induced spontaneous electric polarization in the magnetically ordered phase below 20 K
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We obtain the ANNNI model from a Heisenberg model with large single–ion anisotropy energy, D, as might be relevant for helical spin systems. We treat quantum fluctuations to lowest order in 1/S at zero temperature within an expansion in... more
We obtain the ANNNI model from a Heisenberg model with large single–ion anisotropy energy, D, as might be relevant for helical spin systems. We treat quantum fluctuations to lowest order in 1/S at zero temperature within an expansion in J/D, where J is an exchange energy. The transition from the state with periodicity p = 4 to the uniform state (p = ∞) occurs via an infinite sequence of first order transitions in which p increases monotonically. PACS numbers: 75.30.Et, 71.70.Ej, 75.30.Gw Typeset using REVTEX 1 Systems with long–period modulated structures are surprisingly common in nature. Examples include helical phases in the rare–earths and their compounds [ 1], polytypism [ 2], and the arrangement of antiphase boundaries in binary alloys [ 3]. A given compound may exhibit many different modulated structures of differing wavelength as a control parameter such as the temperature is varied. Some modulated structures can usefully be viewed as an assembly of domain walls when the ene...
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A method for obtaining a 1/σ expansion for certain statistical models is presented, where σ+1 is the coordination number of the lattice. The method depends on being able to generate exact recursion relations for the Cayley tree. By... more
A method for obtaining a 1/σ expansion for certain statistical models is presented, where σ+1 is the coordination number of the lattice. The method depends on being able to generate exact recursion relations for the Cayley tree. By perturbing the recursion relation to take account of the dominant loops in a hypercubic lattice for large σ, we obtain corrections of order σ−2 to the recursion relations. For the tight-binding model on random bond clusters (the quantum-percolation problem) we obtain corrections to this order for the critical concentration p* at which the transition between localized and extended zero-energy eigenfunctions takes place. It is believed that this concentration coincides with the transition when all energies are considered. In addition, we display the relation for the Cayley tree between quantum-percolation and lattice animals (or dilute branched polymers). We show that this relation manifests itself in the appearance of singularities in the quantum-percolati...
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Physics, Statistical Physics, Medicine, Diffusion, Physical, and 4 moreScaling, Harmonic, Resistor, and Scaling Law
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ABSTRACT
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We report a detailed study of single ion anisotropy and crystal field effects in rare-earth cuprates R_2CuO4 (R=Nd, Pr, and Sm). It is found that most of the magnetic properties are mainly due to the coupling between copper and rare-earth... more
We report a detailed study of single ion anisotropy and crystal field effects in rare-earth cuprates R_2CuO4 (R=Nd, Pr, and Sm). It is found that most of the magnetic properties are mainly due to the coupling between copper and rare-earth magnetic subsystem which exhibits a large single ion anisotropy. This anisotropy prefers ordering of rare-earth moments, which is induced by the copper ions, along [100] for R=Pr and Nd and along [001] for R=Sm. Combined with a pseudo dipolar interaction arising from the anisotropy of the R--Cu exchange, we can explain the magnetic structures of these materials. The spin reorientation transitions in N_2CuO4 can be explained in terms of a competition between various interplanar interactions which arises because of the rapid temperature dependence of the Nd moment below about 100 K. Finally we introduce a simple two dimensional model for the Nd-spin--wave spectrum.
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The nature of the ordering of a quantum spin-1/2 Heisenberg antiferromagnet is considered in the presence of the strong lattice frustration associated with the pyrochlore lattice. A field theory indicates that quantum fluctuations lead to... more
The nature of the ordering of a quantum spin-1/2 Heisenberg antiferromagnet is considered in the presence of the strong lattice frustration associated with the pyrochlore lattice. A field theory indicates that quantum fluctuations lead to a state having dimerization that has long-range static correlations not in 〈S〉 but rather in 〈S(r)⋅S(r+δ)〉. A sublattice ordering is found that is consistent with results obtained using degenerate perturbation theory to analyze the ground-state manifold.
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The Kugel-Khomskii (KK) Hamiltonian describes spin and orbital superexchange interactions between d1 ions in an ideal cubic perovskite structure, in which the three t2g orbitals are degenerate in energy and electron hopping is constrained... more
The Kugel-Khomskii (KK) Hamiltonian describes spin and orbital superexchange interactions between d1 ions in an ideal cubic perovskite structure, in which the three t2g orbitals are degenerate in energy and electron hopping is constrained by cubic site symmetry. In this paper we implement a variational approach to mean-field theory in which each site i has its own n×n single-site density matrix ρ(i), where n, the number of allowed single-particle states, is 6 (3 orbital times 2 spin states). The variational free energy from this 35 parameter density matrix is shown to exhibit the unusual symmetries noted previously, which lead to a wave-vector-dependent susceptibility for spins in α orbitals which is dispersionless in the qα direction. Thus, for the cubic KK model itself, mean-field theory does not provide wavevector “selection,” in agreement with rigorous symmetry arguments. We consider the effect of including various perturbations. When spin-orbit interactions are introduced, the ...
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The number of absorption and Raman optical modes for each Wyckoff orbit in the high-temperature tetragonal (I4/mmm) parent lattice of the Ruddlesden-Popper compounds Ca$_3$X$_2$O$_7$, with X=Mn or X=Ti is given. We analyze the effect of... more
The number of absorption and Raman optical modes for each Wyckoff orbit in the high-temperature tetragonal (I4/mmm) parent lattice of the Ruddlesden-Popper compounds Ca$_3$X$_2$O$_7$, with X=Mn or X=Ti is given. We analyze the effect of sequential perturbations which lower the symmetry to Cmcm and Cmc2$_1$ and finally include magnetic ordering. We determine the power law behavior (within mean field theory) for the cross section for photon absorption and Raman scattering of modes which appear as the symmetry is successively lowered. In the Cmc2$_1$ phase we give a symmetry analysis to discuss the magnon-phonon coupling which in other systems gives rise to "electromagnons." From our results we suggest several experiments to clarify the phase diagram and other properties of these systems.
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The 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... more
The 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 nearestneighboring C60 molecules (each carrying charge -3e), and (2) the band energy of the electrons transferred from M+ ions to the C603ions. 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 firstand thirdnearest neighbors, ferromagnetic for secondand fourth-nearest neighbors, and negligible for further neighbors. The total first-neighbor i...
The moments τk of typical diffusion times for ‘‘blind’’ and ‘‘myopic’’ ants on an arbitrary cluster are expressed exactly in terms of resistive correlations for the associated resistor network. For a diluted lattice at bond concentration... more
The moments τk of typical diffusion times for ‘‘blind’’ and ‘‘myopic’’ ants on an arbitrary cluster are expressed exactly in terms of resistive correlations for the associated resistor network. For a diluted lattice at bond concentration p, we introduce ‘‘diffusive’’ susceptibilities χk(p) as the average over clusters of τk. For p→pc, where pc is the percolation threshold, χk(p) diverges as |pc-p|-γk. We show that γk=kΔτ-β with Δτ=β+γ+ζ, where β and γ are percolation exponents and ζ is the resistance scaling exponent. Our analysis provides the first analytic demonstration that the leading exponents γk are the same for a wide class of models, including the two types of ants as special cases, although corrections to scaling are larger for the myopic ant than for the blind one. This class of models includes that for dilute spin waves in Heisenberg ferromagnets. Exact enumerations allow us to study universal amplitude ratios (at p=pc)χk+1χk−1/χk2 as a function of continuous spatial dime...