Classical frustration and quantum disorder in spin-orbital models

The most elementary of all physical spin-orbital models is the Kugel-Khomskii model describing a S=1/2, $e_g$ degenerate Mott-insulator. Recent theoretical work is reviewed revealing that the classical limit is characterized by a point of perfect dynamical frustration. It is suggested that this might give rise to a quantum disordered ground state.Comment: 7 pages Revtex, 3 ps figures, proceedings 1998 NEC symposium, Nasu, Japa

Quantum disorder versus order-out-of-disorder in the Kugel-Khomskii model

The Kugel-Khomskii model, the simplest model for orbital degenerate magnetic insulators, exhibits a zero temperature degeneracy in the classical limit which could cause genuine quantum disorder. Khaliullin and Oudovenko [Phys. Rev. B 56, R14 243 (1997)] suggested recently that instead a particular classical state could be stabilized by quantum fluctuations. Here we compare their approach with standard random phase approximation and show that it strongly underestimates the strength of the quantum fluctuations, shedding doubts on the survival of any classical state.Comment: 4 pages, ReVTeX, 4 figure

Single-electron tunneling in InP nanowires

We report on the fabrication and electrical characterization of field-effect devices based on wire-shaped InP crystals grown from Au catalyst particles by a vapor-liquid-solid process. Our InP wires are n-type doped with diameters in the 40-55 nm range and lengths of several microns. After being deposited on an oxidized Si substrate, wires are contacted individually via e-beam fabricated Ti/Al electrodes. We obtain contact resistances as low as ~10 kOhm, with minor temperature dependence. The distance between the electrodes varies between 0.2 and 2 micron. The electron density in the wires is changed with a back gate. Low-temperature transport measurements show Coulomb-blockade behavior with single-electron charging energies of ~1 meV. We also demonstrate energy quantization resulting from the confinement in the wire.Comment: 4 pages, 3 figure

Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph

We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of $\delta$-functions, and all the modes are localized. The fractional number of modes with frequency less than $\omega$ varies as $\exp (-C/\omega)$ for $\omega$ tending to zero, where $C$ is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time $t$ varies as $\exp(- C' t^{1/3})$, for large $t$, where $C'$ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free-energy per site at temperature $T$, near and above the critical temperature $T_c$, also has an essential singularity of the type $\exp[ -K {(T - T_c)}^{-1/2}]$.Comment: substantially revised, a section adde

Orbital liquid in ferromagnetic manganites: The orbital Hubbard model for ege_g electrons

We have analyzed the symmetry properties and the ground state of an orbital Hubbard model with two orbital flavors, describing a partly filled spin-polarized $e_g$ band on a cubic lattice, as in ferromagnetic manganites. We demonstrate that the off-diagonal hopping responsible for transitions between $x^2-y^2$ and $3z^2-r^2$ orbitals, and the absence of SU(2) invariance in orbital space, have important implications. One finds that superexchange contributes in all orbital ordered states, the Nagaoka theorem does not apply, and the kinetic energy is much enhanced as compared with the spin case. Therefore, orbital ordered states are harder to stabilize in the Hartree-Fock approximation (HFA), and the onset of a uniform ferro-orbital polarization and antiferro-orbital instability are similar to each other, unlike in spin case. Next we formulate a cubic (gauge) invariant slave boson approach using the orbitals with complex coefficients. In the mean-field approximation it leads to the renormalization of the kinetic energy, and provides a reliable estimate for the ground state energy of the disordered state. Using this approach one finds that the HFA fails qualitatively in the regime of large Coulomb repulsion $U\to\infty$ -- the orbital order is unstable, and instead a strongly correlated orbital liquid with disordered orbitals is realized at any electron filling.Comment: 25 pages, 9 figure

Orbital dynamics in ferromagnetic transition metal oxides

We consider a model of strongly correlated $e_g$ electrons interacting by superexchange orbital interactions in the ferromagnetic phase of LaMnO$_3$. It is found that the classical orbital order with alternating occupied $e_g$ orbitals has a full rotational symmetry at orbital degeneracy, and the excitation spectrum derived using the linear spin-wave theory is gapless. The quantum (fluctuation) corrections to the order parameter and to the ground state energy restore the cubic symmetry of the model. By applying a uniaxial pressure orbital degeneracy is lifted in a tetragonal field and one finds an orbital-flop phase with a gap in the excitation spectrum. In two dimensions the classical order is more robust near the orbital degeneracy point and quantum effects are suppressed. The orbital excitation spectra obtained using finite temperature diagonalization of two-dimensional clusters consist of a quasiparticle accompanied by satellite structures. The orbital waves found within the linear spin-wave theory provide an excellent description of the dominant pole of these spectra.Comment: 13 pages, 12 figures, to appear in Phys. Rev.

Orbital and spin physics in LiNiO2 and NaNiO2

We derive a spin-orbital Hamiltonian for a triangular lattice of e_g orbital degenerate (Ni^{3+}) transition metal ions interacting via 90 degree superexchange involving (O^{2-}) anions, taking into account the on-site Coulomb interactions on both the anions and the transition metal ions. The derived interactions in the spin-orbital model are strongly frustrated, with the strongest orbital interactions selecting different orbitals for pairs of Ni ions along the three different lattice directions. In the orbital ordered phase, favoured in mean field theory, the spin-orbital interaction can play an important role by breaking the U(1) symmetry generated by the much stronger orbital interaction and restoring the threefold symmetry of the lattice. As a result the effective magnetic exchange is non-uniform and includes both ferromagnetic and antiferromagnetic spin interactions. Since ferromagnetic interactions still dominate, this offers yet insufficient explanation for the absence of magnetic order and the low-temperature behaviour of the magnetic susceptibility of stoichiometric LiNiO_2. The scenario proposed to explain the observed difference in the physical properties of LiNiO_2 and NaNiO_2 includes small covalency of Ni-O-Li-O-Ni bonds inducing weaker interplane superexchange in LiNiO_2, insufficient to stabilize orbital long-range order in the presence of stronger intraplane competition between superexchange and Jahn-Teller coupling.Comment: 33 pages, 12 postscript figures, uses iopams.sty . This article features in New Journal of Physics as part of a Focus Issue on Orbital Physics - all contributions may be freely accessed at (http://stacks.iop.org/1367-2630/6/i=1/a=E05). The published version of this article may be found at http://stacks.iop.org/1367-2630/7/12

Suppression of static stripe formation by next-neighbor hopping

We show from real-space Hartree-Fock calculations within the extended Hubbard model that next-nearest neighbor (t') hopping processes act to suppress the formation of static charge stripes. This result is confirmed by investigating the evolution of charge-inhomogeneous corral and stripe phases with increasing t' of both signs. We propose that large t' values in YBCO prevent static stripe formation, while anomalously small t' in LSCO provides an additional reason for the appearance of static stripes only in these systems.Comment: 4 pages, 5 figure

Damped orbital excitations in the titanates

A possible mechanism for the removal of the orbital degeneracy in RTiO3 (where R=La, Y, ...) is considered. The calculation is based on the Kugel-Khomskii Hamiltonian for electrons residing in the t2g orbitals of the Ti ions, and uses a self-consistent pe rturbation expansion in the interaction between the orbital and the spin degrees of freedom. The latter are assumed to be ordered in a Neel state, brought about by delicate interactions that are not included in the Kugel-Khomskii Hamiltonian. Within our model calculations, each of the t2g bands is found to acquire a finite, temperature-dependent dispersion, that lifts the orbital degeneracy. The orbital excitations are found to be heavily damped over a rather wide band. Consequently, they do not participate as a separate branch of excitations in the low-temperature thermodynamics.eComment: 6 pages, 3 figure