Electronic origin of magnetic and orbital ordering in insulating LaMnO_3

We derive a spin-orbital model for insulating LaMnO_3 which fulfills the SU(2) symmetry of S=2 spins at Mn^{3+} ions. It includes the complete e_g and t_{2g} superexchange which follows from a realistic Mn^{2+} multiplet structure in cubic site symmetry, and the Jahn-Teller induced orbital interactions. We show that the magnetic ordering observed in LaMnO_3 is stabilized by a purely electronic mechanism due to the e_g-superexchange alone, and provide for the first time a quantitative explanation of the observed transition temperature and the anisotropic exchange interactions.Comment: 4 pages, ReVTeX, 4 figure

Quantum melting of magnetic long-range order near orbital degeneracy. Classical phases and Gaussian fluctuations

We study the effective spin-orbital model derived for the d9 ions in a three-dimensional perovskite lattice, as in KCuF_3, where at each site the doubly degenerate eg orbitals contain a single hole. The model describes the superexchange interactions that depend on the pattern of orbitals occupied. We present the ground state properties of this model, depending on the splitting between the eg orbitals E_z, and the Hund's rule coupling in the excited d8 states, J_H. The classical phase diagram consists of six magnetic phases which all have different orbital ordering: two antiferromagnetic (AF) phases with G-AF order and either x2-y2 or 3z2-r2 orbitals occupied, two phases with mixed orbital (MO) patterns and A-AF order, and two other MO phases with either C-AF or G-AF order. All of them become degenerate at the multicritical point M=(E_z,J_H)=(0,0). Using a generalization of linear spin-wave theory we study both the transverse excitations which are spin-waves and spin-and-orbital-waves, as well as the longitudinal (orbital) excitations. The transverse modes couple to each other, and the spin-and-orbital-wave turns into a soft mode near the M point. Therefore, quantum corrections to the long-range-order parameter are drastically increased near the orbital degeneracy, and classical order is suppressed in a crossover regime between the G-AF and A-AF phases in the (E_z,J_H) plane. This behavior is reminiscent of that found in frustrated spin models, and we conclude that orbital degeneracy provides a new and physically realizable mechanism which stabilizes a spin liquid ground state due to inherent frustration of magnetic interactions. We also point out that such a disordered magnetic phase is likely to be realized in LiNiO_2.Comment: 33 pages, 19 figure

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

Mean-field phase diagram of interacting e_g electrons

We investigate the magnetic phase diagram of the two-dimensional model for e_g electrons which describes layered nickelates. One finds a generic tendency towards magnetic order accompanied by orbital polarization. For two equivalent orbitals with diagonal hopping such orbitally polarized phases are induced by finite crystal field.Comment: 2 pages, 2 figure

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

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

Spin-Orbital Entanglement and Violation of the Goodenough-Kanamori Rules

We point out that large composite spin-orbital fluctuations in Mott insulators with $t_{2g}$ orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, which fluctuate over positive and negative values, and leads to an apparent violation of the Goodenough-Kanamori rules. [{\it Published in Phys. Rev. Lett. {\bf 96}, 147205 (2006).}]Comment: 4 pages, 2 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