Mechanism of the Verwey transition in magnetite

By combining {\it ab initio} results for the electronic structure and phonon spectrum with the group theory, we establish the origin of the Verwey transition in Fe$_3$O$_4$. Two primary order parameters with $X_3$ and $\Delta_5$ symmetries are identified. They induce the phase transformation from the high-temperature cubic to the low-temperature monoclinic structure. The on-site Coulomb interaction $U$ between 3d electrons at Fe ions plays a crucial role in this transition -- it amplifies the coupling of phonons to conduction electrons and thus opens a gap at the Fermi energy. {\it Published in Phys. Rev. Lett. {\bf 97}, 156402 (2006).}Comment: 5 pages, 3 figure

Magnetic and orbital ordering in cuprates and manganites

The mechanisms of magnetic and orbital interactions due to double exchange (DE) and superexchange (SE) in transition metal oxides with degenerate e_g orbitals are presented. Specifically, we study the effective spin-orbital models derived for the d^9 ions as in KCuF_3, and for the d^4 ions as in LaMnO_3, for spins S=1/2 and S=2, respectively. Such models are characterized by three types of elementary excitations: spin waves, orbital waves, and spin-and-orbital waves. The SE interactions between Cu^{2+} (d^9) ions are inherently frustrated, which leads to a new mechanism of spin liquid which operates in three dimensions. The SE between Mn^{3+} (d^4) ions explains the A-type antiferromagnetic order in LaMnO_3 which coexists with the orbital order. In contrast, the ferromagnetic metallic phase and isotropic spin waves observed in doped manganites are explained by DE for degenerate e_g orbitals. It is shown that although a hole does not couple to spin excitations in ferromagnetic planes of LaMnO_3, the orbital excitations change the energy scale for the coherent hole propagation and cause a large redistribution of spectral weight. Finally, we point out some open problems in the present understanding of doped manganites.Comment: 155 pages, 66 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

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

Riparian Meadow Response to Modern Conservation Grazing Management.

Riparian meadows occupy a small proportion of the public lands in the western United States but they provide numerous ecosystem services, including the production of high-quality forage for livestock grazing. Modern conservation management strategies (e.g., reductions in livestock stocking rates and adoption of new riparian grazing standards) have been implemented to better balance riparian conservation and livestock production objectives on publicly managed lands. We examined potential relationships between long-term changes in plant community, livestock grazing pressure and environmental conditions at two spatial scales in meadows grazed under conservation management strategies. Changes in plant community were not associated with either livestock stocking rate or precipitation at the grazing allotment (i.e., administrative) scale. Alternatively, both grazing pressure and precipitation had significant, albeit modest, associations with changes in plant community at the meadow (i.e., ecological site) scale. These results suggest that reductions in stocking rate have improved the balance between riparian conservation and livestock production goals. However, associations between elevation, site wetness, precipitation, and changes in plant community suggest that changing climate conditions (e.g., reduced snowpack and changes in timing of snowmelt) could trigger shifts in plant communities, potentially impacting both conservation and agricultural services (e.g., livestock and forage production). Therefore, adaptive, site-specific management strategies are required to meet grazing pressure limits and safeguard ecosystem services within individual meadows, especially under more variable climate conditions

Order parameters in the Verwey phase transition

The Verwey phase transition in magnetite is analyzed on the basis of the Landau theory. The free energy functional is expanded in a series of components belonging to the primary and secondary order parameters. A low-temperature phase with the monoclinic P2/c symmetry is a result of condensation of two order parameters X_3 and \Delta_5 . The temperature dependence of the shear elastic constant C_44 is derived and the mechanism of its softening is discussed.Comment: 4 pages, 1 figur

Absence of Hole Confinement in Transition Metal Oxides with Orbital Degeneracy

We investigate the spectral properties of a hole moving in a two-dimensional Hubbard model for strongly correlated t_2g electrons. Although superexchange interactions are Ising-like, a quasi-one-dimensional coherent hole motion arises due to effective three-site terms. This mechanism is fundamentally different from the hole motion via quantum fluctuations in the conventional spin model with SU(2) symmetry. The orbital model describes also propagation of a hole in some e_g compounds, and we argue that orbital degeneracy alone does not lead to hole self-localization.Comment: 4 pages, 5 figure

Solvable self-dual impurity models

We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations. This allows us to derive the metric on the corresponding one-dimensional moduli space in an analytical form. Also the generalized translational symmetry is found in an exact form. This symmetry provides a motion on moduli space which transforms one BPS solution into another. Finally, we analyse exactly how vibrational properties (spectral modes) of the BPS solutions depend on the actual position on moduli space. These results are obtained both for the nontrivial topological sector (kinks or antikinks) as well as for the topologically trivial sector, where the motion on moduli space represents a kink-antikink annihilation process