Origin of the Verwey transition in magnetite: Group theory, electronic structure, and lattice dynamics study

The Verwey phase transition in magnetite has been analyzed using the group theory methods. It is found that two order parameters with the symmetries $X_3$ and $\Delta_5$ induce the structural transformation from the high-temperature cubic to the low-temperature monoclinic phase. The coupling between the order parameters is described by the Landau free energy functional. The electronic and crystal structure for the cubic and monoclinic phases were optimized using the {\it ab initio} density functional method. The electronic structure calculations were performed within the generalized gradient approximation including the on-site interactions between 3d electrons at iron ions -- the Coulomb element $U$ and Hund's exchange $J$. Only when these local interactions are taken into account, the phonon dispersion curves, obtained by the direct method for the cubic phase, reproduce the experimental data. It is shown that the interplay of local electron interations and the coupling to the lattice drives the phonon order parameters and is responsible for the opening of the gap at the Fermi energy. Thus, it is found that the metal-insulator transition in magnetite is promoted by local electron interactions, which significantly amplify the electron-phonon interaction and stabilize weak charge order coexisting with orbital order of the occupied $t_{2g}$ states at Fe ions. This provides a scenario to understand the fundamental problem of the origin of the Verwey transition in magnetite.Comment: 17 pages, 5 figures, 8 tables. Accepted version to be published in Phys. Rev.

Magnetite: Raman study of the high-pressure and low-temperature effects

We report the results of a low-temperature (300K-15K) high-pressure (up to 22GPa) Raman study of the Verwey transition in magnetite (Fe3O4). We use additional Raman modes observed below the Verwey transition to determine how the transition temperature changes with the quasihydrostatic pressure. Increase of the pressure results in the linear decrease of the Verwey transition temperature, with no discontinuity. The corresponding pressure coefficient dTV/dP is found to be ~ -5.2 K/GPa. Such a decrease is substantially larger than the one predicted by the mean-field Coulomb interaction model of the transition

Charge and orbital order in Fe_3O_4

Charge and orbital ordering in the low-temperature monoclinic structure of magnetite (Fe_3O_4) is investigated using LSDA+U. While the difference between t_{2g} minority occupancies of Fe^{2+}_B and Fe^{3+}_B cations is large and gives direct evidence for charge ordering, the screening is so effective that the total 3d charge disproportion is rather small. The charge order has a pronounced [001] modulation, which is incompatible with the Anderson criterion. The orbital order agrees with the Kugel-Khomskii theory.Comment: 4 pages, 2 figure

US-Japan Cooperative Program on neutron scattering

The US-Japan Cooperative Program on Neutron Scattering was implemented through arrangements by the United States Department of Energy with the Science and Technology Agency (STA) and the Ministry of Science, Education, and Culture (Monbusho) of Japan. It involves research collaboration in neutron scattering by Japanese scientists with scientists at Oak Ridge National Laboratory (ORNL) and Brookhaven National Laboratory (BNL) and the construction of new neutron scattering equipment at both laboratories with funds provided by the Japanese government. The United States provides neutrons in exchange for the new equipment, and other costs of the program are equally shared by the two countries. The assignments of Japanese scientists to ORNL and BNL vary in length, but they correspond to about two person years annually at each laboratory. An equal number of US scientists also participate in the research program. The main research collaboration is centered around the new equipment provided by the Japanese, but other facilities are utilized when they are needed. The new equipment includes a new type of wide-angle diffractometer and equipment for maintaining extreme sample environments at ORNL and a sophisticated polarized-beam triple-axis spectrometer at BNL. 13 refs., 3 figs

Spin-lattice instability to a fractional magnetization state in the spinel HgCr2O4

Magnetic systems are fertile ground for the emergence of exotic states when the magnetic interactions cannot be satisfied simultaneously due to the topology of the lattice - a situation known as geometrical frustration. Spinels, AB2O4, can realize the most highly frustrated network of corner-sharing tetrahedra. Several novel states have been discovered in spinels, such as composite spin clusters and novel charge-ordered states. Here we use neutron and synchrotron X-ray scattering to characterize the fractional magnetization state of HgCr2O4 under an external magnetic field, H. When the field is applied in its Neel ground state, a phase transition occurs at H ~ 10 Tesla at which each tetrahedron changes from a canted Neel state to a fractional spin state with the total spin, Stet, of S/2 and the lattice undergoes orthorhombic to cubic symmetry change. Our results provide the microscopic one-to-one correspondence between the spin state and the lattice distortion

Landau model for uniaxial systems with complex order parameter

We study the Landau model for uniaxial incommensurate-commensurate systems of the I class by keeping Umklapp terms of third and fourth order in the expansion of the free energy. It applies to systems in which the soft mode minimum lies between the corresponding commensurate wave numbers. The minimization of the Landau functional leads to the sine-Gordon equation with two nonlinear terms, equivalent to the equation of motion for the well-known classical mechanical problem of two mixing resonances. We calculate the average free energies for periodic, quasiperiodic and chaotic solutions of this equation, and show that in the regime of finite strengths of Umklapp terms only periodic solutions are absolute minima of the free energy, so that the phase diagram contains only commensurate configurations. The phase transitions between neighboring configurations are of the first order, and the wave number of ordering goes through harmless staircase with a finite number of steps. These results are the basis for the interpretation of phase diagrams for some materials from the I class of incommensurate-commensurate systems, in particular of those for A$_2$BX$_4$ and BCCD compounds. Also, we argue that chaotic barriers which separate metastable periodic solutions represent an intrinsic mechanism for observed memory effects and thermal hystereses.Comment: 12 pages, 14 figures, LaTeX, to be published in Phys. Rev.

Complex-Orbital Order in Fe_3O_4 and Mechanism of the Verwey Transition

Electronic state and the Verwey transition in magnetite (Fe_3O_4) are studied using a spinless three-band Hubbard model for 3d electrons on the B sites with the Hartree-Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., 1/sqrt(2)[|zx> + i |yz>], ordered (COO) states having noncollinear orbital moments ~ 0.4 mu_B on the B sites are obtained with the cubic lattice structure of the high-temperature phase. The COO state is a novel form of magnetic ordering within the orbital degree of freedom. It arises from the formation of Hund's second rule states of spinless pseudo-d molecular orbitals in the Fe_4 tetrahedral units of the B sites and ferromagnetic alignment of their fictitious orbital moments. A COO state with longer periodicity is obtained with pseudo-orthorhombic Pmca and Pmc2_1 structures for the low-temperature phase. The state spontaneously lowers the crystal symmetry to the monoclinic and explains experimentally observed rhombohedral cell deformation and Jahn-Teller like distortion. From these findings, we consider that at the Verwey transition temperature, the COO state remaining to be short-range order impeded by dynamical lattice distortion in high temperature is developed into that with long-range order coupled with the monoclinic lattice distortion.Comment: 16 pages, 13 figures, 6 tables, accepted for publication in J. Phys. Soc. Jp

The Global Gridded Crop Model Intercomparison: Data and modeling protocols for Phase 1 (v1.0)

We present protocols and input data for Phase 1 of the Global Gridded Crop Model Intercomparison, a project of the Agricultural Model Intercomparison and Improvement Project (AgMIP). The project includes global simulations of yields, phenologies, and many land-surface fluxes using 12–15 modeling groups for many crops, climate forcing data sets, and scenarios over the historical period from 1948 to 2012. The primary outcomes of the project include (1) a detailed comparison of the major differences and similarities among global models commonly used for large-scale climate impact assessment, (2) an evaluation of model and ensemble hindcasting skill, (3) quantification of key uncertainties from climate input data, model choice, and other sources, and (4) a multi-model analysis of the agricultural impacts of large-scale climate extremes from the historical record

Landau Model for Commensurate-Commensurate Phase Transitions in Uniaxial Improper Ferroelectric Crystals

We propose the Landau model for lock-in phase transitions in uniaxially modulated improper ferroelectric incommensurate-commensurate systems of class I. It includes Umklapp terms of third and fourth order and secondary order parameter representing the local polarization. The corresponding phase diagram has the structure of harmless staircase, with the allowed wave numbers obeying the Farey tree algorithm. Among the stable commensurate phases only those with periods equal to odd number of lattice constants have finite macroscopic polarizations. These results are in excellent agreement with experimental findings in some A2BX4 compounds.Comment: 9 pages, 5 figures, revtex, to be published in Journal of Physics: Cond. Matter as a Letter to the Edito

Universal mechanism of discontinuity of commensurate-incommensurate transitions in three-dimensional solids: Strain dependence of soliton self-energy

We show that there exists a universal mechanism of long-range soliton attraction in three-dimensional solids and, therefore, of discontinuity of any commensurate-incommensurate (C-IC) phase transition. This mechanism is due to the strain dependence of the soliton self-energy and specific features of the solid-state elasticity. The role of this mechanism is studied in detail for a class of C-IC transitions where the IC modulation is one-dimensional, the anisotropy in the order parameter space is small, and the symmetry of the systems allows the existence of the Lifshitz invariant. Two other mechanisms of soliton attraction are operative here but the universal mechanism considered in this paper is found to be the most important one in some cases. Comparison with the most extensively studied C-IC transition in $\rm K_2SeO_4$ shows that the experimentally observed thermal anomalies can be understood as a result of the smearing of the theoretically predicted discontinuous transition.Comment: 8 pages (extended version, title changed