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

Discrete charge patterns, Coulomb correlations and interactions in protein solutions

The effective Coulomb interaction between globular proteins is calculated as a function of monovalent salt concentration $c_s$, by explicit Molecular Dynamics simulations of pairs of model proteins in the presence of microscopic co and counterions. For discrete charge patterns of monovalent sites on the surface, the resulting osmotic virial coefficient $B_2$ is found to be a strikingly non-monotonic function of $c_s$. The non-monotonicity follows from a subtle Coulomb correlation effect which is completely missed by conventional non-linear Poisson-Boltzmann theory and explains various experimental findings.Comment: 4 twocolumn pages with 4 figure

Phase Separation in Charge-Stabilized Colloidal Suspensions: Influence of Nonlinear Screening

The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, \PR E {\bf 70}, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, \PR E {\bf 59}, 2010 (1999); P. B. Warren, \JCP {\bf 112}, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of deionized suspensions.Comment: 14 pages of text + 9 figure

High-energy photoemission on Fe3O4: Small polaron physics and the Verwey transition

We have studied the electronic structure and charge ordering (Verwey) transition of magnetite (Fe3O4) by soft x-ray photoemission. Due to the enhanced probing depth and the use of different surface preparations we are able to distinguish surface and volume effects in the spectra. The pseudogap behavior of the intrinsic spectra and its temperature dependence give evidence for the existence of strongly bound small polarons consistent with both dc and optical conductivity. Together with other recent structural and theoretical results our findings support a picture in which the Verwey transition contains elements of a cooperative Jahn-Teller effect, stabilized by local Coulomb interaction

Nonlinear Screening and Effective Electrostatic Interactions in Charge-Stabilized Colloidal Suspensions

A nonlinear response theory is developed and applied to electrostatic interactions between spherical macroions, screened by surrounding microions, in charge-stabilized colloidal suspensions. The theory describes leading-order nonlinear response of the microions (counterions, salt ions) to the electrostatic potential of the macroions and predicts microion-induced effective many-body interactions between macroions. A linear response approximation [Phys. Rev. E 62, 3855 (2000)] yields an effective pair potential of screened-Coulomb (Yukawa) form, as well as a one-body volume energy, which contributes to the free energy. Nonlinear response generates effective many-body interactions and essential corrections to both the effective pair potential and the volume energy. By adopting a random-phase approximation (RPA) for the response functions, and thus neglecting microion correlations, practical expressions are derived for the effective pair and triplet potentials and for the volume energy. Nonlinear screening is found to weaken repulsive pair interactions, induce attractive triplet interactions, and modify the volume energy. Numerical results for monovalent microions are in good agreement with available ab initio simulation data and demonstrate that nonlinear effects grow with increasing macroion charge and concentration and with decreasing salt concentration. In the dilute limit of zero macroion concentration, leading-order nonlinear corrections vanish. Finally, it is shown that nonlinear response theory, when combined with the RPA, is formally equivalent to the mean-field Poisson-Boltzmann theory and that the linear response approximation corresponds, within integral-equation theory, to a linearized hypernetted-chain closure.Comment: 30 pages, 8 figures, Phys. Rev. E (in press

Weak Long-Ranged Casimir Attraction in Colloidal Crystals

We investigate the influence of geometric confinement on the free energy of an idealized model for charge-stabilized colloidal suspensions. The mean-field Poisson-Boltzmann formulation for this system predicts pure repulsion among macroionic colloidal spheres. Fluctuations in the simple ions' distribution provide a mechanism for the macroions to attract each other at large separations. Although this Casimir interaction is long-ranged, it is too weak to influence colloidal crystals' dynamics.Comment: 5 pages 2 figures ReVTe

Direct observation of t2g orbital ordering in magnetite

Using soft-x-ray diffraction at the site-specific resonances in the Fe L23 edge, we find clear evidence for orbital and charge ordering in magnetite below the Verwey transition. The spectra show directly that the (001/2) diffraction peak (in cubic notation) is caused by t2g orbital ordering at octahedral Fe2+ sites and the (001) by a spatial modulation of the t2g occupation.Comment: to appear in Phys. Rev. Let

Effective Interactions and Volume Energies in Charge-Stabilized Colloidal Suspensions

Charge-stabilized colloidal suspensions can be conveniently described by formally reducing the macroion-microion mixture to an equivalent one-component system of pseudo-particles. Within this scheme, the utility of a linear response approximation for deriving effective interparticle interactions has been demonstrated [M. J. Grimson and M. Silbert, Mol. Phys. 74, 397 (1991)]. Here the response approach is extended to suspensions of finite-sized macroions and used to derive explicit expressions for (1) an effective electrostatic pair interaction between pseudo-macroions and (2) an associated volume energy that contributes to the total free energy. The derivation recovers precisely the form of the DLVO screened-Coulomb effective pair interaction for spherical macroions and makes manifest the important influence of the volume energy on thermodynamic properties of deionized suspensions. Excluded volume corrections are implicitly incorporated through a natural modification of the inverse screening length. By including nonlinear response of counterions to macroions, the theory may be generalized to systematically investigate effective many-body interactions.Comment: 13 pages (J. Phys.: Condensed Matter, in press

Screening of Spherical Colloids beyond Mean Field -- A Local Density Functional Approach

We study the counterion distribution around a spherical macroion and its osmotic pressure in the framework of the recently developed Debye-H"uckel-Hole-Cavity (DHHC) theory. This is a local density functional approach which incorporates correlations into Poisson-Boltzmann theory by adding a free energy correction based on the One Component Plasma. We compare the predictions for ion distribution and osmotic pressure obtained by the full theory and by its zero temperature limit with Monte Carlo simulations. They agree excellently for weakly developed correlations and give the correct trend for stronger ones. In all investigated cases the DHHC theory and its computationally simpler zero temperature limit yield better results than the Poisson-Boltzmann theory.Comment: 10 pages, 4 figures, 2 tables, RevTeX4-styl

Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation

The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson--Boltzmann equation, which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concentration saturates to its maximum value. Our results are in agreement with recent experiments.Comment: 4 pages, 2 figure