Statistics on Graphs, Exponential Formula and Combinatorial Physics

The concern of this paper is a famous combinatorial formula known under the name "exponential formula". It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential generating function of a whole structure is equal to the exponential of those of connected substructures. Keeping this descriptive statement as a guideline, we develop a general framework to handle many different situations in which the exponential formula can be applied

t-J model of coupled Cu2_2O5_5 ladders in Sr14−x_{14-x}Cax_xCu24_{24}O41_{41}

Starting from the proper charge transfer model for Cu$_2$O$_5$ coupled ladders in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ we derive the low energy Hamiltonian for this system. It occurs that the widely used ladder t-J model is not sufficient and has to be supplemented by the Coulomb repulsion term between holes in the neighboring ladders. Furthermore, we show how a simple mean-field solution of the derived t-J model may explain the onset of the charge density wave with the odd period in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$.Comment: 8 pages, 4 figures, 2 table

Exchange parameters from approximate self-interaction correction scheme

The approximate atomic self-interaction corrections (ASIC) method to density functional theory is put to the test by calculating the exchange interaction for a number of prototypical materials, critical to local exchange and correlation functionals. ASIC total energy calculations are mapped onto an Heisenberg pair-wise interaction and the exchange constants J are compared to those obtained with other methods. In general the ASIC scheme drastically improves the bandstructure, which for almost all the cases investigated resemble closely available photo-emission data. In contrast the results for the exchange parameters are less satisfactory. Although ASIC performs reasonably well for systems where the magnetism originates from half-filled bands, it suffers from similar problems than those of LDA for other situations. In particular the exchange constants are still overestimated. This reflects a subtle interplay between exchange and correlation energy, not captured by the ASIC.Comment: 10 page

Reversible strain effect on the magnetization of LaCoO3 films

The magnetization of ferromagnetic LaCoO3 films grown epitaxially on piezoelectric substrates has been found to systematically decrease with the reduction of tensile strain. The magnetization change induced by the reversible strain variation reveals an increase of the Co magnetic moment with tensile strain. The biaxial strain dependence of the Curie temperature is estimated to be below 4K/% in the as-grown tensile strain state of our films. This is in agreement with results from statically strained films on various substrates

Research for preparation of cation-conducting solids by high-pressure synthesis and other methods

It was shown that two body-centered-cubic skeleton structures, the Im3 KSbO3 phase and the defect-pyrochlore phase A(+)B2X6, do exhibit fast Na(+)-ion transport. The placement of anions at the tunnel intersection sites does not impede Na(+)-ion transport in (NaSb)3)(1/6 NaF), and may not in (Na(1+2x)Ta2 5F)(Ox). The activation energies are higher than those found in beta-alumina. There are two possible explanations for the higher activation energy: breathing of the bottleneck (site face or edge) through which the A(+) ions must pass on jumping from one site to another may be easier in a layer structure and/or A(+)-O bonding may be stronger in the cubic structures because the O(2-) ion bonds with two (instead of three) cations of the skeleton. If the former explanation is dominant, a lower activation energy may be achieved by optimizing the lattice parameter. If the latter is dominant, a new structural principle may have to be explored

Structural, orbital, and magnetic order in vanadium spinels

Vanadium spinels (ZnV_2O_4, MgV_2O_4, and CdV_2O_4) exhibit a sequence of structural and magnetic phase transitions, reflecting the interplay of lattice, orbital, and spin degrees of freedom. We offer a theoretical model taking into account the relativistic spin-orbit interaction, collective Jahn-Teller effect, and spin frustration. Below the structural transition, vanadium ions exhibit ferroorbital order and the magnet is best viewed as two sets of antiferromagnetic chains with a single-ion Ising anisotropy. Magnetic order, parametrized by two Ising variables, appears at a tetracritical point.Comment: v3: streamlined introductio

Electronic structure and magnetic properties of pyroxenes (Li,Na)TM(Si,Ge)2O6: novel low-dimensional magnets with 90 bonds

The results of the LSDA+U calculations for pyroxenes with diverse magnetic properties (Li,Na)TM(Si,Ge)$_2$O$_6$, where TM is the transition metal ion (Ti,V,Cr,Mn,Fe), are presented. We show that the anisotropic orbital ordering results in the spin-gap formation in NaTiSi$_2$O$_6$. The detailed analysis of different contributions to the intrachain exchange interactions for pyroxenes is performed both analytically using perturbation theory and basing on the results of the band structure calculations. The antiferromagnetic $t_{2g}-t_{2g}$ exchange is found to decrease gradually in going from Ti to Fe. It turns out to be nearly compensated by ferromagnetic interaction between half-filled $t_{2g}$ and empty $e_g$ orbitals in Cr-based pyroxenes. The fine-tuning of the interaction parameters by the crystal structure results in the ferromagnetism for NaCrGe$_2$O$_6$. Further increase of the total number of electrons and occupation of $e_g$ sub-shell makes the $t_{2g}-e_g$ contribution and total exchange interaction antiferromagnetic for Mn- and Fe-based pyroxenes. Strong oxygen polarization was found in Fe-based pyroxenes. It is shown that this effect leads to a considerable reduction of antiferromagnetic intrachain exchange. The obtained results may serve as a basis for the analysis of diverse magnetic properties of pyroxenes, including those with recently discovered multiferroic behavior.Comment: 11 pages, 10 figure

Cooperative Jahn-Teller Effect and Electron-Phonon Coupling in La1−xAxMnO3La_{1-x}A_xMnO_3

A classical model for the lattice distortions of \lax is derived and, in a mean field approximation, solved. The model is based on previous work by Kanamori and involves localized Mn d-electrons (which induce tetragonal distortions of the oxygen octahedra surrounding the Mn) and localized holes (which induce breathing distortions). Parameters are determined by fitting to the room temperature structure of $LaMnO_3$. The energy gained by formation of a local lattice distortion is found to be large, most likely $\approx 0.6$ eV per site, implying a strong electorn-phonon coupling and supporting polaronic models of transport in the doped materials. The structural transition is shown to be of the order-disorder type; the rapid x-dependence of the transition temperature is argued to occur because added holes produce a "random" field which misaligns the nearby sites.Comment: 24 pages. No figures. One Table. Late

Phase Competition in Ln0.5a0.5mno3 Perovskites

Single crystals of the systems Pr0.5(Ca1-xSrx)0.5MnO3, (Pr1-yYy)0.5(Ca1-xSrx)0.5MnO3, and Sm0.5Sr0.5MnO3 were grown to provide a series of samples with fixed ratio Mn(III)/Mn(IV)=1 having geometric tolerance factors that span the transition from localized to itinerant electronic behavior of the MnO3 array. A unique ferromagnetic phase appears at the critical tolerance factor tc= 0.975 that separates charge ordering and localized-electron behavior for t<tc from itinerant or molecular-orbital behavior for t>tc. This ferromagnetic phase, which has to be distinguished from the ferromagnetic metallic phase stabilized at tolerance factors t>tc, separates two distinguishable Type-CE antiferromagnetic phases that are metamagnetic. Measurements of the transport properties under hydrostatic pressure were carried out on a compositions t a little below tc in order to compare the effects of chemical vs. hydrostatic pressure on the phases that compete with one another near t=tc.Comment: 10 pages. To be publised in Phys. Rev.

The Metal-Insulator Transition of NbO2: an Embedded Peierls Instability

Results of first principles augmented spherical wave electronic structure calculations for niobium dioxide are presented. Both metallic rutile and insulating low-temperature NbO2, which crystallizes in a distorted rutile structure, are correctly described within density functional theory and the local density approximation. Metallic conductivity is carried to equal amounts by metal t_{2g} orbitals, which fall into the one-dimensional d_parallel band and the isotropically dispersing e_{g}^{pi} bands. Hybridization of both types of bands is almost negligible outside narrow rods along the line X--R. In the low-temperature phase splitting of the d_parallel band due to metal-metal dimerization as well as upshift of the e_{g}^{pi} bands due to increased p-d overlap remove the Fermi surface and open an optical band gap of about 0.1 eV. The metal-insulator transition arises as a Peierls instability of the d_parallel band in an embedding background of e_{g}^{pi} electrons. This basic mechanism should also apply to VO2, where, however, electronic correlations are expected to play a greater role due to stronger localization of the 3d electrons.Comment: 4 pages, revtex, 6 eps figures, additional material avalable at http://www.physik.uni-augsburg.de/~eyert