Combined effect of frustration and dimerization in ferrimagnetic chains and square lattice

Within the zero-temperature linear spin-wave theory we have investigated the effect of frustration and dimerization of a Heisenberg system with alternating spins $s_{1}$ and $s_{2}$ on one- and two-dimensional lattices. The combined effect most visibly appears in the elementary excitation spectra. In contrast to the ground state energy that decreases with dimerization and increases with frustration, the excitation energies are shown to be suppressed in energy by both dimerization and frustration. The threshold value of frustration that signals a transition from a classical ferrimagnetic state to a spiral state, decreases with dimerization, showing that dimerization further helps in the phase transition. The correlation length and sublattice magnetization decrease with both dimerization and frustration indicating the destruction of the long-range classical ferrimagnetic. The linear spin wave theory shows that in the case of a square lattice, dimerization initially opposes the frustration-led transition to a spiral magnetic state, but then higher magnitudes of lattice deformation facilitate the transition. It also shows that the transition to spiral state is inhibited in a square lattice beyond a certain value of dimerization.Comment: 8 pages, latex, 12 postscript figure

Chain-Selective and Regioselective Ethylene and Styrene Dimerization Reactions Catalyzed by a Well-Defined Cationic Ruthenium-Hydride Complex: New Insights on the Styrene Dimerization Mechanism

The cationic ruthenium hydride complex [(η6-C6H6)(PCy3)(CO)RuH]+BF4− was found to be a highly regioselective catalyst for the ethylene dimerization reaction to give 2-butene products (TOF = 1910 h−1, \u3e95% selectivity for 2-butenes). The dimerization of styrene exclusively produced the head-to-tail dimer (E)-PhCH(CH3)CH═CHPh at an initial turnover rate of 2300 h−1. A rapid and extensive H/D exchange between the vinyl hydrogens of styrene-d8 and 4-methoxystyrene was observed within 10 min without forming the dimer products at room temperature. The inverse deuterium isotope effect of kH/kD = 0.77 ± 0.10 was measured from the first-order plots on the dimerization reaction of styrene and styrene-d8 in chlorobenzene at 70 °C. The pronounced carbon isotope effect on both vinyl carbons of styrene as measured by using Singleton’s method (13C(recovered)/13C(virgin) at C1 = 1.096 and C2 = 1.042) indicates that the C−C bond formation is the rate-limiting step for the dimerization reaction. The Eyring plot of the dimerization of styrene in the temperature range of 50−90 °C led to ΔH⧧ = 3.3(6) kcal/mol and ΔS⧧ = −35.5(7) eu. An electrophilic addition mechanism has been proposed for the dimerization of styrene

Numerical estimation of entropy loss on dimerization: improved prediction of the quaternary structure of the GCN4 leucine zipper

A lattice based model of a protein is used to study the dimerization equilibrium of the GCN4 leucine zipper. Replica exchange Monte Carlo is used to determine the free energy of both the monomeric and dimeric forms as a function of temperature. The method of coincidences is then introduced to explicitly calculate the entropy loss associated with dimerization, and from it the free energy difference between monomer and dimer, as well as the corresponding equilibrium reaction constant. We find that the entropy loss of dimerization is a strong function of energy (or temperature), and that it is much larger than previously estimated, especially for high energy states. The results confirm that it is possible to study the dimerization equilibrium of GCN4 at physiological concentrations within the reduced representation of the protein employed

Quantum Criticality in Dimerized Spin Ladders

We analyze a possibility of quantum criticality (gaplessness) in dimerized antiferromagnetic two- and three-leg spin-1/2 ladders. Contrary to earlier studies of these models, we examine different dimerization patterns in the ladder. We find that ladders with the columnar dimerization order have lower zero-temperature energies and they are always gapped. For the staggered dimerization order, we find the quantum critical lines, in agreement with earlier analyses. The bond mean-field theory we apply, demonstrates its quantitative accuracy and agrees with available numerical results. We conclude that unless some mechanism for locking dimerization into the energetically less favorable staggered configuration is provided, the dimerized ladders do not order into the phase where the quantum criticality occurs.Comment: 7 pages, 9 figure

Charge gap in the one--dimensional dimerized Hubbard model at quarter-filling

We propose a quantitative estimate of the charge gap that opens in the one-dimensional dimerized Hubbard model at quarter-filling due to dimerization, which makes the system effectively half--filled, and to repulsion, which induces umklapp scattering processes. Our estimate is expected to be valid for any value of the repulsion and of the parameter describing the dimerization. It is based on analytical results obtained in various limits (weak coupling, strong coupling, large dimerization) and on numerical results obtained by exact diagonalization of small clusters. We consider two models of dimerization: alternating hopping integrals and alternating on--site energies. The former should be appropriate for the Bechgaard salts, the latter for compounds where the stacks are made of alternating $TMTSF$ and $TMTTF$ molecules. % $(TMTSF)_2 X$ and $(TMTTF)_2 X$ ($X$ denotes $ClO_4$, $PF_6$, $Br$...).Comment: 33 pages, RevTeX 3.0, figures on reques

Phase-field-crystal modeling of the (2x1)-(1x1) phase-transitions of Si(001) and Ge(001) surfaces

We propose a two-dimensional phase-field-crystal model for the (2$\times$1)-(1$\times$1) phase transitions of Si(001) and Ge(001) surfaces. The dimerization in the 2$\times$1 phase is described with a phase-field-crystal variable which is determined by solving an evolution equation derived from the free energy. Simulated periodic arrays of dimerization variable is consistent with scanning-tunnelling-microscopy images of the two dimerized surfaces. Calculated temperature dependence of the dimerization parameter indicates that normal dimers and broken ones coexist between the temperatures describing the charactristic temperature width of the phase-transition, $T_L$ and $T_H$, and a first-order phase transition takes place at a temperature between them. The dimerization over the whole temperature is determined. These results are in agreement with experiment. This phase-field-crystal approach is applicable to phase-transitions of other reconstructed surface phases, especially semiconductor $n\times$1 reconstructed surface phases.Comment: 10 pages with 4 figures include

Dimerization-induced enhancement of the spin gap in the quarter-filled two-leg rectangular ladder

We report density-matrix renormalization group calculations of spin gaps in the quarter-filled correlated two-leg rectangular ladder with bond-dimerization along the legs of the ladder. In the small rung-coupling region, dimerization along the leg bonds can lead to large enhancement of the spin gap. Electron-electron interactions further enhance the spin gap, which is nonzero for all values of the rung electron hopping and for arbitrarily small bond-dimerization. Very large spin gaps, as are found experimentally in quarter-filled band organic charge-transfer solids with coupled pairs of quasi-one-dimensional stacks, however, occur within the model only for large dimerization and rung electron hopping that are nearly equal to the hopping along the legs. Coexistence of charge order and spin gap is also possible within the model for not too large intersite Coulomb interaction

Entropy Driven Dimerization in a One-Dimensional Spin-Orbital Model

We study a new version of the one-dimensional spin-orbital model with spins S=1 relevant to cubic vanadates. At small Hund's coupling J_H we discover dimerization in a pure electronic system solely due to a dynamical spin-orbital coupling. Above a critical value J_H, a uniform ferromagnetic state is stabilized at zero temperature. More surprisingly, we observe a temperature driven dimerization of the ferrochain, which occurs due to a large entropy released by dimer states. This dynamical dimerization seems to be the mechanism driving the peculiar intermediate phase of YVO_3.Comment: 5 pages, 4 figure