A numerical study of the formation of magnetisation plateaus in quasi one-dimensional spin-1/2 Heisenberg models

We study the magnetisation process of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model with modulated couplings over j=1,2,3sites. It turns out that the evolution of magnetisation plateaus depends on j and on the wave number q of the modulation according to the rule of Oshikawa et al. A mapping of two- and three-leg zig-zag ladders on one-dimensional systems with modulated couplings yields predictions for the occurrence of magnetization plateaus. The latter are tested by numerical computations with the DMRG algorithm. Received 14 October 1999 and Received in final form 6 January 2000     

Magnetization plateaus of SrCu(2)(BO(3))(2) from a Chern-Simons theory

The antiferromagnetic Heisenberg model on the frustrated Shastry-Sutherland lattice is studied by a mapping onto spinless fermions carrying one quantum of statistical flux. Using a mean-field approximation these fermions populate the bands of a generalized Hofstadter problem. Their filling leads to the magnetization curve. For SrCu(2)(BO(3))(2) we reproduce plateaus at 1/3 and 1/4 of the saturation moment and predict a new one at 1/2. Gaussian fluctuations of the gauge field are shown to be massive at these plateau values.     

Ground-state properties and quantum entanglement in rung-dimerized spin-1/2 antiferromagnetic ladder

The ground-state properties and quantum entanglement of the two-leg rung-dimerized spin-1/2 Heisenberg antiferromagnetic ladders are investigated based on the Green? function combined with the Bond mean-field theory. Numerical results show that the ground-state energies do not change with the rung dimerization, and the ground-state gaps are almost proportionate to the rung dimerization coefficient δ and coupling strength α  . Magnetization curves and entanglement measurements demonstrate that there are five magnetic phases, which are identified in the h–δ$h\text{–}\delta$ phase diagram. Entanglement measurements in different phases exhibit distinct behaviors, implying the fundamental differences of the five magnetic phases.     

Zero-modes and thermodynamics of disordered spin-1/2 ladders

The influence of non-magnetic doping on the thermodynamic properties of two-leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero-modes) in the framework of a generalized Dirac model. The low-temperature thermodynamic properties are dominated by these zero-modes. We use the single-fermion density of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder. In particular, we find that the magnetic susceptibility χ diverges at T → 0 as 1/T ln²(1/T), and the specific heat behaves as C 1/ln³(1/T). The predictions on magnetic susceptibility are consistent with the most recent results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic susceptibility induced in the system by such defects.     

Magnetic properties of the compounds ThCO2Ge2 and ThCo2Si2

Rather old preparation of the compounds ThCo₂Ge₂ and ThCo₂Si₂ and their magnetic study in the temperature range 100–570 K, published by Omejec and Ban [Z. Anorg. Allg. Chem. 380 (1971) 111], indicated that both compounds ordered ferrromagnetically below 100 K. In order to verify the old data, polycrystalline samples of ThCo₂Ge₂ and ThCo₂Si₂ have been prepared by arc melting and subsequent annealing, and studied by X-ray diffraction at room temperature (RT), by superconducting quantum interference device (SQUID)-magnetization and AC-susceptibility measurements at 2–320 K, and by dc-magnetization measurements in variable magnetic fields up to 120 kOe at 5, 80, and 283 K. The magnetic measurements confirm the ferromagnetic ordering in both compounds, but with totally different Curie temperatures: ≈120(20) K for ThCo₂Ge₂ and above 320 K for ThCo₂Si₂. The paramagnetic values of ThCo₂Ge₂ and the ordering of both compounds are discussed and compared with the old results of Omejec and Ban.     

Antiferromagnetic model and magnetization plateaus on the zigzag ladder with two- and three-site exchanges

The Ising approximation is proposed for the Heisenberg model with two- and three-spin exchange interactions on a zigzag ladder placed in a strong magnetic field. Using the transfer matrix technique the magnetization is calculated and compared with the results obtained in the dynamical recursive approach. Magnetization plateaus are found at m=0 and with the two- and three-spin exchanges. The magnetic susceptibility in small and large zigzag ladders for various exchange parameters and temperatures is also analyzed. As temperature decreases the magnetic susceptibility versus magnetic field shows the formation of spin pseudogaps and transformation from double to four peak structure. Small clusters also exhibit characteristic features of large thermodynamic systems.     

Mean-Field Studies of a Mixed Spin-3/2 and Spin-2 and a Mixed Spin-3/2 and Spin-5/2 Ising System with Different Anisotropies

The magnetic properties of a mixed spin-3/2 and spin-2 and a mixed spin-3/2and spin-5/2 Ising ferromagnetic system with different anisotropies are studied by means of mean-field theory (MFT). The dependence of the phase diagram on single-ion anisotropy strengths is studied too. In the mixed spin-3/2 and spin-2 Ising model, besides the second-order phase transition, the first order-disorder phase transition and the tricritical line are found. In the mixed spin-3/2 and spin-5/2 Ising model, there is no first-order transition and tricritical line.     

Soft acoustic modes in the two-dimensional spin system SrCu2(BO3)(2)

SrCu2(BO3)(2) is a two-dimensional dimerized quantum spin system which is close to a quantum critical point. The sound velocity for the longitudinal and transverse acoustic modes shows strong spin-lattice effects. The shear c(66) mode exhibits a pronounced softening of 4.5% as a function of temperature and softens more than 25% in fields up to 50 T. This huge effect occurs in the vicinity of the magnetization plateaus m/m(0) = 1/4 and 1/3. We can analyze quantitatively the temperature dependence of all measured elastic modes c(11), c(44), and c(66) with an exchange striction mechanism. The soft c(66) mode with B(2g) symmetry enables us to predict the possible symmetry of the condensed triplets in some plateaus.     

Integer quantum Hall effect in Kekulé-patterned graphene

Y-shaped Kekulébond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed.In this paper,the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field.Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula.It is found that the Y-shaped Kekulébond texture lifts the valley degeneracy of all Landau levels except that of the zero mode,leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity.Consequently,the Hall conductivity is quantized as±ne²/h for n=2,4,6,8,10,...,excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones.These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulébond texture amplitude.     

Effects of NH3, O2, and N2 co-implantation on Cu out-diffusion and antimicrobial properties of copper plasma-implanted polyethylene

Metal antibacterial reagents are effective in the enhancement of the antimicrobial properties of medical polymers. However, incorporation of metal antibacterial reagents into polymers using conventional methods usually results in unstable antimicrobial effects. Our previous research demonstrates that plasma immersion ion implantation (PIII) can be used to effectively incorporate metal antibacterial reagents such as Cu into polyethylene (PE) in the near surface region up to several hundred nanometers without causing noticeable damage to the polymer matrix. In this work, various gases including NH₃, O₂, and N₂ were plasma-implanted in concert with Cu plasma immersion ion implantation to study the effects of these gas species on the release rate of Cu from the substrate. Our experimental results reveal that the copper depth profiles are not affected significantly by NH₃, O₂, or N₂ co-implantation and these gas elements have similar depth profiles as Cu. Chemical analyses demonstrate that polar functional CO, CO, CN, CN, and CN bonds formed in the substrate play an important role in regulating Cu out-diffusion. Among the three gas species, N₂ shows the best effects in regulating Cu out-diffusion and produces the best long term antibacterial properties. The Cu retention and out-diffusion mechanism in the ion-implanted polyethylene is described.     

Ab initio studies of electronic spectra of the linear aluminum-bearing carbon chains AlC2nH (n = 1-5)

Geometries and stabilities of the linear aluminum-bearing carbon chains AlC_2nH (n = 1-5) in their ground states have been explored by the DFT-B3LYP and RCCSD(T) methods. Structures of the X¹Σ⁺ and 1¹Π electronic states have also been optimized by the CASSCF approach. The studies indicate that these species have single-triple bond alternate pattern, AlCCCC?CCH, and the electronic excitation from X¹Σ⁺ to 1¹Π leads to the shortening of the AlC bonds. The vertical excitation energies of the 1¹Π ← X¹Σ⁺ and 2¹Π ← X¹Σ⁺ transitions for AlC_2nH (n = 1-5) have been investigated by the CASPT2, EOM-CCSD, and TD-B3LYP levels of theory with the cc-pVTZ basis set, respectively. CASPT2-predicted 1¹Π ← X¹Σ⁺ transition energies are 3.57, 3.44, 3.33, 3.26, and 3.21 eV, respectively. For AlC₂H, our estimate agrees very well with the experimental value of 3.57 eV. In addition, the AlC bond dissociation energies and the exponential-decay curves for these vertical excitation energies are also discussed.     

Surface morphology and composition of c-, a- and m-sapphire surfaces in O2 and H2 environments

This paper reports that monitoring the composition of the c(0 0 0 1), a(11–20) and m(10–10) sapphire surfaces is essential for a proper interpretation of the surface morphologies obtained after annealing at 1253 and 1473 K in ArH₂ or ArO₂ atmospheres. Our experimental investigations, which have used Auger electron spectroscopy (AES) and atomic force microscopy (AFM) on the surfaces of 99.99% pure sapphire wafers, have led to the following original conclusions: (i) Calcium segregates at the c-surface of sapphire both under ArO₂ and ArH₂. (ii) Potassium adsorption enhances the kinetics of step-bunching on the c-surface under ArO₂. (iii) The step edges on the a-surface may develop a comb-like morphology made of parallel strips along the [10–10] direction. (iv) At 1253 K, clean m-surfaces may be stable. (v) Under ArH₂, alumina surface diffusion is much slower than under ArO₂ for all surface orientations, the surface concentration of impurities is low, and the Al–O ratio of the AES signals at the surface is significantly larger.     

Numerical Study of Luttinger Liquid Regime of Two-Leg Hubbard Ladders

We investigate two-leg Hubbard ladders in the Luttinger liquid regime by the density-matrix renormalization group method. Applicability of the bond concept in this region is discussed in a quantitative comparison of power-law decay exponents, energy components and anti-bond occupations between ladders and chains. The interaction between bond and anti-bond bands induced by finite Hubbard repulsion U is emphasized by our numerical results. Our quantitative results are useful for the justification of the validity of various analytical approaches.     

Upper bound to the charge-transfer energy on a 2D Wigner lattice in high-Tc cuprates

Assuming that the energy of a 2D Wigner lattice, which has been frequently observed on the CuO₂ plane in layered high-T_c cuprates, is composed of Coulomb energy, kinetic energy, and charge-transfer energy which is necessary to transfer electrons or holes onto the CuO₂ plane (the magnitude of the energy is expected to be of the order of the work function of the compound constituting the plane from which the electrons are transferred, if the CuO₂ plane easily accepts the electrons or holes, as if the CuO₂ plane were crystal surface), we find in the mean-field approximation, that the total energy for a unit lattice, E₀, can be given by a function of the charge-transfer energy E_φ as E₀= (E_φ−E_φ⁰+O((E_φ−E_φ⁰)₂)(>0), where the value of E_φ⁰(1.5 in the ground state, for example) is independent of the lattice configuration. This relation implies that the upper bound to the charge-transfer energy is given by E_φ⁰. The smallness of E_φ⁰, compared with the work function of ordinary metals and alloys (with the work function around 4 eV), is necessary for the realization of the 2D Wigner lattice in many layered high-T_c cuprates.     

Nucleon–nucleon scattering observables in large-Nc QCD

Nucleon–nucleon scattering observables are considered in the context of the large N_c limit of QCD for initial states with moderately high momenta (pN_c). The scattering is studied in the framework of the time-dependent mean-field approximation. We focus on the dependence of those observables on the spin and isospin of the initial state which may be computed using time-dependent mean-field theory. We show that, up to corrections, all such observables must be invariant under simultaneous spin and isospin flips (i.e., rotations through π/2 in both spin and isospin) acting on either particle. All observables of this class obtained from spin unpolarized measurements must be isospin independent up to 1/N_c corrections. Moreover, it can be shown that the leading correction is of relative order 1/N_c² rather than 1/N_c.     

Structural and magnetic properties of single perovskite Ca(Ti1/2Mn1/2)O3

The synthesis, structural and magnetic properties of a new type high permittivity material Ca(Ti_1/2Mn_1/2)O₃ was reported. The sample was prepared by conventional solid-state reaction route. Rietveld analysis revealed it was single perovskite with space group Pnma. Normalized bond length and bond valence were calculated to investigate the compression/dilation effects of bonds and atoms in unit cell. There were five types of Ca-O bonds and three kinds of (Ti, Mn)-O bonds in Ca(Ti_1/2Mn_1/2)O₃. The susceptibility curve at high temperature followed the Curie-Weiss law with Curie and Weiss constant as 0.8991 emu K/mol and −276.3 K, respectively. The calculated effective moment per Mn is 2.68 μ_B-Bohr magneton. Antiferromagnetism and spin glass state at low temperature were found in Ca(Ti_1/2Mn_1/2)O₃. Frustration parameter was estimated to be about 30, suggesting the cluster-spin-glass resulted from geometrical frustration.     

Crystal-Field Effect of spin-3/2 Transverse Ising Model

The crystal-field effect of spin-3/2 transverse Ising model is studied with the scheme of mean-field approximation. The influences of the crystal field and the transverse field on the phase diagram of the system are discussed.