Interplay between symmetry breaking and quasiperiodicity in spin chains

Summary An isotropicXY spin chain is studied in the presence of symmetry-breaking perturbations and a periodic modulation with wave vector incommensurate with the periodicity of the chain. The ground states of the system are obtained in terms of a two-dimensional area-preserving map defined on a cylinder of finite extent. The spin distributions are found to exhibit KAM and Cantorus phases with the onset of transition being the critical phase. The relationship between these three phases and the magnetic properties of the model is also studied. The presence of two competing easy axes for spin alignment results in incommensurate reentrant phase diagram with fractal boundary.     

Evolution of the commensurate and incommensurate magnetic phases of the S = 3/2 kagome staircase Co?V?O? in an applied field

Single crystal neutron diffraction studies have been performed on the S = 3/2 kagome staircase compound Co(3)V(2)O(8) with a magnetic field applied along the magnetization easy-axis ([Formula: see text]). Previous zero-field measurements (Chen Y et al 2006 Phys. Rev. B 74 014430) reported a rich variety of magnetic phases, with a ferromagnetic ground state as well as incommensurate, transversely polarized spin density wave (SDW) phases (with a propagation vector of [Formula: see text]) interspersed with multiple commensurate lock-in transitions. The magnetic phase diagram with [Formula: see text] adds further complexity. For small applied fields, μ(0)H ≈ 0.05 T, the commensurate lock-in phases are destabilized in favor of the incommensurate SDW ones, while slightly larger applied fields restore the commensurate lock-in phase with δ = 1/2 and yield a new commensurate phase with δ = 2/5. For measurements in an applied field, higher-order scattering is observed that corresponds to the second harmonic.     

Incommensurate structure in the lattice-gas ANNNI model

The phase diagram of the two-dimensional lattice-gas ANNNI model is investigated using the cluster transfer-matrix method. The numerical calculations have shown commensurate, disordered, and floating incommensurate phases. The properties of the incommensurate phase are studied in detail and the position of the Lifshitz point is discussed.     

Competition in low ordered smectics between incommensurate phases and two-dimensional modulated ones for dimesogenic compounds

Systematic physical chemistry studies are in progress concerning the occurrence of incommensurate low ordered smectic phases in non-symmetric dimesogens varying molecular parameters from the standard compound KI-5. In the present study, the selected molecules possess the same spacer length and the same cholesteryl unit. By means of X-ray diffraction on orientated samples, commensurate phases, incommensurate fluid smectics and two-dimensional ones are clearly evidenced depending both on temperature and molecular parameters. So these dimesogenic compounds respond to the frustration connected to the competition between two incommensurate lengths with the formation either of an incommensurate phase or of a two-dimensional modulated phase. A new topology in a phase diagram results from this competition in a binary system composed of two homologous dimesogens. Received: 26 June 1997 / Revised: 7 October 1997 / Accepted: 29 October 1997     

Incommensurate magnetic structures in rhombohedral Heisenberg antiferromagnet

The phase diagram of the ground state has been calculated for a rhombohedral antiferromagnet of the R3m symmetry with frustrated exchange in the base plane and competition of exchanges between the nearest and next-nearest planes. The diagram contains phases of collinear antiferromagnetic ordering of various types separated by five incommensurate magnetic states of the helicoidal type, differing in the ordering type and in the direction of the modulation vector. The commensurate and incommensurate phases converge at multi-critical points lying on a line corresponding to an antiferromagnet with an undistorted simple cubic lattice.     

Incommensurate phases in ferromagnetic spin-chains with weak antiferromagnetic interchain interaction

We study planar ferromagnetic spin-chain systems with weak antiferromagnetic inter-chain interaction and dipole-dipole interaction. The ground state depends sensitively on the relative strengths of antiferromagnetic exchange and dipole energies κ = J′a ² c/(g _L μ _B )². For increasing values of κ, the ground state changes from a ferromagnetic via a collinear antiferromagnetic and an incommensurate phase to a 120° structure for very large antiferromagnetic energy. Investigation of the magnetic phase diagram of the collinear phase, as realized in CsNiF₃, shows that the structure of the spin order depends sensitivly on the direction of the magnetic field in the hexagonal plane. For certain angular domains of the field incommensurate phases appear which are seperated by commensurate phases. When rotating the field, the wave vector characterizing the structure changes continously in the incommensurate phase, whereas in the commensurate phase the wave vector is locked to a fixed value describing a two-sublattice structure. This is a result of the competition between the exchange and the dipole-dipole interaction.     

Controlling the magnetic ground state in Cr1-x Vx films

We demonstrate the ability to control the magnetic phase diagram of Cr1-x Vx(110) thin films grown on a W(110) substrate. Using angle-resolved photoemission, we have mapped paramagnetic and commensurate and incommensurate antiferromagnetic phases as a function of temperature, film thickness, and composition. We show that surface-localized electron states play a key role in the observed phase behaviors and suggest from this that it might be possible to control the magnetic phase by applying an external electric field.     

Determination of incommensurate structures: Choice of atomic parameters

It is argued that in the diffraction diagram of an incommensurate modulated structure only the satellite reflections are sensitive to the relative phases of the atomic modulation functions. The consequences of this fact on the structure refinement and the choice of structural parameters are discussed. Taking into account these considerations, the structure of the incommensurate modulated phase of K₂SeO₄ is determined from new experimental data.     

Phase diagram of the fcc(1 1 0) surfaces with adsorbate-induced missing-row reconstructions

The phase diagram of the fcc(1 1 0) surfaces with missing-row reconstructions induced by adatoms, is calculated by use of the Blume–Emmery–Griffiths model. In the model, we introduce adatom–adatom interactions to determine surface structures and dipole–dipole interactions to describe the effect of zigzag adsorption. The interactions between nearest-neighbor (NN) and next-nearest-neighbor (NNN) rows are considered. The calculation of the temperature versus adatom chemical potential phase diagram is performed using mean-field approximation. It is indicated that if NN and NNN interactions are competitive, there appear either dipole or coverage modulated (incommensurate) phases at high temperatures for a wide range of the interactions.     

Symmetry and magnetic field driven transitions in the 2D triangular lattice compound RbFe(MoO4)2

The temperature versus magnetic field phase diagram of the 2D triangular lattice and multiferroic compound RbFe(MoO(4))(2) is analysed from the point of view of symmetry. The paramagnetic space group and its irreducible representations are used in order to obtain the magnetic symmetry of the possible modulated phases and characterize the restrictions imposed by this symmetry on the corresponding magnetic structures. Superspace symmetry is considered in the case of incommensurate phases. It is shown that the experimentally observed phases correspond to different isotropy subgroups originating in the same irreducible representation of the paramagnetic symmetry group. The relevant couplings between the primary transverse spin modulation and the electric polarization, the in-plane magnetization and the secondary longitudinal magnetic modulation are discussed. The mechanisms for the destabilization of the improper ferroelectric chiral phase and the origin of the different orientation of the spins with respect to the external field in the two collinear phases are analysed from a symmetry based perspective.     

Lattice disorder and impurity induced variation of electrical transport properties of the Heavy Fermion systems CeCu2Si2 and CeCu6

X-ray diffraction experiments have been performed on mono- and submonolayers of CF₃Cl physisorbed on the (001) surfaces of exfoliated graphite. Five quasi-twodimensional solid phases including the commensurate 2×2 phase, an electrically ordered phase and a disordered incommensurate phase have been observed. A phase diagram is proposed and the various phase transitions are discussed.     

Ising model with frustration,elasticity, and competing interactions

The Ising model on a compressible triangular lattice with axial next-nearestneighbor interactions is studied in the mean-field approximation. A representative phase diagram is generated, which exhibits first- and second-order phase transitions to commensurate modulated phases. The crossover point from first to second order transitions is calculated. The stability of the modulated phases is calculated analytically in a low-temperature approximation. These results are very different from the ANNNI model, which exhibits a second-order transition to a continuum of commensurate and incommensurate phases.     

Incommensurate-commensurate phase transitions in an anisotropic antiferromagnetic model on triangular lattice

An anisotropic antiferromagnetic model on a triangular lattice with competing interactions is investigated by the cluster transfer-matrix method. A phase diagram with ferrimagnetic, incommensurate, and disordered phases is found. Three order parameters are introduced. At commensurate-incommensurate and incommensurate-disorder phase transition lines two of them change in continuous and one in discontinuous way.     

Phase diagram of dipolar hard and soft spheres: manipulation of colloidal crystal structures by an external field

Phase diagrams of hard and soft spheres with a fixed dipole moment are determined by calculating the Helmholtz free energy using simulations. The pair potential is given by a dipole-dipole interaction plus a hard-core and a repulsive Yukawa potential for soft spheres. Our system models colloids in an external electric or magnetic field, with hard spheres corresponding to uncharged and soft spheres to charged colloids. The phase diagram of dipolar hard spheres shows fluid, face-centered-cubic (fcc), hexagonal-close-packed (hcp), and body-centered-tetragonal (bct) phases. The phase diagram of dipolar soft spheres exhibits, in addition to the above mentioned phases, a body-centered-orthorhombic (bco) phase, and it agrees well with the experimental phase diagram [Nature (London) 421, 513 (2003)]. Our results show that bulk hcp, bct, and bco crystals can be realized experimentally by applying an external field.     

Laws of formation of polar smectic phases under a frustrated interaction

The Landau theory of phase transitions with a two-component order parameter is used to systematically calculate the structures and phase diagrams of polar liquid crystals. Commensurate and incommensurate structures with a layer-type period form as a result of a frustration interaction. Phase diagrams are calculated when various short- and long-range interlayer interactions are sequentially introduced. As a result, the nature of formation of various structures is revealed. The calculated phase diagrams explain the formation of various phases, their temperature sequence (including so-called “unusual” sequence of phases), and the nature of forces responsible for the formation of a certain structure and the shape of a phase diagram.     

Structure and orientational ordering of nitrogen molecules physisorbed on graphite

The structure and orientational ordering of nitrogen molecules physisorbed on graphite have been studied by low-energy diffraction (LEED). A two-sublattice in-plane herringbone structure with glide lines along two perpendicular directions is inferred from LEED patterns at T < 30 K from the monolayer where the molecular centers have the commensurate $\text{(}\text{3}\text{×}\text{3}\text{)}$ 30° structure. The orientational order-disorder transition of this commensurate phase was examined by superlattice spot intensity and angular profile measurements for 20 < T < 38 K. A rapid drop in superlattice intensity is observed near 27 K. The persistence of some intensity to 38 K. is suggestive of residual short-range orientational ordering and perhaps finite size or heterogeneity effects. For increasing coverage at T = 15 K, there is first a transition to a previously unobserved uniaxial incommensurate phase and then a transition to an apparently triangular incommensurate phase. The orientational superlattice spots are clearly present in the uniaxial phase, but are much weaker in the triangular incommensurate phase. At 31 < T < 35 K, an apparently triangular incommensurate phase with no detectable orientational superlattice spots is observed. The lattice constant versus equilibrium vapor pressure curve has been determined in the latter case assuming a continuous transition. The lattice constants of the incommensurate phases are used to place limits on the extent of possible phase-coexistence regions between the commensurate, uniaxial incommensurate, and triangular incommensurate phases. The LEED patterns from the bilayer at T = 15 K indicate a double-period superlattice structure of the triangular incommensurate phase which does not have the glide line symmetries of the commensurate monolayer. Some effects of heterogeneity on these phase transitions are discussed. A phase diagram for 10 < T < 40 K is proposed.     

The magnetic phases of NdCu2

The magnetic phase diagram of a NdCu₂ single crystal is investigated by means of specific-heat measurements and neutron diffraction as a function of temperature and external magnetic field applied along the crystallographic b-direction. In the low temperature region we observe three commensurate phases AF1, F1, and F2. Their magnetic structures all consist of ferromagnetic (bc)-planes with different stacking sequences along the a-direction comprising 5, 3 and 8 chemical unit cells, respectively. Above 2.8 T the system is in a ferromagnetically aligned state (F3). Furthermore, there is an incommensurate phase AF3 between the low temperature commensurate phases and the paramagnetic state and, in a very narrow temperature region of only 0.2 K, an intermediate phase AF2 between AF1 and AF3. The Nd-moments are oriented along the b-direction in all phases.     

Exact ground states with deconfined gapless excitations for the three-leg spin-1/2 tube

We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators-one on the triangles and the other on the square plaquettes on the side of the tube-that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i)?for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet bonds between nearest triangles; (ii)?for ferromagnetic exchange on the triangles, we recover the phase of the spin-3/2 Heisenberg chain; (iii)?between these two phases, a gapless incommensurate phase exists. We construct an exact ground state with two deconfined domain walls and a gapless excitation spectrum at the quantum phase transition point between the incommensurate and dimerized phases.     

Phase diagram of the ground state of a classical anisotropic frustrated ferromagnet

The phase diagram of the ground state is obtained for the one-dimensional easy-axis model of classical spins coupled by ferromagnetic and antiferromagnetic exchanges between nearest and next-nearest neighbors, respectively. The parameters of the incommensurate magnetic structure with a variable step (soliton lattice) are calculated in the mean field approximation from the condition of the collinearity of spins to the effective exchange fields in the continuous approximation. The ground state of the soliton lattice and interfaces between soliton and collinear (ferromagnetic and “up–up–down–down”) phases are determined by the numerical minimization of the average energy over the initial angular velocity of spins.     

Influence of Coulomb interactions on the phase diagram of quasi-one dimensional metals

The influence of only partially screened Coulomb interactions on the phase diagram and the order parameter of quasi-one dimensional metals is investigated. Using a standard microscopic model, the free energy functional is derived by means of the heat kernel method. It is assumed that the Peierls gap and the mismatch are small compared to the band width and the reciprocal lattice vectors, respectively. Furthermore we neglect interchain to intrachain hopping elements. The resulting mean field phase diagram and the properties of the order parameter are discussed. We show in particular that the Coulomb forces are responsible for:a) a first-order transition between the incommensu-rate and the commensurate phase;b) only small deviations of the order parameter from a single plane wave over the entire incommensurate phase; andc) the approximate temperature independence of the wavelength of the modulation throughout the incommensurate phase. The possible relevance of these results for quasi-one dimensional systems exhibiting nonlinear conduction is pointed out.