Helical Phases Research Articles

Floating zone growth of large single crystals of [formula omitted

The Fe4+-containing cubic perovskite phase SrFeO3−δ is of interest both for its high-temperature, oxygen-conducting properties as a solid oxide fuel cell component, and at low temperatures, where it exhibits a plethora of helical magnetic phases and a candidate Skyrmion lattice. However, a sequence of structural phase transitions encountered on cooling to room temperature has limited the size of single crystals. We report the floating-zone growth and oxygen-annealing of multiple-cubic-centimetre-sized single crystals of SrFeO3−δ, suitable for inelastic neutron scattering and other measurement techniques requiring large sample volumes.

Black holes dual to helical current phases

We consider the class of $d=4$ conformal field theories at finite temperature and chemical potential that are holographically described within $D=5$ Einstein-Maxwell theory with a Chern-Simons term. The high temperature phase, which is spatially homogeneous and isotropic, is dual to the AdS-Reissner-N\"ordstrom black brane solution. For sufficiently large Chern-Simons coupling, we construct new electrically charged AdS black hole solutions that are dual to the low temperature, spatially modulated phase. In this phase the current, associated with the Abelian global symmetry, spontaneously acquires a helical order. The new black holes are stationary and also have Bianchi ${\mathrm{VII}}_{0}$ symmetry.

The complex multiferroic phase diagram of Mn1−xCoxWO4

The complete magnetic and multiferroic phase diagram of Mn1−xCoxWO4 single crystals is investigated by means of magnetic, heat capacity and polarization experiments. We show that the ferroelectric (FE) polarization in the multiferroic state abruptly changes its direction twice upon increasing Co content, x. At xc1 = 0.075, rotates from the b-axis into the a–c-plane and at xc2 = 0.15 it flips back to the b-axis. The origin of the multiple polarization flops is identified as an effect of the Co anisotropy on the orientation and shape of the spin helix leading to thermodynamic instabilities caused by the decrease of the magnitude of the polarization in the corresponding phases. A qualitative description of the FE polarization is derived by taking into account the intrachain (c-axis) as well as the interchain (a-axis) exchange pathways connecting the magnetic ions. In a narrow Co concentration range (0.1 ⩽ x ⩽ 0.15), an intermediate phase, sandwiched between the collinear high-temperature and the helical low-temperature phases, is discovered. The new phase exhibits a collinear and commensurate spin modulation similar to the low-temperature magnetic structure of MnWO4.

Effect of intralayer inhomogeneity on helical superstructures of liquid crystals

A mechanism to form distorted helical structures in ferroelectric liquid crystals is presented. It is shown that the deformation of helical interlayer structures of thin smectic systems can be considered as a direct consequence of the surface-induced spatial inhomogeneity in the distribution of the azimuthal molecular orientation within smectic layers. The intralayer azimuthal nonuniformity occurring in helical phases is argued to generate a local depolarizing electric field of the strength varying not only in smectic layers but also between the layers. The resulting modulation of the depolarization level in the direction of helical axes is shown to lead to a distortion of helices. Using a simple model, including the depolarization interaction, it is demonstrated that the degree of the helix deformation strongly varies as parameters of the model are changed. It is also shown that strong deformations of extremely short helices, found for appropriate values of the parameters, reflect nonuniformity of helicoidal superstructures of respective smectic subphases in real liquid crystalline systems.

Cover Picture: Structure of the B4 Liquid Crystal Phase near a Glass Surface (ChemPhysChem 1/2012)

Bent-core mesogenic molecules organize into layered smectic liquid-crystal phases that have a strong inherent tendency for saddle-splay deformation of the molecular layers. One important class of such materials are the helical nanofilament phases, hierarchical self-assemblies in which growth of the liquid crystal is limited to twisted filaments that have saddle-splayed layers exhibiting Gaussian curvature but no net curvature (insets). These filaments pack to fill space in the bulk phase, but at the liquid-crystal–glass interface they exhibit a variety of exotic intermediate focal conic-related structures (background) having both Gaussian and net curvature, formed from the competition between the surface constraints and the tendency for layer twist. The work is presented by D. Chen, N. A. Clark et al. on p. 155 Ms. Heulwen Price is kindly acknowledged for putting the finishing touches to the cover image.

Low-temperature thermodynamics of the classical frustrated ferromagnetic chain in a magnetic field

Low-temperature magnetization curves of the classical frustrated ferromagnetic chain in the external magnetic field near the transition point between the ferromagnetic and the helical phases is studied. It is shown that the calculation of the partition function in the scaling limit reduces to the solution of the Schr\"{o}dinger equation of the special form for the quantum particle. It is proposed that the magnetization of the classical model in the ferromagnetic part of the phase diagram including the transition point defines the universal scaling function which is valid for quantum model as well. Explicit analytical formulae for the magnetization are given in the limiting cases of low and high magnetic fields. The influence of the easy-axis anisotropy on the magnetic properties of the model is studied. It is shown that even small anisotropy essentially changes the behavior of the susceptibility in the vicinity of the transition point.

Emergence and Stability of Helical Superstructures in ABC Triblock Copolymers

The emergence and stability of superstructured cylindrical phases in frustrated ABC linear triblock copolymers are investigated by the self-consistent field theory. Our results reveal that the complex single/double/triple helices-on-cylinder phases are formed when the straight cylinders-on-cylinder and rings-on- cylinder phases are frustrated due to packing constraints. A free energy comparison indicates that the double and triple helical phases are stable, whereas the other cylinders-on-cylinder phases are metastable. In addition, the chirality and rotation for the helical supercylinders are considered in our calculations. Our theoretical prediction is consistent with a number of experimental observations.

Thermodynamic and bias field investigation of an antiferroelectric liquid crystal

Dielectric spectroscopy of an antiferroelectric liquid crystal material (S)-4-(1-methylheptyloxycarbonyl)phenyl-4′-(6-pentanoyloxyhex-1-oxy)biphenyl-4-carboxylate 4H6Bi(S) for its helical phases has been carried out under bias electric field in the frequency range 0.1 Hz–10 MHz. Bias field investigation has been carried out in order to explore new relaxation modes. Dielectric characterization of the material, when carried out as a function of DC bias, reveals soft mode around 350 kHz and domain mode at ∼100 Hz in the SmC ⁎ phase as a consequence of suppression of Goldstone mode due to helix unwinding. In the SmC ⁎ A phase a field induced new relaxation mode has been investigated at 8.0 kV/cm having relaxation frequency from 100 Hz to 600 Hz with increasing bias electric field.

Helical phase of chiral nematic liquid crystals as the Bianchi VII0group manifold

We show that the optical structure of the helical phase of a chiral nematic is naturally associated with the Bianchi VII(0) group manifold, of which we give a full account. The Joets-Ribotta metric governing propagation of the extraordinary rays is invariant under the simply transitive action of the universal cover E(2) of the three-dimensional Euclidean group of two dimensions. Thus extraordinary light rays are geodesics of a left-invariant metric on this Bianchi type VII(0) group. We are able to solve, by separation of variables, both the wave equation and the Hamilton-Jacobi equation for this metric. The former reduces to Mathieu's equation, and the latter to the quadrantal pendulum equation. We discuss Maxwell's equations for uniaxial optical materials where the configuration is invariant under a group action and develop a formalism to take advantage of these symmetries. The material is not assumed to be impedance matched, thus going beyond the usual scope of transformation optics. We show that for a chiral nematic in its helical phase Maxwell's equations reduce to a generalized Mathieu equation. Our results may also be relevant to helical phases of some magnetic materials and to light propagation in certain cosmological models.

Frustrated quantum two-dimensional J 1-J 2-J 3 antiferromagnet in a spherically symmetric self-consistent approach

In the framework of a spherically symmetric self-consistent approach to two-time retarded spin-spin Green’s functions, we develop the theory of a two-dimensional frustrated J1-J2-J3 quantum S=1/2 antiferromagnet. We show that taking the damping of spin fluctuations into account is decisive in forming both the spin-liquid state and the state with long-range order. In particular, the existence of damping allows explaining the scaling behavior of the susceptibility χ(q, ω) of the CuO2 cuprate plane, the behavior of the spin spectrum in the two-plane case, and the occurrence of an incommensurable χ(q, ω) peak. In the case of the complete J1-J2-J3 model, in a single analytic approach, we find continuous transitions between three phases with long-range order (“checkerboard,” stripe, and helical (q, q) phases) through the spin-liquid state. We obtain good agreement with cluster computations for the J1-J2-J3 model and agreement with the neutron scattering data for the J1-J2 model of cuprates.

Universal low-temperature properties of frustrated classical spin chain near the ferromagnet-helimagnet transition point

The thermodynamics of the classical frustrated spin chain near the transition point between the ferromagnetic and the helical phases is studied. The calculation of the partition and spin correlation functions at low temperature limit is reduced to the quantum mechanical problem of a particle in potential well. It is shown that the thermodynamic quantities are universal functions of the temperature normalized by the chiral domain wall energy. The obtained behavior of the static structure factor indicates that the short-range helical-type correlations existing at low temperatures on the helical side of the transition point disappear at some critical temperature, defining the Lifshitz point. It is also shown that the low-temperature susceptibility in the helical phase near the transition point has a maximum at some temperature. Such behavior is in agreement with that observed in several materials described by the quantum s = 1/2 version of this model.

Influence of crystallite size and temperature on the antiferromagnetic helices of terbium and holmium metal

We report on the results of grain-size and temperature-dependent magnetization, specific-heat, and neutron-scattering experiments on the heavy rare-earth metals terbium and holmium, with particular emphasis on the temperature regions where the helical antiferromagnetic phases exist. In contrast to Ho, we find that the helical structure in Tb is relative strongly affected by microstructural disorder, specifically, it can no longer be detected for the smallest studied grain size of $D=18$ nm. Moreover, in coarse-grained Tb a helical structure persists even in the ferromagnetic regime, down to about $T=215$ K, in agreement with angle-resolved photoelectron spectroscopy (ARPES) data, which reveal a nesting feature of the bulk Fermi surface at the $L$ point of the Brillouin zone at $T=210$ K. As samples for the ARPES measurements, we used 10-nm-thick single-crystalline Tb films that show a bulk electronic valance-band structure. Thus our ARPES measurements are used to discuss temperature-induced effects observed in the coarse-grained samples.

Statistical mechanics of helical wormlike chain model

We investigate the statistical mechanics of polymers with bending and torsional elasticity described by the helical wormlike model. Noticing that the energy function is factorizable, we provide a numerical method to solve the model using a transfer matrix formulation. The tangent-tangent and binormal-binormal correlation functions have been calculated and displayed rich profiles which are sensitive to the combination of the temperature and the equilibrium torsion. Their behaviors indicate that there is no finite temperature Lifshitz point between the disordered and helical phases. The asymptotic behavior at low temperature has been investigated theoretically and the predictions fit the numerical results very well. Our analysis could be used to understand the statics of dsDNA and other chiral polymers.

Controllable rotation of optical beams with bored helical phases

We achieve controllable noninterferometric rotation of a bored helical beam by introducing a phase shift exclusively to the annular helical region of the phase. We present a derivation based on the decomposition of the beams, which shows that a constant phase shift of DeltaPhi between the bore and the surrounding helical phase with topological charge l will rotate the intensity profile by -DeltaPhi/l about its center. The effect of the phase shifting is verified with experiments. This technique is simple, while it preserves the transverse intensity profiles of the beams. Our report may find applications in optical manipulation and trapping.

Experimental validation of Villain's conjecture about magnetic ordering in quasi-1D helimagnets

Low-temperature magnetic susceptibility, zero-field muon spin resonance and specific heat measurements have been performed in the quasi-one-dimensional (1D) molecular helimagnetic compound Gd ( hfac ) 3 NITEt . The specific heat presents two anomalies at T 0 = 2.19 ( 2 ) K and T N = 1.88 ( 2 ) K , while susceptibility and zero-field muon spin resonance show anomalies only at T N = 1.88 ( 2 ) K . The results suggest an experimental validation of Villain's conjecture of a two-step magnetic ordering in quasi-1D XY helimagnets: the paramagnetic phase and the helical spin solid phases are separated by a chiral spin liquid, where translational invariance is broken without violation of rotational invariance.

Quantum Theory of Multiferroic Helimagnets: Collinear and Helical Phases

We study the quantum fluctuation in the cycloidal helical magnet in terms of the Schwinger boson approach. In sharp contrast to the classical fluctuation, the quantum fluctuation is collinear in nature which gives rise to the collinear spin density wave state slightly above the helical cycloidal state as the temperature is lowered. Physical properties such as the reduced elliptic ratio of the spiral, the neutron scattering and infrared absorption spectra are discussed from this viewpoint with the possible relevance to the quasi-one dimensional LiCu2O2 and LiCuVO4.

Tilted and Helical Columnar Phases for an Axially Symmetric Discoidal System

We report novel phase behavior for a system of disclike ellipsoidal particles interacting via a pair potential. We identify a structural phase transition between two hexagonal columnar phases, both tilted, induced by spatial ordering of the tilt about the columnar axis and positional correlations between neighboring columns upon cooling. The local minima of the potential energy surface support irregular helical arrangements of the discoids about the columnar axis for the high-temperature hexagonal columnar phase, and a tilted arrangement for both phases. Our study demonstrates that dispersion-repulsion forces corresponding to oblate ellipsoids are sufficient to produce a columnar phase that is tilted and helical.

Elastic motion of RecA filaments and its role in recombination

RecA filaments form two types of structures having different helical pitches according to the nucleotide condition. We have investigated the effect of nucleotide cofactor exchange upon the RecA-ssDNA filaments by observing a fluorescently-labelled single molecule in water solution. The result indicated that the RecA-ssDNA filamentous complex is an elastic helical molecule whose length is controlled by binding and release of nucleotide cofactors. We propose that this elastic motion couples to the DNA rotation within the filament by synchronizing the helical phases, and promotes exchange of homologous strands of two DNAs.

Elastic Behavior of RecA-DNA Helical Filaments

Escherichia coli RecA protein forms a right-handed helical filament with DNA molecules and has an ATP-dependent activity that exchanges homologous strands between single-stranded DNA (ssDNA) and duplex DNA. We show that the RecA–ssDNA filamentous complex is an elastic helical molecule whose length is controlled by the binding and release of nucleotide cofactors. RecA–ssDNA filaments were fluorescently labelled and attached to a glass surface inside a flow chamber. When the chamber solution was replaced by a buffer solution without nucleotide cofactors, the RecA–ssDNA filament rapidly contracted approximately 0.68-fold with partial filament dissociation. The contracted filament elongated up to 1.25-fold when a buffer solution containing ATPγS was injected, and elongated up to 1.17-fold when a buffer solution containing ATP or dATP was injected. This contraction–elongation behavior was able to be repeated by the successive injection of dATP and non-nucleotide buffers. We propose that this elastic motion couples to the elastic motion and/or the twisting rotation of DNA strands within the filament by adjusting their helical phases.

Magnetic-field-induced helical and stripe phases in Rashba superconductors

Due to the lack of both parity and time-reversal symmetries, the Rashba superconductors $\mathrm{Ce}{\mathrm{Pt}}_{3}\mathrm{Si}$, $\mathrm{Ce}\mathrm{Rh}{\mathrm{Si}}_{3}$, and $\mathrm{Ce}\mathrm{Ir}{\mathrm{Si}}_{3}$, in the presence of a magnetic field, are unstable to helical (single plane wave) order. We develop a microscopic theory for such superconductors and examine the stability of this helical phase. We show that the helical phase typically occupies most of the magnetic field--temperature phase diagram. However, we also find that this phase is sometimes unstable to a multiple-$q$ phase (loosely called a stripe phase), in which both the magnitude and the phase of the order parameter are spatially varying. We find the position of this helical to multiple-$q$ phase transition. We further examine the density of states and identify features unique to the helical phase.