Long-range Chiral Order Research Articles

Schwinger boson theory of the J1, J2=J3 kagome antiferromagnet

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus.

Magnetism and magnetotransport in the kagome antiferromagnet Mn3Ge

We perform classical Monte Carlo and stochastic Landau-Lifshitz-Gilbert simulations to study the temperature-dependent magnetism of the kagome antiferromagnet Weyl metal ${\text{Mn}}_{3}\text{Ge}$, and we find that a long-range chiral order sets in at a transition temperature well below the N\'eel temperature (${T}_{N}$). Based on the crystalline symmetries imposed by the chiral magnetic order, we argue for the presence of multiple isoenergetic Weyl nodes (nodes that are at the same energy and with a congruent Fermi surface around them) near the chemical potential. Using the semiclassical Boltzmann equations, we show that the combined contribution to the net longitudinal magnetoconductance (LMC) and the planar Hall conductance (PHC) from tilted Weyl nodes can lead to signatures that are qualitatively distinct from that of a single pair of Weyl nodes. In particular, we show that magnetic orders with different chiralities can give rise to different periods in LMC and PHC as a function of the in-plane magnetic field direction. This is ultimately related to differences in the symmetry-imposed constraints on the Weyl nodes.

Role of Protein-Water Interface in the Stacking Interactions of Granum Thylakoid Membranes-As Revealed by the Effects of Hofmeister Salts.

The thylakoid membranes of vascular plants are differentiated into stacked granum and unstacked stroma regions. The formation of grana is triggered by the macrodomain formation of photosystem II and light-harvesting complex II (PSII-LHCII) and thus their lateral segregation from the photosystem I—light-harvesting complex I (PSI-LHCI) super-complexes and the ATP-synthase; which is then stabilized by stacking interactions of the adjacent PSII-LHCII enriched regions of the thylakoid membranes. The self-assembly and dynamics of this highly organized membrane system and the nature of forces acting between the PSII-LHCII macrodomains are not well understood. By using circular dichroism (CD) spectroscopy, small-angle neutron scattering (SANS) and transmission electron microscopy (TEM), we investigated the effects of Hofmeister salts on the organization of pigment-protein complexes and on the ultrastructure of thylakoid membranes. We found that the kosmotropic agent (NH4)2SO4 and the Hofmeister-neutral NaCl, up to 2 M concentrations, hardly affected the macro-organization of the protein complexes and the membrane ultrastructure. In contrast, chaotropic salts, NaClO4, and NaSCN destroyed the mesoscopic structures, the multilamellar organization of the thylakoid membranes and the chiral macrodomains of the protein complexes but without noticeably affecting the short-range, pigment-pigment excitonic interactions. Comparison of the concentration- and time-dependences of SANS, TEM and CD parameters revealed the main steps of the disassembly of grana in the presence of chaotropes. It begins with a rapid diminishment of the long-range periodic order of the grana membranes, apparently due to an increased stacking disorder of the thylakoid membranes, as reflected by SANS experiments. SANS measurements also allowed discrimination between the cationic and anionic effects—in stacking and disorder, respectively. This step is followed by a somewhat slower disorganization of the TEM ultrastructure, due to the gradual loss of stacked membrane pairs. Occurring last is the stepwise decrease and disappearance of the long-range chiral order of the protein complexes, the rate of which was faster in LHCII-deficient membranes. These data are interpreted in terms of a theory, from our laboratory, according to which Hofmeister salts primarily affect the hydrophylic-hydrophobic interactions of proteins, and the stroma-exposed regions of the intrinsic membrane proteins, in particular—pointing to the role of protein-water interface in the stacking interactions of granum thylakoid membranes.

Topological defects and critical phenomena in two-dimensional frustrated helimagnets

Using a simple model of a frustrated helimagnet, the critical behavior is numerically investigated for planar or isotropic spins, and for cases of one or two chiral order parameters. The helical structure in this model arises from the competition between exchange interactions of spins of the first two range orders in one direction (in both directions) of a square lattice. The main result is that the critical and temperature behavior is primarily determined by topological defects that are present in all cases. In the case of planar spins, vortices, fractional vortices and domain walls are present in the system. Their interaction leads to the appearance of the phase of a chiral spin liquid, or induces a single first-order transition, and in the vicinity of the Lifshitz point vortices lead to a reentrant phase transition to the phase with a collinear quasi-long-range order. When transitions in the chiral and continuous order parameters are separated in temperature, they are of the 2D Ising and Kosterlitz-Thouless types correspondingly. In the case of isotropic spins, so-called $\mathbb{Z}_2$ vortices are present. They do not lead to the appearance of a phase with long-range or quasi-long-range order in the case of one chiral order parameter. However, their interaction leads to a sharp change in the temperature dependence of the correlation length (crossover). In the case of two chiral parameters, there are long-range chiral order of the Ising type (chiral spin liquid) and domain walls. However, as a result of the interaction of vortices and walls, the crossover and chiral transition occur at the same temperature as a first-order transition.

Iridescent cellulose nanocrystal films: the link between structural colour and Bragg’s law

Structural colour is a phenomenon found in nature, which provides plants and animals with vibrant optical properties. The production of this colour is based on the interaction of incident light with the hierarchical organisation of submicron- and micron-sized layered structures. Cellulose nanocrystals (CNCs) are anisotropic building units formed by acid hydrolysis of native cellulose microfibers, which can disperse in aqueous media to form a photonic liquid crystal. One fascinating example of the appearance of biomimetic colour is the supramolecular assembly of CNCs into iridescent layered structures that rotate along a helical screw to yield a long-range chiral nematic order. A quick, simple and engaging experiment that allows the establishment of a direct relation between the structural colour and underlying mechanism of the light interaction with these hierarchically structured materials is reported. The obtained colour changes are explained within the theoretical framework provided by Bragg’s law and may provide an easy way to observe the macroscopic manifestation of this often abstract concept.

Modulation of the multilamellar membrane organization and of the chiral macrodomains in the diatom Phaeodactylum tricornutum revealed by small-angle neutron scattering and circular dichroism spectroscopy

Diatoms possess effective photoprotection mechanisms, which may involve reorganizations in the photosynthetic machinery. We have shown earlier, by using circular dichroism (CD) spectroscopy, that in Phaeodactylum tricornutum the pigment-protein complexes are arranged into chiral macrodomains, which have been proposed to be associated with the multilamellar organization of the thylakoid membranes and shown to be capable of undergoing light-induced reversible reorganizations (Szabó et al. Photosynth Res 95:237, 2008). Recently, by using small-angle neutron scattering (SANS) on the same algal cells we have determined the repeat distances and revealed reversible light-induced reorganizations in the lamellar order of thylakoids (Nagy et al. Biochem J 436:225, 2011). In this study, we show that in moderately heat-treated samples, the weakening of the lamellar order is accompanied by the diminishment of the psi-type CD signal associated with the long-range chiral order of the chromophores (psi, polymer or salt-induced). Further, we show that the light-induced reversible increase in the psi-type CD is associated with swelling in the membrane system, with magnitudes larger in high light than in low light. In contrast, shrinkage of the membrane system, induced by sorbitol, brings about a decrease in the psi-type CD signal; this shrinkage also diminishes the non-photochemical quenching capability of the cells. These data shed light on the origin of the psi-type CD signal, and confirm that both CD spectroscopy and SANS provide valuable information on the macro-organization of the thylakoid membranes and their dynamic properties; these parameters are evidently of interest with regard to the photoprotection in whole algal cells.

Chiral Order in Spin-SXY Chains

We consider the issue of chiral ordering in spin chains for an arbitrary value of the spins S. By use of bosonization according to a scheme developped by H.-J. Schulz, we obtain a phase diagram of the chain with XY exchange couplings between the nearest and the next-to-nearest neighbors. We obtain a satisfactory picture including a so-called chiral spin nematic phase which is gapless, has long-range chiral order and incommensurate spin correlations. We perform a stability analysis of this phase and point out that this analysis is in conflict with existing DMRG results that show a difference between integer and half-integer spin cases.

Thermooptic effect in chloroplast thylakoid membranes. Thermal and light stability of pigment arrays with different levels of structural complexity.

In chloroplast thylakoid membranes, chiral macrodomains, i.e., large arrays of pigment molecules with long-range chiral order, have earlier been shown to undergo light-induced reversible and irreversible structural changes; such reorganizations did not affect the short-range, excitonic pigment-pigment interactions. These structural changes and similar changes in lamellar aggregates of the main chlorophyll a/b light-harvesting complexes exhibited a linear dependence on the intensity of light that was not utilized in photosynthesis. It has been hypothesized that the light-induced rearrangements are driven by a thermooptic effect, i.e., thermal fluctuations due to the dissipation of excess excitation energies [Barzda, V., et al. (1996) Biochemistry 35, 8981-8985]. To test this hypothesis, we have utilized circular dichroism (CD) spectroscopy to investigate the structural stability of the chiral macrodomains and the constituent bulk pigment-protein complexes of granal thylakoid membranes against heat and prolonged, intense illumination. (i) In intact thylakoid membranes, the chiral macrodomains displayed high stability below 40 degrees C, but they were gradually disassembled between 50 and 60 degrees C; the thermal stability of the chiral macrodomains could be decreased substantially by suspending the membranes in reaction media that were hypotonic or had low ionic strength. (ii) The chiral macrodomains were also susceptible to high light: prolonged illumination with intense white light (25 min, 2500 microE m(-)(2) s(-)(1), 25 degrees C) induced similar, irreversible disassembly to that observed at high temperatures; in different preparations, lower thermal stability was coupled to lower light stability. (iii) The light stability depended significantly on the temperature: between about 5 and 15 degrees C, the macrodomains in the intact thylakoids were virtually not susceptible to high light; in contrast, the same preillumination at 35-40 degrees C almost completely destroyed the chiral macrodomains. (iv) As testified by the excitonic CD bands, the molecular organization of the pigment-protein complexes in all samples exhibited very high thermal stability between about 15 and 65 degrees C, and virtually total immunity against intense illumination. These data are fully consistent with the hypothesis of a thermooptic effect, and are interpreted within the frame of a simple model.

Role of LHCII-containing macrodomains in the structure, function and dynamics of grana

In higher plants and green algae two types of thylakoids are distinguished, granum (stacked) and stroma (unstacked) thylakoids. They form a three-dimensional (3D) network with large lateral heterogeneity: photosystem II (PSII) and the associated main chlorophyll a/b light-harvesting complex (LHCII) are found predominantly in the stacked region, while PSI and LHCI are located mainly in the unstacked region of the membrane. This picture emerged from the discovery of the physical separation of the two photosystems (Boardman and Anderson 1964). Granal chloroplasts possess significant flexibility, which is essential for optimizing the photosynthetic machinery under various environmental conditions. However, our understanding concerning the assembly, structural dynamics and regulatory functions of grana is far from being complete. In this paper we overview the significance of the three-dimensional structure of grana in the absorption properties, ionic equilibrations, and in the diffusion of membrane components between the stacked and unstacked regions. Further, we discuss the role of chiral macrodomains in the grana. Lateral heterogeneity of thylakoid membranes is proposed to be a consequence of the formation of macrodomains constituted of LHCII and PSII; their long range order permits long distance migration of excitation energy, which explains the energetic connectivity of PSII particles. The ability of macrodomains to undergo light-induced reversible structural changes lends structural flexibility to the granum. In purified LHCII, which has also been shown to form stacked lamellar aggregates with long range chiral order, excitation energy migrates for large distances; these macroaggregates are also capable of undergoing light-induced reversible structural changes and fluorescence quenching. Hence, some basic properties of grana appear to originate from its main constituent, the LHCII.

Circularly polarized chlorophyll luminescence reflects the macro-organization of grana in pea chloroplasts.

Circular polarization of luminescence (CPL; Steinberg IZ (1978) Annu Rev Biophys Bioeng 7: 113-137) was applied to study pea chloroplasts in different structural states. The structural changes of chloroplasts were induced by variation of osmotic pressure, concentration of magnesium-ions or photoinhibition. Both large CPL and psi-type circular dichroism (psi, polymerization and salt induced) signals appeared in the presence of granal macrostructure and were sensitive to structural changes of the grana. The relation was studied between the amount of CPL expressed as an emission anisotropy factor g(em) and amplitudes of the red psi-type CD bands. The positive psi-type CD band was not directly correlated with g (em) possibly due to a large contribution of circular intensity differential scattering to the measured CD spectra. However, a linear correlation between the amplitude of the negative psi-type CD band and g (em) was found. The CPL signal of pea chloroplasts was attributed to a psi-type origin, which is observed in macroaggregates with densely packed chromophores with a long-range chiral order, and directly depends on the level of macroorganization. With the use of CPL-based microscopy, the long-range packing of LHC II particles can be studied in individual chloroplasts in future. In addition, the CPL method in general allows the study of the macro-organization of grana in green leaves, where conventional light-transmission methods fail.

Role of LHCII-containing macrodomains in the structure, function and dynamics of grana

In higher plants and green algae two types of thylakoids are distinguished, granum (stacked) and stroma (unstacked) thylakoids. They form a three-dimensional (3D) network with large lateral heterogeneity: photosystem II (PSII) and the associated main chlorophyll a/b light-harvesting complex (LHCII) are found predominantly in the stacked region, while PSI and LHCI are located mainly in the unstacked region of the membrane. This picture emerged from the discovery of the physical separation of the two photosystems (Boardman and Anderson 1964). Granal chloroplasts possess significant flexibility, which is essential for optimizing the photosynthetic machinery under various environmental conditions. However, our understanding concerning the assembly, structural dynamics and regulatory functions of grana is far from being complete. In this paper we overview the significance of the three-dimensional structure of grana in the absorption properties, ionic equilibrations, and in the diffusion of membrane components between the stacked and unstacked regions. Further, we discuss the role of chiral macrodomains in the grana. Lateral heterogeneity of thylakoid membranes is proposed to be a consequence of the formation of macrodomains constituted of LHCII and PSII; their long range order permits long distance migration of excitation energy, which explains the energetic connectivity of PSII particles. The ability of macrodomains to undergo light-induced reversible structural changes lends structural flexibility to the granum. In purified LHCII, which has also been shown to form stacked lamellar aggregates with long range chiral order, excitation energy migrates for large distances; these macroaggregates are also capable of undergoing light-induced reversible structural changes and fluorescence quenching. Hence, some basic properties of grana appear to originate from its main constituent, the LHCII.

Role of LHCII-containing macrodomains in the structure, function and dynamics of grana

In higher plants and green algae two types of thylakoids are distinguished, granum (stacked) and stroma (unstacked) thylakoids. They form a three-dimensional (3D) network with large lateral heterogeneity: photosystem II (PSII) and the associated main chlorophyll a/b light-harvesting complex (LHCII) are found predominantly in the stacked region, while PSI and LHCI are located mainly in the unstacked region of the membrane. This picture emerged from the discovery of the physical separation of the two photosystems (Boardman and Anderson 1964). Granal chloroplasts possess significant flexibility, which is essential for optimizing the photosynthetic machinery under various environmental conditions. However, our understanding concerning the assembly, structural dynamics and regulatory functions of grana is far from being complete. In this paper we overview the significance of the three-dimensional structure of grana in the absorption properties, ionic equilibrations, and in the diffusion of membrane components between the stacked and unstacked regions. Further, we discuss the role of chiral macrodomains in the grana. Lateral heterogeneity of thylakoid membranes is proposed to be a consequence of the formation of macrodomains constituted of LHCII and PSII; their long range order permits long distance migration of excitation energy, which explains the energetic connectivity of PSII particles. The ability of macrodomains to undergo light-induced reversible structural changes lends structural flexibility to the granum. In purified LHCII, which has also been shown to form stacked lamellar aggregates with long range chiral order, excitation energy migrates for large distances; these macroaggregates are also capable of undergoing light-induced reversible structural changes and fluorescence quenching. Hence, some basic properties of grana appear to originate from its main constituent, the LHCII.

Magnetic ordering and phase transitions in planar antiferromagnetic systems with a Kagomé lattice

We study the process of magnetic ordering in planar antiferromagnetic systems with a Kagome lattice. It is found that if the interaction between next-nearest-neighbor spins is taken into account, the heat capacity of such systems has a singularity at a finite temperature T. On the basis of a scaling analysis of finite-size systems we study the behavior of thermodynamic quantities in the neighborhood of a phase transition. We find that the phase transition at the critical point is due to discrete-and continuous-symmetry breaking, in which the long-range chiral order and the power-law translational spin order emerge simultaneously. Finally, we calculate the temperatures of the transition to different (with three and nine spins per unit cell) ordered states.

Isolation of Lamellar Aggregates of the Light-Harvesting Chlorophyll a/b Protein Complex of Photosystem II with Long-Range Chiral Order and Structural Flexibility

Isolation of LHCII, the light-harvesting chlorophyll a/b complex of photosystem II, based on the procedure described by Krupaet al.(1987,Plant Physiol.84, 19–24), was optimized for obtaining purified lamellar aggregates with long-range chiral order and structural flexibility (the capability of undergoing light-induced reversible structural changes). By varying the concentration of the detergent Triton X-100 for the solubilization of thylakoid membranes, we obtained four types of LHCII aggregates: (i) With low detergent concentration, ≤0.6% (v/v), the aggregates contained lipids in high amount. These preparations with Chl a/b ratios of about 1.4 contained minor antenna complexes with a fingerprint of an additional CD band at (+) 505 nm; they formed disordered lamellae and exhibited no or weak psi-type CD bands (psi, polymerization- or salt-induced), which did not possess the ability to undergo light-induced changes (ΔCD). (ii) At the optimal concentration, around 0.7 ± 0.1% (v/v), the detergent removed some lipids and most of the minor complexes, and the Chl a/b ratio dropped to 1.0–1.1. LHCII formed loosely stacked two-dimensional lamellae which exhibited psi-type CD bands and large light-induced reversible structural changes (ΔCD). (iii) At detergent concentration above the optimum, around 0.8–1% (v/v), the lipid content of LHCII decreased and minor complexes could not be detected. LHCII formed disordered aggregates and showed neither psi-type CD nor ΔCD. (iv) High concentrations (≥1.1% (v/v)) Triton X-100 led to very pure but largely delipidated samples assembled into tightly stacked three-dimensional lamellar structures with intense psi-type CD but no ΔCD.

Phase diagrams of the S= quantum antiferromagnetic XY model on the triangular lattice in magnetic fields

We study the S=1/2 quantum antiferromagnetic XY model on finite triangular lattices with N sites in both longitudinal and transverse magnetic fields. We calculate physical quantities in the ground state using a diagonalization for spins $N \leq 27$, and those at finite temperatures using a quantum transfer Monte Carlo method for $N \leq 24$. In the longitudinal magnetic field, the long-range chiral order parameter seems to have a finite, nonzero value at low temperatures suggesting the occurrence of a classical umbrella-type phase. In the transverse magnetic field, the 1/3-plateau of the magnetization curve appears even at low temperatures, in contrast with the classical model. The magnetic field dependences of the order parameters suggest that the chiral-ordered, the ferrimagnetic, and the spin flop phases appear successively as the magnetic field is increased. The transition temperatures are estimated from the peak position of the specific heat, and the phase diagrams are predicted in both longitudinal and transverse magnetic fields.

Vector Chiral Order in the QuantumXXZAntiferromagnet on a Triangular Lattice Analyzed with the Super-Effective-Field Theory

The chiral order in the spin 1/2 X X Z antiferromagnet H = J ∑(σ i x σ j x +σ i y σ j y +Δσ i z σ j z ) and especially in the X Y antiferromagnet on a two-dimensional triangular lattice is studied using the super-effective-field theory. In the X Y model the size dependence of the critical temperatures indicates the existence of the long-range chiral-order at sufficiently low temperatures in the infinite system. Phase diagram of the chiral order in the X X Z antiferromagnet is studied.

Static and dynamical correlations in a spin-1/2 frustrated antiferromagnet.

We study the frustrated spin-1/2 antiferromagnetic Heisenberg model on a square lattice of 16 sites, using a Lanczos algorithm and group-theoretical techniques. We investigate the competition between collinear, dimer, chiral, and spiral orders by calculating the dynamical and spatial correlation functions. Our numerical results strongly suggest the presence of long-range collinear order in the interval 0.55\ensuremath{\le}${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\le}0.9 (we cannot show numerically that this order exists for larger values of ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$). Dimer- and chiral-order parameters both show increasing low-energy fluctuations and a longer range of the correlations in space around ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\sim}0.55. We propose an order parameter for chiral order exhibiting the full symmetry of the cluster and hence being less sensitive to finite-size effects. The mean value of the square of this plaquette chiral-order parameter is enhanced for ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$\ensuremath{\sim}0.55, where the characteristic chiral spin-fluctuation frequency is reduced, but no indications of long-range chiral order were found. Although the correlation function of the twist-order parameter is not a simple monotonically decreasing function of distance, little change is induced by frustration, suggesting that spiral order is not strongly favored. The energy gap corresponding to dimer order is smaller than those of spin waves, spiral order, and chiral order; thus, this state is the best candidate for an intermediate-(${\mathit{J}}_{2}$/${\mathit{J}}_{1}$) phase in the ${\mathit{J}}_{1}$-${\mathit{J}}_{2}$ model.

Direct observation of large chiral domains in chloroplast thylakoid membranes by differential polarization microscopy.

Long-range chiral organization of the pigment-protein complexes in mature granal chloroplasts has been established by differential polarization imaging and local circular dichroism spectra. Linear and circular dichroism images of oriented chloroplasts were obtained in a confocal differential polarization microscope. The circular dichroism images display signals of opposite signs emerging from discrete regions with local dichroic values much larger than anticipated, indicating domains in the thylakoid membranes having long-range chiral organization. These domains are associated with positive and negative circular dichroism bands obtained at specific locations on the chloroplasts. Surprisingly, the local circular dichroism spectra do not display the excitonic shape of spectra obtained for macroscopic suspensions, but the latter can be produced by superposition of two local spectra of opposite sign. These data are evidence for the existence of long-range chiral order of the pigment-protein complexes in thylakoid membranes. The possible role of the long-range chiral domains in the efficiency of energy delocalization through the thylakoid membranes is discussed.