Ladder Materials Research Articles

Revealing three-dimensional quantum criticality by Sr substitution in Han purple

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An exemplary controlled QPT is the field-induced magnetic ordering of a gapped quantum magnet. Although numerous "quasi-one-dimensional" coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-2D systems are special for several physical reasons. Motivated by the ancient pigment Han Purple (BaCuSi$_{2}$O$_{6}$), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of Ba$_{0.9}$Sr$_{0.1}$CuSi$_{2}$O$_{6}$. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the magnetic Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque and magnetocalorimetric measurements with low-temperature nuclear magnetic resonance studies near the QPT. By a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Sr-substitution in Han Purple.

Structural, electrical, magnetic, and optical properties of iron-based ladder compounds BaFe2(S1−xSex)3

We performed a comprehensive study on structural, electrical, magnetic, and optical properties for iron-based ladder materials ${\mathrm{BaFe}}_{2}{({\mathrm{S}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x})}_{3}\phantom{\rule{4pt}{0ex}}(0\ensuremath{\le}x\ensuremath{\le}1)$, which shows pressure-induced superconductivity in the vicinity of the Mott transition at $x=0$ and 1. We obtain a complete electronic phase diagram in a temperature-composition plane, which reveals that the magnetic ground state switches from the stripe-type to the block-type phase without any intermediate phase at $x=0.23$ with increasing $x$. This behavior is in sharp contrast to the filling controlled system ${\mathrm{Ba}}_{1\ensuremath{-}x}\phantom{\rule{4pt}{0ex}}{\mathrm{Cs}}_{x}{\mathrm{Fe}}_{2}{\mathrm{Se}}_{3}$, in which a paramagnetic state down to the lowest temperature is realized between two magnetic ordered states. The structural transition, which is considered to be relevant to the orbital order, occurs far above the magnetic transition temperature. The magnetic and structural transition temperatures exhibit a similar composition dependence, indicating a close relationship between magnetic and orbital degrees of freedom. In addition, we found that charge dynamics are considerably influenced not only by the magnetic order but also by the structural change (orbital order) from the detailed measurements of electrical resistivity and optical conductivity spectra. We discuss the magnetism and orbital order by comparing the experimental results with the proposed theory based on the multiorbital Hubbard model. The relationship between the charge dynamics and the magnetic/orbital order is also discussed.

Block–spiral magnetism: An exotic type of frustrated order

Competing interactions in quantum materials induce exotic states of matter such as frustrated magnets, an extensive field of research from both the theoretical and experimental perspectives. Here, we show that competing energy scales present in the low-dimensional orbital-selective Mott phase (OSMP) induce an exotic magnetic order, never reported before. Earlier neutron-scattering experiments on iron-based 123 ladder materials, where OSMP is relevant, already confirmed our previous theoretical prediction of block magnetism (magnetic order of the form [Formula: see text]). Now we argue that another phase can be stabilized in multiorbital Hubbard models, the block-spiral state. In this state, the magnetic islands form a spiral propagating through the chain but with the blocks maintaining their identity, namely rigidly rotating. The block-spiral state is stabilized without any apparent frustration, the common avenue to generate spiral arrangements in multiferroics. By examining the behavior of the electronic degrees of freedom, parity-breaking quasiparticles are revealed. Finally, a simple phenomenological model that accurately captures the macroscopic spin spiral arrangement is also introduced, and fingerprints for the neutron-scattering experimental detection are provided.

High performance organic light-emitting diodes with tunable color range from orange to warm white based on single thermally activated delayed fluorescence emitter

In this work, we reported the highly efficient organic light-emitting diodes based on orange-emitting thermally activated delayed fluorescence emitter 1,4-dicyano- 2,3,5,6-tetrakis(3,6-diphenyl-carbazol-9-yl)benzene (4CzTPN-Ph). By utilizing the bipolar material 2,6-bis(3-(9H-carbazol-9-yl)phenyl)-pyridine (26DCzPPy) and hole type material 4,4′,4″-Tri(9-carbazoyl)triphenylamine (TcTa) as host and ladder materials, respectively, the optimized single light-emitting layer (EML) orange device obtained the maximum brightness, external quantum efficiency, current efficiency and power efficiency up to 41791 cd/m2, 13.1%, 42.97 cd/A and 44.98 lm/W, respectively. Except for the 570 nm characteristic emission, interestingly, there is another emission peak at about 475 nm, which increases rapidly with decreasing doping concentration. Therefore, device color shifts gradually from orange to warm white with decreasing doping concentration due to the increasing relative intensity of exciplex emission. Finally, warm white device (Commission Internationale de L'Eclairage (CIE) Coordinates at (0.337, 0.476)) based on single TADF emitter with the maximum brightness, external quantum efficiency, current efficiency and power efficiency up to 23560 cd/m2, 10.2%, 32.33 cd/A and 32.75 lm/W, respectively, was also obtained.

Orbital order and fluctuations in the two-leg ladder materials BaFe2X3 ( X=S and Se) and CsFe2Se3

The electronic structure of BaFe$_2X_3$ ($X$ = S and Se) and CsFe$_2$Se$_3$ in which two-leg ladders are formed by the Fe sites are studied by means of x-ray absorption and resonant inelastic x-ray scattering spectroscopy. The x-ray absorption spectra at the Fe L edges for BaFe$_2X_3$ exhibit two components, indicating that itinerant and localized Fe 3$d$ sites coexist. Substantial x-ray linear dichroism (XLD) is observed in polarization dependent spectra, indicating the existence of orbital order or fluctuation in the Fe-ladder even above the N\'{e}el temperature $T_N$. Direct exchange interaction along the legs of the Fe-ladder stabilizes the orbital and antiferromagnetic orders in BaFe$_2$S$_3$, while the ferromagnetic molecular orbitals are realized between the rungs in CsFe$_2$Se$_3$.

Structural design and electronic properties of halogen-bridged mixed-valence ladder systems with even numbers of legs

Ladder materials situated in a dimensional crossover region have attracted significant attention because of their unique physical properties, which depend strongly on the number of their constituent legs. Among them, metal–organic halogen-bridged ladder systems are currently of particular interest. These new series of ladder materials are composed of two or four halogen-bridged transition-metal complexes, the so-called MX-chains, as legs that are connected to each other by organic rung units. To date, a variety of two- and four-legged halogen-bridged ladder compounds, called MX-ladders, have been synthesized. We present an overview of design strategies, crystal structures, and unique electronic properties of MX-ladder materials with even numbers of legs. Utilization of coordination chemistry provides a high number of structural and electronic degrees of freedom, a striking feature of the MX-ladder system compared with transition-metal-oxide ladder systems. Not only their structural features including tunability via rung substitution but also their unique electronic properties depending on the number of legs and electronic states have recently been revealed.

B1g-like pairing states in two-leg ladder iron superconductors

Motivated by the recent report of superconductivity in Fe-based ladder materials, we study the pairing state of a multiorbital $t$-$J$ model defined on two-leg ladders using the standard mean-field theory. We find that the superconducting order parameters change sign between the ${d}_{xz}$ and ${d}_{yz}$ orbitals in most of the phase diagram. By analogy with the two-dimensional Fe planes, we conclude that the leading pairing channel of this state belongs to the ${B}_{1g}$ symmetry class, which is distinct from the common ${s}_{\ifmmode\pm\else\textpm\fi{}}$ gap with ${A}_{1g}$ symmetry. By smoothly interpolating from planes into ladders, we show that a first-order transition occurs between these two competing phases when the dimension of the system is reduced.

Resonant soft X-ray scattering, stripe order, and the electron spectral function in cuprates

We review the current state of efforts to use resonant soft X-ray scattering (RSXS), which is an elastic, momentum-resolved, valence band probe of strongly correlated electron systems, to study stripe-like phenomena in copper-oxide superconductors and related materials. We review the historical progress including RSXS studies of Wigner crystallization in spin ladder materials, stripe order in 214-phase nickelates, 214-phase cuprates, and other systems.One of the major outstanding issues in RSXS concerns its relationship to more established valence band probes, namely angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM). These techniques are widely understood as measuring a one-electron spectral function, yet a relationship between RSXS and a spectral function has so far been unclear. Using physical arguments that apply at the oxygen K edge, we show that RSXS measures the square modulus of an advanced version of the Green’s function measured with STM. This indicates that, despite being a momentum space probe, RSXS is more closely related to STM than to ARPES techniques.Finally, we close with some discussion of the most promising future directions for RSXS. We will argue that the most promising area lies in high magnetic field studies, particularly of edge states in strongly correlated heterostructures, and the vortex state in superconducting cuprates, where RSXS may clarify the anomalous periodicities observed in recent quantum oscillation experiments.

Boundary effects on the local density of states of one-dimensional Mott insulators and charge density wave states

We determine the local density of states (LDOS) for spin-gapped one-dimensional charge density wave (CDW) states and Mott insulators in the presence of a hard-wall boundary. We calculate the boundary contribution to the single-particle Green function in the low-energy limit using field theory techniques and analyze it in terms of its Fourier transform in both time and space. The boundary LDOS in the CDW case exhibits a singularity at momentum 2kF, which is indicative of the pinning of the CDW order at the impurity. We further observe several dispersing features at frequencies above the spin gap, which provide a characteristic signature of spin-charge separation. This demonstrates that the boundary LDOS can be used to infer properties of the underlying bulk system. In presence of a boundary magnetic field mid-gap states localized at the boundary emerge. We investigate the signature of such bound states in the LDOS. We discuss implications of our results on STM experiments on quasi-1D systems such as two-leg ladder materials like Sr14Cu24O41. By exchanging the roles of charge and spin sectors, all our results directly carry over to the case of one-dimensional Mott insulators.

Field-dependent spin and heat conductivities of dimerized spin-12chains

We study the spin and heat conductivity of dimerized spin-1/2 chains in homogeneous magnetic fields at finite temperatures. At zero temperature, the model undergoes two field-induced quantum phase transitions from a dimerized, into a Luttinger, and finally into a fully polarized phase. We search for signatures of these transitions in the spin and heat conductivities. Using exact diagonalization, we calculate the Drude weights, the frequency dependence of the conductivities, and the corresponding integrated spectral weights. As a main result, we demonstrate that both the spin and heat conductivity are enhanced in the gapless phase and most notably at low frequencies. In the case of the thermal conductivity, however, the field-induced increase seen in the bare transport coefficients is suppressed by magnetothermal effects, caused by the coupling of the heat and spin current in finite magnetic fields. Our results complement recent magnetic transport experiments on spin ladder materials with sufficiently small exchange couplings allowing access to the field-induced transitions.

Pair density waves in coupled doped two-leg ladders

Motivated by Resonant X-ray scattering experiments in cuprate ladder materials showing charge order modulation of period $\lambda=3$ and 5 at specific hole densities, we investigate models involving the electronic t-J ladders and bosonic chains coupled via screened Coulomb repulsion. Extensive density matrix renormalization group calculations applied to the ladders/chains supplemented by a self-consistent mean-field treatment of the inter-ladder/chain coupling provide quantitative estimates of the charge order for $\lambda=3,4$ and 5. As previously proposed, such patterns correspond to the emergence of pair density waves which stem from the strong electronic correlations. We comment on the existence of a $\lambda=4$ modulation not seen so far in experiment.

Ladder π‐Conjugated Materials Containing Main‐Group Elements

Ladder pi-conjugated compounds, which have fully ring-fused polycyclic skeletons, are an important class of materials possessing significant potentials for application in organic electronics. The incorporation of main-group elements, such as B, Si, P, S, and Se, into the ladder skeletons as bridging moieties is a powerful strategy to endow unusual electronic structures as well as suitable molecular arrangements in the solid state, giving rise to attractive photophysical and electronic properties. Recent efforts have produced a number of fascinating ladder materials, some of which indeed showed high performance as light-emitting materials and charge carrier transporting materials. This Focus Review is an overview of the progress in this chemistry, focusing on several important pi-conjugated skeletons.

Collective Spin and Charge Excitations in (Sr,La)14‐xCaxCu24O41 Quantum Spin Ladders

AbstractFor Abstract see ChemInform Abstract in Full Text.

Raman response of magnetic excitations in cuprate ladders and planes

An unified picture for the Raman response of magnetic excitations in cuprate spin-ladder compounds is obtained by comparing calculated two-triplon Raman line-shapes with those of the prototypical compounds SrCu2O3 (Sr123), Sr14Cu24O41 (Sr14), and La6Ca8Cu24O41 (La6Ca8). The theoretical model for the two-leg ladder contains Heisenberg exchange couplings J_parallel and J_perp plus an additional four-spin interaction J_cyc. Within this model Sr123 and Sr14 can be described by x:=J_parallel/J_perp=1.5, x_cyc:=J_cyc/J_perp=0.2, J_perp^Sr123=1130 cm^-1 and J_perp^Sr14=1080 cm^-1. The couplings found for La6Ca8 are x=1.2, x_cyc=0.2, and J_perp^La6Ca8=1130 cm^-1. The unexpected sharp two-triplon peak in the ladder materials compared to the undoped two-dimensional cuprates can be traced back to the anisotropy of the magnetic exchange in rung and leg direction. With the results obtained for the isotropic ladder we calculate the Raman line-shape of a two-dimensional square lattice using a toy model consisting of a vertical and a horizontal ladder. A direct comparison of these results with Raman experiments for the two-dimensional cuprates R2CuO4 (R=La,Nd), Sr2CuO2Cl2, and YBa2Cu3O(6+delta) yields a good agreement for the dominating two-triplon peak. We conclude that short range quantum fluctuations are dominating the magnetic Raman response in both, ladders and planes. We discuss possible scenarios responsible for the high-energy spectral weight of the Raman line-shape, i.e. phonons, the triple-resonance and multi-particle contributions.

Magnetostriction in an array of spin chains under a magnetic field

We consider an array of XX spin-1/2 chains coupled to acoustic phonons and placed in a magnetic field. Treating the phonons in the mean field approximation, we show that this system presents a first order transition as a function of the magnetic field between a partially magnetized distorted state and the fully polarized undistorted state at low temperature. This behavior results from the magnetostriction of the coupled chain system. A dip in the elastic constant of the material near the saturation field along with an anomaly in the magnetic susceptibility is predicted. We also predict the contraction of the material as the magnetic field is reduced (positive magnetostriction) and the reciprocal effect i.e. a decrease of magnetization under applied pressure. At higher temperature, the first order transition is replaced by a crossover. However, the anomalies in the susceptibilities in the system near the saturation field are still present. We discuss the relevance of our analysis in relation to recent experiments on spin-1/2 chain and ladder materials in strong magnetic fields.

Polaron Delocalization in Ladder Macromolecular Systems

Organic macromolecules with conjugated building blocks have been the focus of extensive research that is motivated, in part, by the potential to create optical and electronic devices. We have shown that palladium-catalyzed amination can assemble triarylamine ladder materials with extended structures. Two ladder macromolecules have been prepared in high yields by a series of twelve or sixteen C-N coupling reactions. Studies of the electronic and optical properties of neutral and oxidized forms of the ladder structures were conducted. The optical and electronic properties of the ladder systems are compared to those of the linear tetra-phenyl-p-phenylenediamine as well as the tetra-p-anisyl-p-tetraazacyclophane. The electrochemistry of the ladder systems consists of a multiwave voltammogram with a relatively low first oxidation potential. Electron paramagnetic resonance spectroscopy of the ladder systems suggests the presence of a large density of delocalized polarons. Linear absorption measurements of the chemically oxidized ladders revealed both polaron and intervalence absorption bands. Steady-state and time-resolved fluorescence measurements were also carried out to characterize the dynamics in these novel systems.

Quantum Physics in One Dimension

Quantum Physics in One Dimension

Re-Entrant Quantum Phase Transitions in Antiferromagnetic Spin-1 Ladders

In response to recent chemical attempts to construct higher-spin ladder materials from organic polyradicals, we study the ground-state properties of a wide class of antiferromagnetic spin-1 ladders. Employing various numerical tools, we reveal the rich phase diagram and correct a preceding nonlinear-sigma-model prediction. A variational analysis well interprets the phase competition with particular emphasis on the {\it re-entrant phase boundary} as a function of the rung interaction.

Simulation of infinitely strongly interacting fermions from one to two dimensions

The limit of infinitely strong interaction is the relevant one for understanding the low energy sector of strongly correlated electronic systems like high-temperature superconductors and new related compounds like the so-called ladder materials. The t-J model is the generic one, where strong correlation is taken into account by projecting out doubly occupied sites. We present simulations for both the single-hole and finite doping cases of the t-J model performed with newly developed quantum Monte Carlo algorithms, in chains, ladders, and planes, where the spectral function and the quasiparticle weight are obtained.

Raman scattering through surfaces having biaxial symmetry

Magnetic Raman scattering in two-leg spin ladder materials and the relationship between the anisotropic exchange integrals are analyzed by P. J. Freitas and R. R. P. Singh in Phys. Rev. B, {\bf 62}, 14113 (2000). The angular dependence of the two-magnon scattering is shown to provide information for the magnetic anisotropy in the Sr_14Cu_24O_41 and La_6Ca_8Cu_24O_41 compounds. We point out that the experimental results of polarized Raman measurements at arbitrary angles with respect to the crystal axes have to be corrected for the light ellipticity induced inside the optically anisotropic crystals. We refer quantitatively to the case of Sr_14Cu_24O_41 and discuss potential implications for spectroscopic studies in other materials with strong anisotropy.