We report on a sequence of field-induced transitions in the zigzag ladder compound BaDy2O4 studied with powder neutron diffraction and magnetisation measurements. In agreement with the previously published results, the low temperature zero-field structure is characterised by two half-integer propagation vectors, k1=[1/2 0 1/2] and k2= 1/2 1/2 1/2]. However, on application of an external magnetic field, the Bragg peaks corresponding to the zero-field structure lose their intensity rather rapidly and disappear completely in a field of 2.5 kOe. In the intermediate fields, 2.5 to 22.5 kOe, new peaks are observed characterised by the propagation vector k0=[0 0 1/3] corresponding to an up-up-down (uud) structure as well k=0 ferromagnetic peaks. This regime of fields corresponds to a pronounced plateau in the magnetisation curve. Remarkably, the uud structure survives heating to at least 1.4 K, three times higher temperature than the TN of 0.48 K for the zero-field structure. Above 22.5 kOe, the k0 peaks disappear while the k = 0 peaks gain significant intensity indicating an increase in the polarisation of the system. The analysis of the intensities of the field-induced reflections allows for a clear identification of the magnetic structures in both the intermediate and high field regimes.
Strong co-operative interactions occur between four different broken symmetries involving charge-ordering and bond distortions in the quarter-filled correlated zigzag electron ladder. The ground state is singlet, with spin gap several times larger than in the spin-Peierls state of the one-dimensional quarter-filled chain with the same parameters. We propose the quarter-filled zigzag electron ladder model for several different organic charge-transfer solids with coupled pairs of quasi-one-dimensional stacks, the spin-gap transition temperatures in which are unusually high.
Using bosonization approach, we derive an effective low-energy theory for XXZ-symmetric spin-1/2 zigzag ladders and discuss its phase diagram by a variational approach. A spin nematic phase emerges in a wide part of the phase diagram, either critical or massive. Possible crossovers between the spontaneously dimerized and spin nematic phases are discussed, and the topological excitations in all phases identified.
An exact solution (incomplete) of the ground-state problem for an Ising model in an external field on a 3D honeycomb zigzag-ladder lattice with two types of sites is found. It is shown that the geometrical frustration due to the presence of triangle elements leads to the emergence of a variety of magnetic phases. The majority of these are partially disordered (highly degenerate). The theoretical results are used to explain the sequence of experimentally observed phase transitions in the honeycomb zigzag-ladder magnets and to predict the appearance of new phases.
The ground state properties of a frustrated spin-1/2 system is studied on a trellis ladder which is composed of two zigzag ladders interacting through rung interactions. The presence of rung interaction between the zigzag ladders induces a non-magnetic ground state, although, each of zigzag ladders has ferromagnetic order in weak antiferromagnetic leg interaction limit. The rung interaction also generates rung dimers and opens spin gap which increases rapidly with rung interaction strength. The correlation between spins decreases exponentially with the distance between them.
We derive the exact ground states for a one dimensional family of $S=1/2$ XXZ Hamiltonians on the zigzag ladder. These states exhibit true long range spiral order that spontaneously breaks the U(1) invariance of the Hamiltonian. Besides breaking a continuous symmetry in $d=1$, this spiral ordering has a ferromagnetic component along the symmetry axis that can take any value between zero and full saturation. In this sense, our canted spiral solutions are a generalization of the SU(2) Heisenberg ferromagnet to non-zero ordering wave-vectors of the transverse spin components. We extend this resul…
We investigate the low-lying excitation of the antiferromagnetic zigzag spin ladder with Möbius boundary condition. Using the Lanczos and Householder diagonalization methods, we calculate the excitation spectrum of the zigzag ladder in the momentum space. We then show that the topological defect generated by the Möbius boundary provides the clear evidence of the single spinon excitation. On the basis of the obtained single-spinon dispersion curve, we analyze the two-spinon scattering states under the usual periodic boundary condition. We further discuss the interaction effect between the spino…
We investigate filling dependence of the zigzag Hubbard ladder, using density matrix renormalization group method. We illustrate the chemical-potential vs. electron-density and spin gap vs. electron density curves, which reflect characteristic properties of the electron state.On the basis of the obtained phase diagram, we discuss the connection to a novel quasi-one-dimensional superconductor Pr$_2$Ba$_4$Cu$_7$O$_{15-δ}$.
We study two Heisenberg spin-1/2 chains coupled by a frustrating ``zigzag'' interaction. We are particularly interested in the regime of weak interchain coupling, which is difficult to analyse by either numerical or analytical methods. Previous density matrix renormalisation group (DMRG) studies of the isotropic model with open boundary conditions and sizeable interchain coupling have established the presence of incommensurate correlations and of a spectral gap. By using twisted boundary conditions with arbitrary twist angle, we are able to determine the incommensurabilities both in the isotro…
We report the magnetic structure of TaFe1+yTe3 single crystals by means of neutron diffraction measurements. TaFe1+yTe3 possesses a layered structure with a formation of two-leg zigzag ladders along the b-axis. We find that TaFe1+yTe3 undergoes an antiferromagnetic transition at 178 K with Fe1 spins of the intra-ladders ferromagnetically aligned while spins of the inter-ladders antiferromagneitcally coupled. Furthermore, spins of the neighboring interstitial Fe2 (y) ions order parallel to the Fe1 spins of each ladder. These findings are distinct from the magnetic structure of the recently-disc…
Exact and rigorous solutions of the ground-state problem for the classical Heisenberg model with nearest-neighbor interactions on two- and three-dimensional lattices composed of zigzag (triangular) ladders are obtained in a very simple way, with the use of a cluster method. It is shown how the geometrical frustration due to the presence of triangles as structural units leads to the emergence of incommensurate spiral orderings and their collinear limits. Interestingly, these orderings are determined by a single angle (along with the signs of the interactions between neighboring spins); therefor…
We study an asymmetric $J_1$-$J_2$ zigzag ladder consisting of two different spin-$\frac{1}{2}$ antiferromagnetic (AFM; $J_2$, $γJ_2>0$) Heisenberg legs coupled by zigzag-shaped ferromagnetic (FM; $J_1<0$) inter-leg interaction. On the basis of density-matrix renormalization group based calculations the ground-state phase diagram is obtained as functions of $γ$ and $J_2/|J_1|$. It contains four kinds of frustration-induced ordered phases except a trivial FM phase. Two of the ordered phases are valence bond solid (VBS) with spin-singlet dimerization, which is a rather conventional order by diso…
We consider the simplest example of lattice frustration in the 1/4-filled band, a one-dimensional chain with next-nearest neighbor interactions. For this zigzag ladder with electron-electron as well as electron-phonon interactions we present numerical results for ground state as well as thermodynamic properties. In this system the ground state bond distortion pattern is independent of electron-electron interaction strength. The spin gap in the ground state of the zigzag ladder increases with the degree of frustration. Unlike in one-dimension, where the spin-gap and charge ordering transitions …
The interplay between Kondo effect, indirect magnetic interaction and geometrical frustration is studied in the Kondo lattice on the one-dimensional zigzag ladder. Using the density-matrix renormalization group (DMRG), the ground state and various short- and long-range spin- and density-correlation functions are calculated for the model at half-filling as a function of the antiferromagnetic Kondo interaction down to $J=0.3t$ where $t$ is the nearest-neighbor hopping on the zigzag ladder. Geometrical frustration is shown to lead to at least two critical points: Starting from the strong-$J$ limi…
The spin-1/2 zig-zag Heisenberg ladder (J_1 - J_2 model) is considered. A new representation for the model is found and a saddle point approximation over the spin-liquid order parameter < \vec σ_{n-1}(\vec σ_{n}\times \vec σ_{n+1}) > is performed. Corresponding effective action is derived and analytically analyzed. We observe the presence of phase transitions at values J_2/J_1=0.231 and J_2/J_1=1/2.
The effect of next-nearest-neighbor hopping $t_{2}$ on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite $t_{2}$, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that $t_{2}$ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong $J$, we find …
Two-leg spin-1/2 ladder systems consisting of a ferromagnetic leg and an antiferromagnetic leg are considered where the spins on the legs interact through antiferromagnetic rung couplings $J_1$. These ladders can have two geometrical arrangements either zigzag or normal ladder and these systems are frustrated irrespective of their geometry. This frustration gives rise to incommensurate spin density wave, dimer and spin fluid phases in the ground state. The magnetization in the systems decreases linearly with $J^2_1$, and the systems show an incommensurate phase for $0.0<J_1<1.0$. The spin-spin…
We consider electrons on a two-leg triangular ladder at half-filling and in an orbital magnetic field. In a two-band regime in the absence of the field, the electronic system remains conducting for weak interactions since there is no four-fermion Umklapp term. We find that in the presence of the orbital field there is a four-fermion Umklapp and it is always relevant for repulsive interactions. Thus in this special ladder, the combination of the orbital magnetic field and interactions provides a mechanism to drive metal-insulator transition already at weak coupling. We discuss properties of the…
We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic inter-edge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of …
We study an isotropic Heisenberg spin-1/2 model on a trellis ladder which is composed of two $J_1-J_2$ zigzag ladders interacting through anti-ferromagnetic rung couplings $J_3$. The $J_1$ and $J_2$ are ferromagnetic zigzag spin interaction between two legs and anti-ferromagnetic interaction along each leg of a zigzag ladder. A quantum phase diagram of this model is constructed using the density matrix renormalization group (DMRG) method and linearized spin wave analysis. In small $J_2$ limit a short range stripe collinear phase is found in the presence of $J_3$, whereas, in the large $J_2/J_3…
The random antiferromagnetic two-leg and zigzag spin-1/2 ladders are investigated using the real space renormalization group scheme and their complete phase diagrams are determined. We demonstrate that the first system belongs to the same universality class of the dimerized random spin-1/2 chain. The zigzag ladder, on the other hand, is in a random singlet phase at weak frustration and disorder. Otherwise, we give additional evidence that it belongs to the universality class of the random antiferromagnetic and ferromagnetic quantum spin chains, although the universal fixed point found in the l…
We study the low-energy properties of a Heisenberg spin-1/2 zigzag ladder with different exchange constants on the two chains. Using a nonlinear sigma-model field theory and abelian bosonization, we find that the excitations are gapless, with a finite spin wave velocity, if the values of the chain exchanges are small. If the chain exchanges are large, the system is gapped, and the energy spectra of the kink and antikink excitations are different from each other.
Although the frustrated spin chain (zigzag chain) is a Drosophila of frustrated magnetism, the understanding of a pair of coupled zigzag chains (frustrated spin ladder) in a magnetic field is incomplete. We address this problem through nuclear magnetic resonance (NMR) experiments on $\text{BiCu}_2\text{PO}_6$ in magnetic fields up to 45 T, revealing a field-induced spiral magnetic structure. Conjointly, we present advanced numerical calculations showing that even moderate rung coupling dramatically simplifies the phase diagram below half-saturation magnetization by stabilizing a field-induced …
By using the density matrix renormalization group method, we investigate ground- and excited-state properties of the e_g-orbital degenerate Hubbard model at quarter filling for two kinds of lattices, zigzag chain and ladder. In the zigzag chain, the system is effectively regarded as a decoupled double chain of the S=1/2 antiferromagnetic Heisenberg model, and the spin gap is approximately zero, similar to the case of weakly coupled Heisenberg chains. On the other hand, in the ladder, the spin correlation on the rung remains robust and the spin gap exists.
In order to clarify a crucial role of orbital degree of freedom in geometrically frustrated systems, we investigate both ground- and excited-state properties of the e_g-orbital degenerate Hubbard model on two kinds of lattices, ladder and zigzag chain, by using numerical techniques. In the ladder, spin correlation extends on the whole system, while the zigzag chain is decoupled to a double chain and spin excitation is confined in one side of the double chain due to the selection of a specific orbital. We envision a kind of self-organization phenomenon that the geometrically frustrated multi-or…
We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions (or Ising models). After reexamining the bosonization rules for two Ising models, taking particular care of order and disorder operators, we obtain a bosonic description of the spin-1 ladder. From renormalization-group and mean-field arguments, we conclude that, for a small interchain coupling, the spin-1 ladder is approximately described by three decoupled, two-frequency sine-Gordon models. We then predict that, start…
We investigated the iron-based ladder compounds (Ba,Cs)Fe$_2$Se$_3$. Their parent compounds, BaFe$_2$Se$_3$ and CsFe$_2$Se$_3$, have different space groups, formal valences of Fe and magnetic structures. Electrical resistivity, specific heat, magnetic susceptibility, X-ray diffraction and powder neutron diffraction measurements were conducted to obtain temperature and composition phase diagram of this system. Block magnetism observed in BaFe$_2$Se$_3$ is drastically suppressed with Cs doping. In contrast, stripe magnetism observed in CsFe$_2$Se$_3$ is not so fragile against Ba doping. New type…
A possible ground state of NaV_2O_5 is proposed based on the Hartree approximation for both on-site and intersite Coulomb interactions. The results indicate that the intersite Coulomb interaction induces a zigzag type of charge disproportionation (i.e. charge ordering) along the ladders of V-ions resulting in the localized spins between neighboring ladders to form a spin gap. This new state, which is different from the spin-Peierls state so far believed, seems to be consistent with the existing experimental results.
We have investigated the electronic structure of the zigzag ladder (chain) compound SrCuO2 combining polarized optical absorption, reflection, photoreflectance and pseudo-dielectric function measurements with the model calculations. These measurements yield an energy gap of 1.42 eV (1.77 eV) at 300 K along (perpendicular) to the Cu-O chains. We have found that the lowest energy gap, the correlation gap, is temperature independent. The electronic structure of this oxide is calculated using both the local-spin-density-approximation with gradient correction method, and the tight-binding theory fo…
We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a ladder geometry using the density matrix renormalization group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=\sinϕ$ and $J=\cosϕ$ with an angle parameter $ϕ$. Based on the results for several types of order parameters, excitation gaps, and entanglement spectra, the $ϕ$-dependent ground-state phase diagram is determined. Remarkably, the phase diagram is quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice, exhibiting the sam…
The low-temperature (LT) superstructure of $α'$-NaV$_2$O$_5$ was determined by synchrotron radiation x-ray diffraction. Below the phase transition temperature associated with atomic displacement and charge ordering at 34K, we observed the Bragg peak splittings, which evidence that the LT structure is monoclinic. It was determined that the LT structure is $(a-b)\times 2b \times 4c$ with the space group $A112$ where $a, b$ and $c$ represent the high temperature orthorhombic unit cell. The valence estimation of V ions according to the bond valence sum method shows that the V sites are clearly sep…
We study the spin-pseudospin Hamiltonian of the Ising Model in Transverse Field (IMTF) for pseudospins, coupled to the XY-spins on a triangular lattice. This model appears from analyses of the quarter-filled ladder compound $NaV_2O_5$, and pseudospins represent its charge degrees of freedom. In the molecular-field approximation we find that the model possesses two phases: charge-disordered without spin gap; and a low-temperature phase containing both the anti-ferroelectric (zigzag) charge order and spin dimerization (spin gap). The phase transition is of the second kind, and the calculated phy…
We present Density Matrix Renormalization Group calculations of the ground-state properties of quarter-filled ladders including static electron-lattice coupling. Isolated ladders and two coupled ladders are considered, with model parameters obtained from band-structure calculations for $α^\prime$-NaV$_2$O$_5$. The relevant Holstein coupling to the lattice causes static out-of-plane lattice distortions, which appear concurrently with a charge-ordered state and which exhibit the same zigzag pattern observed in experiments. The inclusion of electron-lattice coupling drastically reduces the critic…
We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to …
We study the ground state phase diagram of a frustrated spin tube in a strong external magnetic field. This model can be viewed as two coupled zigzag spin chains, or as a two-leg spin ladder with frustrating next-nearest-neighbor couplings along the legs, and its study is motivated by the physics of such materials as Sulfolane-Cu_{2}Cl_{4} and BiCu_{2}PO_{6}. In magnetic fields right below the saturation, the system can be effectively represented as a dilute gas of two species of bosonic quasiparticles that correspond to magnons with inequivalent incommensurate momenta at two degenerate minima…
As one of the most promising Kitaev quantum-spin-liquid (QSL) candidates, $α$-RuCl$_3$ has received a great amount of attention. However, its ground state exhibits a long-range zigzag magnetic order, which defies the QSL phase. Nevertheless, the magnetic order is fragile and can be completely suppressed by applying an external magnetic field. Here, we explore the evolution of magnetic excitations of $α$-RuCl$_3$ under an in-plane magnetic field, by carrying out inelastic neutron scattering measurements on high-quality single crystals. Under zero field, there exist spin-wave excitations near th…
