Interladder Coupling Research Articles

Strongly Correlated Ladders in K-Doped p-Terphenyl Crystals.

Potassium-doped terphenyl has recently attracted attention as a potential host for high-transition-temperature superconductivity. Here, we elucidate the many-body electronic structure of recently synthesized potassium-doped terphenyl crystals. We show that this system may be understood as a set of weakly coupled one-dimensional ladders. Depending on the strength of the interladder coupling, the system may exhibit insulating spin-gapped valence-bond solid or antiferromagnetic phases, both of which upon hole doping may give rise to superconductivity. This terphenyl-based ladder material serves as a new platform for investigating the fate of ladder phases in the presence of three-dimensional coupling as well as for novel superconductivity.

Intertwined charge, spin, and pairing orders in doped iron ladders

Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe$_2$S$_3$. The model is constructed by using {\it ab initio} hopping parameters and the ground state properties are investigated using the density matrix renormalization group method. We show that the $(\pi,0)$ magnetic ordering at half-filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard $U$ coupling, other magnetic patterns, such as $(0,\pi)$, are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interaction strength, indicating hole pairing. Due to the crystal-field split among orbitals, the holes primarily reside in one orbital, with the other one remaining half-filled. This resembles orbital selective Mott states. The formation of tight hole pairs continues with increasing hole density, as long as the magnetic order remains antiferromagnetic in one direction. The study of pair-pair correlations indicates the dominance of the intra-orbital spin-singlet channel, as opposed to other pairing channels. Although in a range of hole doping pairing correlations decay slowly, our results can also be interpreted as corresponding to a charge-density-wave made of pairs, a precursor of eventual superconductivity after interladder couplings are included. Such scenario of intertwined orders has been extensively discussed before in the cuprates, and our results suggest a similar physics could exist in ladder iron-based superconductors. Finally, we also show that a robust Hund's coupling is needed for pairing to occur.

Optimization of infinite projected entangled pair states: The role of multiplets and their breaking

The infinite projected entangled pair states (iPEPS) technique [J. Jordan {\it et al.}, Phys. Rev. Lett. {\bf 101}, 250602 (2008)] has been widely used in the recent years to assess the properties of two-dimensional quantum systems, working directly in the thermodynamic limit. This formalism, which is based upon a tensor-network representation of the ground-state wave function, has several appealing features, e.g., encoding the so-called area law of entanglement entropy by construction; still, the method presents critical issues when dealing with the optimization of tensors, in order to find the best possible approximation to the exact ground state of a given Hamiltonian. Here, we discuss the obstacles that arise in the optimization by imaginary-time evolution within the so-called simple and full updates and connect them to the emergence of a sharp multiplet structure in the "virtual" indices of tensors. In this case, a generic choice of the bond dimension $D$ is not compatible with the multiplets and leads to a symmetry breaking (e.g., generating a finite magnetic order). In addition, varying the initial guess, different final states may be reached, with very large deviations in the magnetization value. In order to exemplify this behavior, we show the results of the $S=1/2$ Heisenberg model on an array of coupled ladders, for which a vanishing magnetization below the critical interladder coupling is recovered only for selected values of $D$, while a blind optimization with a generic $D$ gives rise to a finite magnetization down to the limit of decoupled ladders.

Bloch oscillations of spin-orbit-coupled cold atoms in an optical lattice and spin-current generation

We study the Bloch oscillation dynamics of a spin-orbit-coupled cold atomic gas trapped inside a one-dimensioanl optical lattice. The eigenspectra of the system is identified as two interpenetrating Wannier-Stark ladder. Based on that, we carefully analyzed the Bloch oscillation dynamics and found out that intraladder coupling between neighboring rungs of Wannier-Stark ladder give rise to ordinary Bloch oscillation while interladder coupling lead to small amplitude high frequency oscillation superimposed on it. Specifically spin-orbit interaction breaks Galilean invariance, which can be reflected by out-of-phase oscillation of the two spin components in the accelerated frame. The possibility of generating spin current in this system are also explored.

Spin dynamics of coupled spin ladders near quantum criticality in Ba2CuTeO6

We report inelastic neutron scattering measurements of the magnetic excitations in Ba2CuTeO6, proposed by ab initio calculations to magnetically realize weakly coupled antiferromagnetic two-leg spin-1/2 ladders. Isolated ladders are expected to have a singlet ground state protected by a spin gap. Ba2CuTeO6 orders magnetically, but with a small Neel temperature relative to the exchange strength, suggesting that the interladder couplings are relatively small and only just able to stabilize magnetic order, placing Ba2CuTeO6 close in parameter space to the critical point separating the gapped phase and Neel order. Through comparison of the observed spin dynamics with linear spin wave theory and quantum Monte Carlo calculations, we propose values for all relevant intra- and interladder exchange parameters, which place the system on the ordered side of the phase diagram in proximity to the critical point. We also compare high field magnetization data with quantum Monte Carlo predictions for the proposed model of coupled ladders.

S=12quantum critical spin ladders produced by orbital ordering inBa2CuTeO6

The ordered hexagonal perovskite Ba2CuTeO6 hosts weakly coupled S=1/2 spin ladders produced by an orbital ordering of Cu2+. The magnetic susceptibility chi(T) of Ba2CuTeO6 is well described by that expected for isolated spin ladders with exchange coupling of J~86 K but shows a deviation from the expected thermally activated behavior at low temperatures below T*~25 K. An anomaly in chi(T), indicative of magnetic ordering, is observed at T_mag=16 K. No clear signature of long-range ordering, however, is captured in NMR, specific heat or neutron diffraction measurements at and below T_mag. The marginal magnetic transition, indicative of strong quantum fluctuations, is evidence that Ba2CuTeO6 is in very close proximity to a quantum critical point between a magnetically ordered phase and a gapped spin liquid controlled by inter-ladder couplings.

Minimal model for the frustrated spin ladder systemBiCu2PO6

To establish the microscopic model of the compound BiCu$_2$PO$_6$ is a challenging task. Inelastic neutron scattering experiments showed that the dispersion of this material is non-degenerate suggesting the existence of anisotropic interactions. Here we present a quantitative description of the excitation spectrum for BiCu$_2$PO$_6$ on the one-particle level. The solution of the isotropic frustrated spin ladder by continuous unitary transformations is the starting point of our approach. Further couplings such as isotropic interladder couplings and anisotropic interactions are included on the mean-field level. Our aim is to establish a minimal model built on the symmetry allowed interactions and to find a set of parameters, which allow us to describe the low-energy part of the dispersion without assuming unrealistic couplings.

Tellurium-bridged two-leg spin ladder inBa2CuTeO6

We present single-crystal growth and magnetic property studies of tellurium-bridged copper spin-$\frac{1}{2}$ system ${\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}$. The spin-exchange interaction among copper spins via $\mathrm{Cu}\text{\ensuremath{-}}\mathrm{O}\text{\ensuremath{-}}\mathrm{Te}\text{\ensuremath{-}}\mathrm{O}\text{\ensuremath{-}}\mathrm{Cu}$ super-superexchange route leads to a novel two-leg spin ladder system. Spin susceptibility $\ensuremath{\chi}(T)$ data indicate that the triclinic ${\mathrm{Ba}}_{2}{\mathrm{CuTeO}}_{6}$ undergoes a stepwise crossover for exchange couplings revealed by a broad maximum of $\ensuremath{\chi}(T)$ near ${T}_{max}\ensuremath{\sim}75$ K and an anisotropic cusp in $\frac{d\ensuremath{\chi}}{dT}(T)$ at ${T}_{N}\ensuremath{\sim}15$ K to signify a three-dimensional (3D) antiferromagnetic long-range ordering (LRO). The 3D LRO has been suggested from the anisotropic behavior of $\ensuremath{\chi}(T)$ with strong $c$-axis spin anisotropy and the signature of spin-flop transition from the isothermal magnetization below ${\mathit{T}}_{N}$. Analysis of magnetic heat capacity (${C}_{m}$) at ${T}_{N}\ensuremath{\sim}15$ K indicates that most of the spin entropy $(\ensuremath{\sim}92%)$ has already been released above ${T}_{N}$, which supports the picture of consecutive spin entropy reduction upon cooling with Te-bridged two-leg spin ladder system with strong intraladder and interladder couplings. Theoretical $\mathrm{DFT}+U$ calculations have been performed to search for the ground-state magnetic configuration and also to evaluate exchange-coupling constants that support the magnetic model deduced from the combined spin susceptibility and crystal structure symmetry analysis.

The effect of FM inter-ladder coupling in spin-1/2 AFM two-leg ladders in the presence of a magnetic field: Quantum Monte Carlo study

We study the effect of inter-ladder ferromagnetic (FM) coupling in spin-1/2 two-leg ladders with antiferromagnetic (AFM) legs and rungs interactions using the stochastic series expansion quantum Monte Carlo. We have compared the results with the experimental measurement on Sr14−xCaxCu24O41 cuprate which is the candidate for spin-1/2 AFM two-leg ladders with FM inter-ladder interaction. A remarkable asymptotic behavior of susceptibility is observed at very low temperature. In the absence of the magnetic field, thermodynamic behavior of an individual spin-1/2 two-leg ladder is similar to coupled one up to −0.5Jleg interaction. But, the gaped phase is not clear in the Jin=−0.2Jleg of FM coupled two-leg ladder even at low magnetic fields, which shows that the inter-ladder FM interaction can induce a new quantum ordered gapless phase at zero temperature.

Magnetic transitions in the spin-52frustrated magnetBiMn2PO6and strong lattice softening inBiMn2PO6andBiZn2PO6below 200 K

The crystallographic, magnetic, and thermal properties of polycrystalline $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ and its nonmagnetic analog $\mathrm{Bi}{\mathrm{Zn}}_{2}{\mathrm{PO}}_{6}$ are investigated by x-ray diffraction, magnetization $M$, magnetic susceptibility $\ensuremath{\chi}$, heat capacity ${C}_{p}$, and $^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) measurements versus applied magnetic field $H$ and temperature $T$ as well as by density-functional band theory and molecular-field calculations. Both compounds show a strong monotonic lattice softening on cooling, where the Debye temperature decreases by a factor of two from ${\ensuremath{\Theta}}_{\mathrm{D}}\ensuremath{\sim}650$ K at $T=300$ K to ${\ensuremath{\Theta}}_{\mathrm{D}}\ensuremath{\sim}300$ K at $T=2$ K. The $\ensuremath{\chi}(T)$ data for $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ above 150 K follow a Curie-Weiss law with a Curie constant consistent with a Mn${}^{+2}$ spin $S=5/2$ with $g$ factor $g=2$ and an antiferromagnetic (AFM) Weiss temperature ${\ensuremath{\theta}}_{\mathrm{CW}}\ensuremath{\simeq}\ensuremath{-}78$ K. The $\ensuremath{\chi}$ data indicate long-range AFM ordering below ${T}_{\mathrm{N}}\ensuremath{\simeq}30$ K, confirmed by a sharp $\ensuremath{\lambda}$-shaped peak in ${C}_{\mathrm{p}}(T)$ at 28.8 K. The magnetic entropy at 100 K extracted from the ${C}_{\mathrm{p}}(T)$ data is consistent with spin $S=5/2$ for the Mn${}^{+2}$ cations. The band-theory calculations indicate that $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$ is an AFM compound with dominant interactions ${J}_{1}/{k}_{\mathrm{B}}\ensuremath{\simeq}6.7$ K and ${J}_{3}/{k}_{\mathrm{B}}\ensuremath{\simeq}5.6$ K along the legs and rungs of a Mn two-leg spin-ladder, respectively. However, sizable and partially frustrating interladder couplings lead to an anisotropic three-dimensional magnetic behavior with long-range AFM ordering at ${T}_{\mathrm{N}}\ensuremath{\simeq}30$ K observed in the $\ensuremath{\chi}$, ${C}_{\mathrm{p}}$, and NMR measurements. A second magnetic transition at $\ensuremath{\approx}$10 K is observed from the $\ensuremath{\chi}$ and NMR measurements but is not evident in the ${C}_{\mathrm{p}}$ data. The ${C}_{\mathrm{p}}$ data at low $T$ suggest a significant contribution from AFM spin waves moving in three dimensions and the absence of a spin-wave gap. A detailed analysis of the NMR spectra indicates commensurate magnetic order between 10 and 30 K, while below 10 K additional features appear that may arise from an incommensurate modulation and/or spin canting. The commensurate order is consistent with microscopic density functional calculations that yield a collinear N\'eel-type AFM spin arrangement both within and between the ladders, despite the presence of multiple weak interactions frustrating this magnetic structure of the Mn spins. Frustration for AFM ordering and the one-dimensional spatial anisotropy of the three-dimensional spin interactions are manifested in the frustration ratio $f=|{\ensuremath{\theta}}_{\mathrm{CW}}|/{T}_{\mathrm{N}}\ensuremath{\simeq}2.6$, indicating a suppression of ${T}_{\mathrm{N}}$ from 68 K in the absence of these effects to the observed value of about 30 K in $\mathrm{Bi}{\mathrm{Mn}}_{2}{\mathrm{PO}}_{6}$.

Field-induced incommensurate phase in the strong-rung spin ladder with ferromagnetic legs

We report magnetization, specific heat, and NMR measurements of 3-Br-4-F-V [=3-(3-bromo-4-fluorophenyl)-1,5-diphenylverdazyl], a strong-rung $S=1/2$ Heisenberg spin ladder with ferromagnetic leg interactions. We explain the magnetic and thermodynamic properties based on the strong-rung regime. Furthermore, we find a field-induced successive phase transition in the specific heat and the nuclear spin-lattice relaxation rate $1/{T}_{1}$. ${}^{19}$F-NMR spectra for higher- and lower-temperature phases indicate partial magnetic order and incommensurate long-range order, respectively, evidencing the presence of frustration due to weak interladder couplings.

Magnetic ordering induced by interladder coupling in the spin-12Heisenberg two-leg ladder antiferromagnetC9H18N2CuBr4

We present specific-heat and neutron-scattering results for the $S=1/2$ quantum antiferromagnet (dimethylammonium)(3,5-dimethylpyridinium)${\mathrm{CuBr}}_{4}$. The material orders magnetically at ${\mathit{T}}_{N}=1.99(2)$ K, and magnetic excitations are accompanied by an energy gap of 0.30(2) meV due to spin anisotropy. The system is best described as coupled two-leg spin-1/2 ladders with the leg exchange ${J}_{\mathrm{leg}}=0.60(2)$ meV, rung exchange ${J}_{\mathrm{rung}}=0.64(9)$ meV, interladder exchange ${J}_{\mathrm{int}}=0.19(2)$ meV, and an interaction-anisotropy parameter $\ensuremath{\lambda}=0.93(2)$, according to inelastic neutron-scattering measurements. In contrast to most spin ladders reported to date, the material is a rare example in which the interladder coupling is very near the critical value required to drive the system to a N\'eel-ordered phase without the assistance of a magnetic field.

Charge-density wave and one-dimensional electronic spectra in blue bronze: Incoherent solitons and spin-charge separation

We present new high resolution angle resolved photoemission (ARPES) data for K$_{0.3}$MoO$_3$ (blue bronze) and propose a novel theoretical description of these results. The observed Fermi surface, with two quasi-one-dimensional sheets, is consistent with a ladder material with a weak inter-ladder coupling. Hence, we base our description on spectral properties of one-dimensional ladders. The marked broadening of the ARPES lineshape, a significant fraction of an eV, is interpreted in terms of spin-charge separation. A high energy feature, which is revealed for the first time in the spectra near the Fermi momentum thanks to improved energy resolution, is seen as a signature of a higher energy bound state of soliton excitations on a ladder.

Statics and dynamics of weakly coupled antiferromagnetic spin-12ladders in a magnetic field

We investigate weakly coupled spin-1/2 ladders in a magnetic field. The work is motivated by recent experiments on the compound (C5H12N)2CuBr4 (BPCB). We use a combination of numerical and analytical methods, in particular the density matrix renormalization group (DMRG) technique, to explore the phase diagram and the excitation spectra of such a system. We give detailed results on the temperature dependence of the magnetization and the specific heat, and the magnetic field dependence of the nuclear magnetic resonance (NMR) relaxation rate of single ladders. For coupled ladders, treating the weak interladder coupling within a mean-field or quantum Monte Carlo approach, we compute the transition temperature of triplet condensation and its corresponding antiferromagnetic order parameter. Existing experimental measurements are discussed and compared to our theoretical results. Furthermore we compute, using time dependent DMRG, the dynamical correlations of a single spin ladder. Our results allow to directly describe the inelastic neutron scattering cross section up to high energies. We focus on the evolution of the spectra with the magnetic field and compare their behavior for different couplings. The characteristic features of the spectra are interpreted using different analytical approaches such as the mapping onto a spin chain, a Luttinger liquid (LL) or onto a t-J model. For values of parameters for which such measurements exist, we compare our results to inelastic neutron scattering experiments on the compound BPCB and find excellent agreement. We make additional predictions for the high energy part of the spectrum that are potentially testable in future experiments.

Magnetostrictive Néel ordering of the spin-52ladder compound BaMn2O3: Distortion-induced lifting of geometrical frustration

The crystal structure and the magnetism of BaMn$_2$O$_3$ have been studied by thermodynamic and by diffraction techniques using large single crystals and powders. BaMn$_2$O$_3$ is a realization of a $S = 5/2$ spin ladder as the magnetic interaction is dominant along 180$^\circ$ Mn-O-Mn bonds forming the legs and the rungs of a ladder. The temperature dependence of the magnetic susceptibility exhibits well-defined maxima for all directions proving the low-dimensional magnetic character in BaMn$_2$O$_3$. The susceptibility and powder neutron diffraction data, however, show that BaMn$_2$O$_3$ exhibits a transition to antiferromagnetic order at 184 K, in spite of a full frustration of the nearest-neighbor inter-ladder coupling in the orthorhombic high-temperature phase. This frustration is lifted by a remarkably strong monoclinic distortion which accompanies the magnetic transition.

Bridging frustrated-spin-chain and spin-ladder physics: Quasi-one-dimensional magnetism ofBiCu2PO6

We derive and investigate the microscopic model of the quantum magnet BiCu2PO6 using band structure calculations, magnetic susceptibility and high-field magnetization measurements, as well as ED and DMRG techniques. The resulting quasi-one-dimensional spin model is a two-leg AFM ladder with frustrating next-nearest-neighbor couplings along the legs. The individual couplings are estimated from band structure calculations and by fitting the magnetic susceptibility with theoretical predictions, obtained using ED. The nearest-neighbor leg coupling J1, the rung coupling J4, and one of the next-nearest-neighbor couplings J2 amount to 120-150 K, while the second next-nearest-neighbor coupling is J2'~J2/2. The spin ladders do not match the structural chains, and although the next-nearest-neighbor interactions J2 and J2' have very similar superexchange pathways, they differ substantially in magnitude due to a tiny difference in the O-O distances and in the arrangement of non-magnetic PO4 tetrahedra. An extensive ED study of the proposed model provides the low-energy excitation spectrum and shows that the system is in the strong rung coupling regime. The strong frustration by the next-nearest-neighbor couplings leads to a triplon branch with an incommensurate minimum. This is further corroborated by a strong-coupling expansion up to second order in the inter-rung coupling. Based on high-field magnetization measurements, we estimate the spin gap of 32 K and suggest the likely presence of antisymmetric DM anisotropy and inter-ladder coupling J3. We also provide a tentative description of the physics of BiCu2PO6 in magnetic field, in the light of the low-energy excitation spectra and numerical calculations based on ED and DMRG. In particular, we raise the possibility for a rich interplay between one- and two-component Luttinger liquid phases and a magnetization plateau at 1/2 of the saturation value.

Luttinger liquid physics in the spin ladder material CuBr4(C5H12N)2

AbstractWe present a 14N nuclear magnetic resonance study of a single crystal of CuBr4(C5H12N)2 consisting of weakly coupled spin‐1/2 Heisenberg antiferromagnetic ladders. When placed in a magnetic field, such a ladder is theoretically predicted to exhibit a quantum critical Luttinger liquid (LL) behaviour in the gapless phase, i.e. between the two critical fields. Treating ladders as LLs and interaction between them as a perturbation, we are indeed able to fully account for (i) the spin dynamics accessed by measuring the spin–lattice relaxation rate $T_1^{ - 1}$, and for (ii) the phase transition to a 3D ordered phase occurring below 110 mK due to the weak interladder coupling.

Field-controlled magnetic order in the quantum spin-ladder system(Hpip)2CuBr4

Neutron diffraction is used to investigate the field-induced, antiferromagnetically ordered state in the two-leg spin-ladder material (Hpip)2CuBr4. This “classical” phase, a consequence of weak interladder coupling, is nevertheless highly unconventional: its properties are influenced strongly by the spin Luttinger-liquid state of the ladder subunits. We determine directly the order parameter (transverse magnetization), the ordering temperature, the spin structure, and the critical exponents around the transition. We introduce a minimal microscopic model for the interladder coupling and calculate the quantum fluctuation corrections to the mean-field interaction.

Modeling magnetic fluctuations in the stripe ordered state

In this work we study the magnetic behavior of a simple model of the stripe ordered phase of the cuprates, an array of alternating coupled doped and undoped two-leg Hubbard-type ladders. To obtain the coupled ladders' magnetic response, we employ available dynamical susceptibilities of the individual two-leg ladders and treat the interladder coupling in a random phase approximation. Strikingly, we find two possible scenarios for the ordered state induced by the coupling between ladders: the spin modulation may both occur in the conventional fashion, perpendicular to the direction of the stripes, but it may also occur parallel to the stripe direction. These two scenarios are differentiated according to different microscopic realizations of the component doped ladders. We argue that inelastic neutron scattering experiments on two stripe ordered cuprates, ${\text{La}}_{1.875}{\text{Ba}}_{0.125}{\text{CuO}}_{4}$ and ${\text{La}}_{2\ensuremath{-}x}{\text{Sr}}_{x}{\text{CuO}}_{4}$ at $x\ensuremath{\sim}0.125$, do not readily distinguish between these scenarios due to manner in which stripes form in these materials.

Fragility of string orders

One-dimensional gapped systems are often characterized by a ``hidden'' nonlocal order parameter, the so-called string order. Due to the gap, thermodynamic properties are robust against a weak higher-dimensional coupling between such chains or ladders. On the contrary, we find that the string order is not stable and decays for arbitrary weak interchain or interladder coupling. We investigate the vanishing of the order for three different systems: spin-1 Haldane chains, band insulators, and the transverse-field Ising model. Using perturbation theory and bosonization, we show that the fragility of the string order arises from nonlocal commutation relations between the nonlocal order parameter and the perturbation.