Antiferromagnetic Ladder Research Articles

Exact dynamics of two holes in two-leg antiferromagnetic ladders

Exact dynamics of two holes in two-leg antiferromagnetic ladders

Magnetically mediated hole pairing in fermionic ladders of ultracold atoms

Conventional superconductivity emerges from pairing of charge carriers—electrons or holes—mediated by phonons1. In many unconventional superconductors, the pairing mechanism is conjectured to be mediated by magnetic correlations2, as captured by models of mobile charges in doped antiferromagnets3. However, a precise understanding of the underlying mechanism in real materials is still lacking and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies predicted magnetic-mediated pairing of dopants in ladder systems4–8, in which idealized theoretical toy models explained how pairing can emerge despite repulsive interactions9. Here we experimentally observe this long-standing theoretical prediction, reporting hole pairing due to magnetic correlations in a quantum gas of ultracold atoms. By engineering doped antiferromagnetic ladders with mixed-dimensional couplings10, we suppress Pauli blocking of holes at short length scales. This results in a marked increase in binding energy and decrease in pair size, enabling us to observe pairs of holes predominantly occupying the same rung of the ladder. We find a hole–hole binding energy of the order of the superexchange energy and, upon increased doping, we observe spatial structures in the pair distribution, indicating repulsion between bound hole pairs. By engineering a configuration in which binding is strongly enhanced, we delineate a strategy to increase the critical temperature for superconductivity.

Approaching the isotropic spin-ladder regime: structure and magnetism of all-pyrazine-bridged copper(II)-based antiferromagnetic ladders.

The crystal structure and magnetic properties of two all-pyrazine-bridged antiferromagnetic spin ladders are reported. The complexes, catena-(bis(3-X-4-pyridone)(μ-pyrazine)copper(II)(-μ-pyrazine)diperchlorate ([Cu(pz)1.5(L)2](ClO4)2 where L = 3-X-4-pyridone and X = Br (1) or Cl (2)), contain copper(II)-based ladders in which both the rung and rail bridges are pyrazine molecules bonded through the x2-y2 orbital of the copper(II) ions. This structural scaffold is proposed to approach the isotropic spin-ladder regime. 1 and 2 crystallize in the monoclinic space group P21/c. Due to the bulk of the 3-X-4-HOpy ligands, the ladders are well isolated in the a-direction (1, 15.6 Å; 2, 15.5 Å). The ladders, which run in the b-direction, are stacked in the c-direction with the separation (1, 7.87 Å; 2, 7.82 Å) between copper(II) ions caused by the bulk of a semi-coordinate perchlorate ion coordinated in the axial position. Computational evaluation of magnetic JAB couplings between Cu-moieties of 2 supports the experimentally proposed magnetic topology and agrees with an isolated isotropic spin-ladder (Jrail = -4.04 cm-1 (-5.77 K) and Jrung = -3.89 cm-1 (-5.56 K)). These complexes introduce a convenient scaffold for synthesizing isotropic spin-ladders with modest superexchange interactions, the strength of which may be tuned by variations in L. The magnetic susceptibility down to 1.8 K, for both compounds, is well described by the strong-rung ladder model giving nearly isotropic exchange with Jrung ≈ Jrail ≈ -5.5 K (1) and -5.9 K (2) using the Hamiltonian. Theoretical simulations of the magnetic response of 2 using the isotropic ladder model are in excellent agreement with experiment. The measured magnetization to 5 T indicates a quantum-dominated magnetic spectrum. Again, calculated lower and saturation (4.3 and 24 T, respectively) critical fields for 2 are consistent with experimental measurements, and magnetization data at very low temperatures indeed suggest the presence of quantum effects. Further, the computational study of short- and long-range spin ordering indicates that a 2D-to-3D crossover might be feasible at lower temperatures. Analysis of the Boltzmann population corroborates the presence of accessible triplet states above the singlet ground state enabling the aforementioned 2D-to-3D crossover.

Spin filtration in an antiferromagnetic ladder

In this work we explore how a two-stranded magnetic ladder with vanishing net magnetization can be utilized to generate polarized spin current from a completely unpolarized one. Considering three different types (A-, C- and G-type) of antiferromagnetic ladders within a tight-binding framework, we make a comparative study to find the best suitable ladder for spin filtration. Our analysis can be implemented to design efficient spintronic devices with the help of antiferromagnetic materials, circumventing the use of conventional ferromagnetic systems.

Ground-state phase diagram of the dimerized spin-1/2 two-leg ladder* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11474218 and 11575116).

Dimerized spin-1/2 ladders exhibit a variety of phase structures, which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder. Using the density matrix renormalization group (DMRG) algorithm, we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J ×. Two types of spin systems, staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder, are investigated. To clarify the phase transition behaviors, we simultaneously analyze the string order parameter (SOP), the twisted order parameter (TOP), as well as a measurement of the quantum information analysis. Based on measuring this different observables, we establish the phase diagram accurately and give the fitting functions of the phase boundaries. In addition, the phase transition of cross-coupled spin ladder (in the absence of intrinsic dimerization) is also discussed.

Magnetism in an antiferromagnetic Ising nano-ladder under an applied transverse field

ABSTRACTThe phase diagram and magnetization curves of an antiferromagnetic Ising nano-ladder in an applied transverse field are investigated by using the effective-field theory with correlations. They are compared with those in the antiferromagnetic Ising ladder (or bulk). Some characteristic features, such as the reentrant phenomena, are found in these properties, when a finite transverse field h is applied or even when h = 0.0.

Magnetic-Order Crossover in Coupled Spin Ladders.

We report a novel crossover behavior in the long-range-ordered phase of a prototypical spin-1/2 Heisenberg antiferromagnetic ladder compound (C_{7}H_{10}N)_{2}CuBr_{4}. The staggered order was previously evidenced from a continuous and symmetric splitting of ^{14}N NMR spectral lines on lowering the temperature below T_{c}≃330 mK, with a saturation towards ≃150 mK. Unexpectedly, the split lines begin to further separate away below T^{*}∼100 mK, while the linewidth and the line shape remain completely invariable. This crossover behavior is further corroborated by the NMR relaxation rate T_{1}^{-1} measurements. A very strong suppression reflecting the ordering, T_{1}^{-1}∼T^{5.5}, observed above T^{*}, is replaced by T_{1}^{-1}∼T below T^{*}. These original NMR features are indicative of the unconventional nature of the crossover, which may arise from a unique arrangement of the ladders into a spatially anisotropic and frustrated coupling network.

Strong ferromagnetic exchange interaction under ambient pressure in BaFe2S3

Inelastic neutron scattering measurements have been performed to investigate the spin waves of the quasi-one-dimensional antiferromagnetic ladder compound BaFe$_2$S$_3$, where a superconducting transition was observed under pressure [H. Takahashi {\it et al.}, Nat. Mater. 14, 1008-1012 (2015); T. Yamauchi {\it et al.}, Phys. Rev. Lett. 115, 246402 (2015)]. By fitting the spherically averaged experimental data collected on a powder sample to a Heisenberg Hamiltonian, we find that the one-dimensional antiferromagnetic ladder exhibits a strong nearest neighbor ferromagnetic exchange interaction ($SJ_R=-71\pm4$ meV) along the rung direction, an antiferromagnetic $SJ_L=49\pm3$ meV along the leg direction and a ferromagnetic $SJ_2=-15\pm2$ meV along the diagonal direction. Our data demonstrate that the antiferromagnetic spin excitations are a common characteristic for the iron-based superconductors, while specific relative values for the exchange interactions do not appear to be unique for the parent states of the superconducting materials.

Dichotomy between Attractive and Repulsive Tomonaga-Luttinger Liquids in Spin Ladders.

We present a direct NMR method to determine whether the interactions in a Tomonaga-Luttinger liquid (TLL) state of a spin-1/2 Heisenberg antiferromagnetic ladder are attractive or repulsive. For the strong-leg spin ladder compound (C_{7}H_{10}N)_{2}CuBr_{4} we find that the isothermal magnetic field dependence of the NMR relaxation rate T_{1}^{-1}(H) displays a concave curve between the two critical fields bounding the TLL regime. This is in sharp contrast to the convex curve previously reported for a strong-rung ladder, (C_{5}H_{12}N)_{2}CuBr_{4}. We show that the concavity and the convexity of T_{1}^{-1}(H), which is a fingerprint of spin fluctuations, directly reflect the attractive and repulsive fermionic interactions in the TLL, respectively. The interaction sign is alternatively determined from an indirect method combining bulk magnetization and specific heat data.

Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

Magnetic excitations in the strong-leg quantum spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$ (known as DIMPY) in the field-induced Tomonaga-Luttinger spin liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual non-linear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe its ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Scattering particles in quantum spin chains

A variational approach for constructing an effective particle description of the low-energy physics of one-dimensional quantum spin chains is presented. Based on the matrix product state formalism, we compute the one- and two-particle excitations as eigenstates of the full microscopic Hamiltonian. We interpret the excitations as particles on a strongly-correlated background with non-trivial dispersion relations, spectral weights and two-particle S matrices. Based on this information, we show how to describe a finite density of excitations as an interacting gas of bosons, using its approximate integrability at low densities. We apply our framework to the Heisenberg antiferromagnetic ladder: we compute the elementary excitation spectrum and the magnon-magnon S matrix, study the formation of bound states and determine both static and dynamic properties of the magnetized ladder.

Thermodynamic properties of anisotropic spin ladder in a longitudinal magnetic field

We address thermodynamic properties of quasi-one dimensional two leg antiferromagnetic ladder in the presence of magnetic field. A generalized bond operator formalism is used to transform the spin model to a hard core bosonic gas. We have implemented Green's function approach to obtain the temperature dependence of spin excitation spectrum in field induced spin polarized phase. The results show energy gap that vanishes at critical magnetic field for fixed values of temperatures. We have also found the temperature dependence of the specific heat and magnetization component in the magnetic field direction for various magnetic field strengths and anisotropies in the Heisenberg interactions on both leg and rung couplings. At low temperatures, the specific heat is found to be monotonically increasing with temperature for magnetic fields in the spin polarized phase region. Furthermore we studied the temperature dependence of the longitudinal magnetization for different magnetic field and anisotropy parameters.

Strange correlations in spin-1 Heisenberg antiferromagnets

We study the behavior of the recently proposed "strange correlator" [Phys. Rev. Lett. {\bf 112}, 247202 (2014)] in spin-1 Heisenberg antiferromagnetic chains with uniaxial single-ion anisotropy. Using projective quantum Monte Carlo, we are able to directly access the strange correlator in a variety of phases, as well as to examine its critical behavior at the quantum phase transition between trivial and non-trivial symmetry protected topological phases. After finding the expected long-range behavior in these two symmetry conserving phases, we go on to verify the topological nature of two-leg and three-leg spin-1 Heisenberg antiferromagnetic ladders. This demonstrates the power of the strange correlator in distinguishing between trivial and non-trivial symmetry protected topological phases.

Thermal conductivity of anisotropic spin-1/2 two leg ladder: Green’s function approach

We study the thermal transport of a spin-1/2 two leg antiferromagnetic ladder in the direction of legs. The possible effect of spin-orbit coupling and crystalline electric field are investigated in terms of anisotropies in the Heisenberg interactions on both leg and rung couplings. The original spin ladder is mapped to a bosonic model via a bond-operator transformation where an infinite hard-core repulsion is imposed to constrain one boson occupation per site. The Green's function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. The thermal conductivity is found to be monotonically decreasing with temperature due to increased scattering among triplet excitations at higher temperatures. A tiny dependence of thermal transport on the anisotropy in the leg direction at low temperatures is observed in contrast to the strong one on the anisotropy along the rung direction, due to the direct effect of the triplet density. Our results reach asymptotically the ballistic regime of the spin - 1/2 Heisenberg chain and compare favorably well with exact diagonalization data.

Magnetization Process of the Spin-1/2 Two-Leg Ladder Compound (C5H12N)2 CuBr4: The Jordan-Wigner Approach

We have studied the magnetization process in the spin S = 1/2 antiferromagnetic two-leg ladder compound (C5H12N)2 CuBr4 by using the analytical fermionization technique. The magnetization and the susceptibility are calculated as functions of the temperature and the external magnetic field. The magnetization of the system shows various behaviors in different regions of the magnetic field. The field-dependence of the susceptibility is almost symmetric about the average of quantum critical fields in the low-temperature region leading to a complete agreement with the experimental results.

Attractive Tomonaga-Luttinger liquid in a quantum spin ladder.

We present NMR measurements of a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder compound (C7H10N)2CuBr4 under magnetic fields up to 15 T in the temperature range from 1.2 K down to 50 mK. From the splitting of NMR lines, we determine the phase boundary and the order parameter of the low-temperature (three-dimensional) long-range-ordered phase. In the Tomonaga-Luttinger regime above the ordered phase, NMR relaxation reflects characteristic power-law decay of spin correlation functions as 1/T1∝T(1/2K-1), which allows us to determine the interaction parameter K as a function of field. We find that field-dependent K varies within the 1<K<2 range, which signifies attractive interaction between the spinless fermions in the Tomonaga-Luttinger liquid.

Ground-state properties and quantum entanglement in rung-dimerized spin-1/2 antiferromagnetic ladder

Abstract The ground-state properties and quantum entanglement of the two-leg rung-dimerized spin-1/2 Heisenberg antiferromagnetic ladders are investigated based on the Greenʼ function combined with the Bond mean-field theory. Numerical results show that the ground-state energies do not change with the rung dimerization, and the ground-state gaps are almost proportionate to the rung dimerization coefficient δ and coupling strength α. Magnetization curves and entanglement measurements demonstrate that there are five magnetic phases, which are identified in the h – δ phase diagram. Entanglement measurements in different phases exhibit distinct behaviors, implying the fundamental differences of the five magnetic phases.

Anomalous behavior of the spin gap of a spin‐1/2 two‐leg antiferromagnetic ladder with Ising‐like rung interactions

AbstractUsing mainly numerical methods, we investigate the width of the spin gap of a spin‐1/2 two‐leg ladder described by ${\cal H} = J_{{\rm l}} \sum\nolimits_{j = 1}^{N/2} {} [{\bf S}_{j,a} \cdot {\bf S}_{j + 1,a} + {\bf S}_{j,b} \cdot {\bf S}_{j + 1,b} ] + J_{{\rm r}} \sum\nolimits_{j = 1}^{N/2} {} [\lambda (S_{j,a}^{x} S_{j,b}^{x} + S_{j,a}^{y} S_{j,b}^{y} ) + S_{j,a}^{z} S_{j,b}^{z} ]$, where $S_{j,a(b)}^{\alpha } $ denotes the α‐component of the spin‐1/2 operator at the j‐th site of the a (b) chain. We mainly focus on the $J_{{\rm r}}$ ≫ $J_{{\rm l}} &gt; 0$ and $|\lambda |\ll 1$ case. The width of the spin gap between the M = 0 and 1 subspaces (M is the total magnetization) as a function of λ anomalously increases near λ = 0; for instance, for $- 0.1 $ ≲ $\lambda$ ≲ $0.1$ when Jl/Jr = 0.1. The gap formation mechanism is thought to be different for the λ &lt; 0 and λ &gt; 0 cases. Since, in usual cases, the width of the gap becomes zero or small at the point where the gap formation mechanism changes, the above gap‐increasing phenomenon in the present case is anomalous. We explain the origin of this anomalous phenomenon by use of the degenerate perturbation theory. We also draw the ground‐state phase diagram.

Melting of a frustration-induced dimer crystal and incommensurability in theJ1-J2two-leg ladder

The phase diagram of an antiferromagnetic ladder with frustrating next-nearest neighbor couplings along the legs is determined using numerical methods (exact diagonalization and density-matrix renormalization group) supplemented by strong-coupling and mean-field analysis. Interestingly, this model displays remarkable features, bridging the physics of the J_1-J_2 chain and of the unfrustated ladder. The phase diagram as a function of the transverse coupling J_{\perp} and the frustration J_2 exhibits an Ising transition between a columnar phase of dimers and the usual rung-singlet phase of two-leg ladders. The transition is driven by resonating valence bond fluctuations in the singlet sector while the triplet spin gap remains finite across the transition. In addition, frustration brings incommensurability in the real-space spin correlation functions, the onset of which evolves smoothly from the J_1-J_2 chain value to zero in the large-J_{\perp} limit. The onset of incommensurability in the spin structure-factor and in the dispersion relation is also analyzed. The physics of the frustrated rung-singlet phase is well understood using perturbative expansions and mean-field theories in the large-J_{\perp} limit. Lastly, we discuss the effect of the non-trivial magnon dispersion relation on the thermodynamical properties of the system. The relation of this model and its physics to experimental observations on compounds which are currently investigated, such as BiCu_2PO_6, is eventually addressed.

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.