Two-leg Spin Research Articles

Low temperature Raman study of the spin ladder compound BiCu2PO6

We have investigated the temperature (40–295K) dependence of the Raman active phonons of BiCu2PO6 single crystals oriented along a- and b- axis. The comparison between the two orientations did not show any remarkable effect along the b-axis (two-leg zigzag spin ladder direction). At low temperatures the modes appear shifted and narrowed. The spectral characteristics of the modes below ∼60 K show constant values, indicating strong coupling between the formation of spin-ladder and the crystal lattice.

Magnetic Field-Induced Phase Transitions in theS=1/2 Two-Leg Spin-Ladder Material Cu(DEP)Br2

From heat capacity ( C p ) measurements on a single crystal sample of the spin ( S ) 1/2 two-leg spin-ladder material Cu(DEP)Br 2 above a critical magnetic field ( H c0 ) where the energy gap between the singlet ground state and the excited magnetic state closes, we have observed a peak anomaly, which is indicative of a magnetic long-range ordering. We have examined how the position of the anomaly in C p changes with temperature ( T ) and magnetic field ( H ) to obtain the experimental H – T phase diagram of this S =1/2 two-leg spin ladder material. From the low-temperature specific heat below H c0 , we have evaluated the field-dependent energy gap that vanishes at about 7.6 T.

Inverse magnetocaloric effects in two-leg spin ladder system

Magnetocaloric properties of the two-leg frustrated spin ladder system are investigated by the use of transfer-matrix method. Exact results for the magnetization, entropy, entropy change and magnetocaloric cooling rate versus temperature and field are presented and discussed in detail. Large inverse magnetocaloric effects induced by the field arise at low temperature, and exhibit strong dependency relationship on the exchange couplings. In the vicinity of the critical field, the enhanced inverse magnetocaloric effects and normal magnetocaloric effects are both observed. Besides, the influences of the single-ion anisotropy on the entropy change are discussed as well.

Enhanced perturbative continuous unitary transformations

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary transformation (pCUT) among others. So far, this approach required an equidistant unperturbed spectrum. Here, we pursue two goals: First, we extend its applicability to non-equidistant spectra with the particular focus on an efficient derivation of the differential flow equations, which define the enhanced perturbative continuous unitary transformation (epCUT). Second, we show that the numerical integration of the flow equations yields a robust scheme to extract data from the epCUT. The method is illustrated by the perturbation of the harmonic oscillator with a quartic term and of the two-leg spin ladders in the strong-rung-coupling limit for uniform and alternating rung couplings. The latter case provides an example of perturbation around a non-equidistant spectrum.

Entanglement entropy of the low-lying excited states and critical properties of an exactly solvable two-leg spin ladder with three-spin interactions

In this work, we investigate an exactly solvable two-leg spin ladder with three-spin interactions. We obtain analytically the finite-size corrections of the low-lying energies and determine the central charge as well as the scaling dimensions. The model considered in this work is in the same universality class of critical behavior of the $XX$ chain with central charge $c=1$. By using the correlation matrix method, we also study the finite-size corrections of the R\'enyi entropy of the ground state and of the excited states. Our results are in agreement with the predictions of the conformal field theory.

Tensor network states and ground-state fidelity for quantum spin ladders

We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice site, a universal phase transition marker, thus offering a powerful tool to unveil quantum many-body physics underlying spin ladders. To illustrate our scheme, we consider the two-leg and three-leg Heisenberg spin ladders with staggering dimerization, the two-leg Heisenberg spin ladder with cyclic four-spin exchange, and the ferromagnetic frustrated two-leg ladder. The ground-state phase diagrams thus yielded are reliable, compared with the previous studies based on the the exact diagonalization and the density matrix renormalization group. Our results indicate that the ground-state fidelity per lattice site successfully captures quantum criticalities in spin ladders.

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

We investigate the competition between different orders in the two-leg spin ladder with a ring-exchange interaction by means of a bosonic approach. The latter is defined in terms of spin-1 hardcore bosons which treat the N\'eel and vector chirality order parameters on an equal footing. A semiclassical approach of the resulting model describes the phases of the two-leg spin ladder with a ring-exchange. In particular, we derive the low-energy effective actions which govern the physical properties of the rung-singlet and dominant vector chirality phases. As a by-product of our approach, we reveal the mutual induction phenomenon between spin and chirality with, for instance, the emergence of a vector-chirality phase from the application of a magnetic field in bilayer systems coupled by four-spin exchange interactions.

Theory ofL-edge resonant inelastic x-ray scattering for magnetic excitations in two-leg spin ladders

We study the magnetic excitation spectra of Cu ${L}_{2,3}$-edge resonant inelastic x-ray scattering (RIXS) from the spin-liquid ground state in two-leg spin ladder cuprates. By applying the projection method developed by the present authors, we have derived the formulas of the magnetic RIXS spectra, which are expressed by one- and two-spin correlation functions in the polarization changing and preserving channels, respectively. The one-spin correlation function includes both one- and two-triplon excitations and they are picked up separately by choosing rung wave vectors $\ensuremath{-}{q}_{a}=\ensuremath{\pi}$ and 0, respectively. An application to Sr${}_{14}$Cu${}_{24}$O${}_{41}$ reveals that the calculated RIXS spectrum captures well the dispersive behavior shown by the lower boundary of two-triplon continuum. An exception is absence of the intensity at zero-momentum transfer where weak but finite intensity was observed in the experiment. By adjusting the geometrical configuration of the measurement, one-triplon dispersion around the zone center could be detectable in the RIXS experiment. The observed weak intensity in the higher-energy region might be attributed to the two-spin correlation function, which could be detected more clearly at the ${M}_{3}$-edge RIXS spectra.

Quantum phase diagram of the frustrated spin ladder with next-nearest-neighbor interactions

Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J2 = 0 is carefully analyzed.

Confinement: A real-time visualization

Due to the mechanism of confinement, as known from quantum chromodynamics, it is difficult to observe individual particles carrying fractional quantum number (e.g., quark with fractional electric charge). A condensed-matter example of fractionalized particles is spinons in quasi-one-dimensional spin systems, which are domain walls in the background of N\'eel configurations carrying spin-$\frac{1}{2}$. Using the time-evolving block decimation algorithm, we visualize the nontrivial spinon dynamics induced by the confine mechanism in a two-leg spin-$\frac{1}{2}$ ladder. It can be illustrated by a simple single-particle picture of Bloch oscillation, not only qualitatively but also quantitatively. We propose the experimental realization and the real time detection of the spinon dynamics in the ultracold boson systems of ${}^{87}$Rb.

Numerical Diagonalization Study on the S = 1/2 Frustrated Three-Leg Quantum Spin Ladder Systems

The spin ladder systems have attracted a lot of interest in the field of low-dimensional physics. It is well known that the S = 1/2 two-leg spin ladder has a spin gap, while the three-leg one has a gapless spin liquid ground state. Some spin liquid behaviors were observed in the recent experiments of some frustrated systems; the distorted triangular lattice and kagome lattice antiferromagnets etc. Thus we consider the S = 1/2 three-leg spin ladder system with the next-nearest-neighbor interaction to investigate the effect of frustration on the spin liquids. Using the exact numerical diagonalization of finite-cluster systems, we study the ground state of this system. The phase diagram with respect to some exchange interaction constants is presented. It is revealed that sufficiently large next-nearest-neighbor coupling leads to a ferrimagnetic phase, which has a frustration-induced spontaneous magnetization. In addition we find two spin liquid phases, one of which corresponds to a Néel-like spin configuration and the other a collinear spin configuration. As a result of the numerical study, we find a new phase which is different from three phases.

Synthesis, structural and magnetic properties of spin ladder compound Ca1−xCoxCu2O3

MCu2O3 (M=Ca and Co) system has two-leg spin ladder structure similar to that of the prototype SrCu2O3 system except that the rungs are buckled with an angle of 123° and 105° for CaCu2O3 and CoCu2O3 compounds, respectively. We have synthesized powder samples of (Ca1−xCox)Cu2O3 (x=0.00–1.00) by the solid state reaction method and their structural and magnetic properties have been investigated. All the synthesized compounds crystallize in orthorhombic structure with space group Pmmn. Lattice parameters of (Ca1−xCox)Cu2O3 decrease with the increase in Co content. DC magnetic susceptibility χ(T) results of the end products CaCu2O3 and CoCu2O3 show antiferromagnetic transition (TN) at 27 and 215K, respectively. Co doping into (Ca1−xCox)Cu2O3 enhances its TN systematically with increasing Co concentration. The χ(T) of CoCu2O3 shows a broad transition with the peak temperature around 215K and it was found to be field independent up to 90kOe. The ambiguity concerning the transition was ruled out by recording the temperature dependent X-ray diffraction pattern on CoCu2O3 system, which indicated that there is no structural transition in the investigated temperature range of 115–300K. Further, specific heat measurement on CoCu2O3 confirms the magnetic phase transition by the appearance of a sharp peak at 215K.

Electronic Structure of the Two-Leg Spin Ladder (C5H12N)2CuBr4

A density functional theory study of the two-leg spin ladder (C(5)H(12)N)(2)CuBr(4) reveals antiferromagnetic interactions through the rungs and legs, although the latter are significantly smaller. Our work suggests interest in manipulating the physical behavior of this prototypical system by doping or chemical modifications.

Magnetic excitations in the site-centered stripe phase: Spin-wave theory of coupled three-leg ladders

The success of models of coupled two-leg spin ladders in describing the magnetic excitation spectrum of La${}_{2\ensuremath{-}x}$Ba${}_{x}$CuO${}_{4}$ had been interpreted previously as evidence for bond-centered stripes. In a recent article, however, we determined the magnetic coupling induced by the charge stripes between bond- or site-centered spin stripes modeled by two- or three-leg ladders, respectively. We found that only the site-centered models order, while the coupling in bond-centered models is insufficient to trigger the quantum phase transition into the magnetically ordered state. We further indicated excellent agreement of a fully consistent analysis of coupled three-leg ladders using a spin wave theory of bond with the experimental data. Here, we provide a full and detailed account of this analysis.

Pressure-Induced Structural, Magnetic, and Transport Transitions in the Two-Legged Ladder Sr3Fe2O5

The layered compound SrFeO(2) with an FeO(4) square-planar motif exhibits an unprecedented pressure-induced spin state transition (S = 2 to 1), together with an insulator-to-metal (I-M) and an antiferromagnetic-to-ferromagnetic (AFM-FM) transition. In this work, we have studied the pressure effect on the structural, magnetic, and transport properties of the structurally related two-legged spin ladder Sr(3)Fe(2)O(5). When pressure was applied, this material first exhibited a structural transition from Immm to Ammm at P(s) = 30 ± 2 GPa. This transition involves a phase shift of the ladder blocks from (1/2,1/2,1/2) to (0,1/2,1/2), by which a rock-salt type SrO block with a 7-fold coordination around Sr changes into a CsCl-type block with 8-fold coordination, allowing a significant reduction of volume. However, the S = 2 antiferromagnetic state stays the same. Next, a spin state transition from S = 2 to S = 1, along with an AFM-FM transition, was observed at P(c) = 34 ± 2 GPa, similar to that of SrFeO(2). A sign of an I-M transition was also observed at pressure around P(c). These results suggest a generality of the spin state transition in square planar coordinated S = 2 irons of n-legged ladder series Sr(n+1)Fe(n)O(2n+1) (n = 1, 2, 3, ...). It appears that the structural transition independently occurs without respect to other transitions. The necessary conditions for a structural transition of this type and possible candidate materials are discussed.

FIDELITY AND ENTANGLEMENT CLOSE TO QUANTUM PHASE TRANSITION IN A TWO-LEG XXZ SPIN LADDER

The fidelity susceptibility and entanglement entropy in a system of two-leg XXZ spin ladder with rung coupling is investigated by using exact diagonalization of the system. The effects of rung coupling on fidelity susceptibility, entanglement entropy, and quantum phase transition are analyzed. It is found that the quantum phase transition between two different XY phases can be well-characterized by the fidelity susceptibility. Although the quantum phase transition from XY phase to rung singlet phase can be hardly detected by fidelity susceptibility, it can be predicted by the first derivative of the entanglement entropy of the system.

Regulating low-dimensional magnetic behavior of organic radicals in crystalline hydrogen-bonded host frameworks

A series of S = ½ organic radicals—TEMPO (TEMPO = 2,2,6,6-tetramethylpiperidine-1-oxyl), 4-methoxy-TEMPO, and 4-oxo-TEMPO—have been included in the cavities of porous lamellar host frameworks constructed from guanidinium (G) cations and organodisulfonate (DS) anions, which assemble into hydrogen-bonded guanidinium sulfonate (GS) sheets connected by organodisulfonate pillars that create cavities between the sheets. The pillars can project above or below the GS sheet in different configurations, affording various architectural framework isomers whose selectivity is determined by the relative sizes of the guests and the pillars. Each framework isomer is endowed with uniquely sized and shaped cavities, which influence the molecular arrangement of the radical guests included within the host lattice. Notably, TEMPO guests in the 1-D channels of simple brick G22BPDShost (BPDS = biphenyl-4,4′-disulfonate) arrange as a two-leg ladder (a chain of dimers), whereas TEMPO guests in the cavities of zigzag brick G22NDShost (NDS = naphthalene-2,6-disulfonate) form dimers that are distributed into a 2-D square-planar lattice. The high-temperature magnetic susceptibility, χmol, conformed with Curie–Weiss behavior, with negative Weiss constants, consistent with bulk antiferromagnetic ordering. The Neel temperatures (TN) for G22BPDS·2(TEMPO) and G22NDS·2(TEMPO) were found to be 3.83 K and 4.10 K, respectively, as indicated by the presence of a broad maximum in χmol near these temperatures. In contrast, TN for host-free crystalline TEMPO is lower at 2.3 K, suggesting that enforced ordering can alter the magnetic properties of the TEMPO guests. The low-temperature χmol data for G22BPDS·2(TEMPO) agreed well with the Troyer two-leg ladder spin model, with J/kB = −7.29 K along the rungs of the ladder (intra-dimer) and J/kB = −0.45 K along the legs of the ladder (inter-dimer). The χmol data for G22NDS·2(TEMPO) agreed best with Bleaney–Bowers behavior for isolated dimers with J/kB = −3.31 K for the encapsulated TEMPO dimer. These results demonstrate that magnetic behavior, including dimensionality, can be manipulated through judicious selection of host and magnetic guests.

Entanglement storage through a spin ladder with cyclic interaction

The entanglement dynamics of two qubits coupled to a two-leg spin ladder with cyclic interaction is investigated. The entanglement is a periodic function of time and is affected by both the cyclic interaction in the ladder and the exchange interaction between the qubits and the ladder. If the number of spins in the ladder is increased with suitable external magnetic field, the maximum entanglement can exist for quite long time. Thus the entangled states can be stored and even can be "trapped" with high entanglement. The quantum manipulation of quantum states is possible in such systems.

Evidence for site-centered stripes from magnetic excitations in cuprate superconductors

The success of models of coupled two-leg spin ladders in describing the magnetic excitation spectrum of ${\text{La}}_{2\ensuremath{-}x}{\text{Ba}}_{x}{\text{CuO}}_{4}$ has been widely interpreted as evidence for bond-centered stripes. Here, we determine the magnetic coupling induced by the charge stripes between bond- or site-centered spin stripe modeled by two- or three-leg ladder, respectively. We find that only the site-centered models order. We further report excellent agreement of a fully consistent analysis of coupled three-leg ladders using a spin-wave theory of bond operators with the experiment.

Field-Induced Tomonaga-Luttinger Liquid Phase of a Two-Leg Spin-1/2 Ladder with Strong Leg Interactions

We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an S=1/2 two-leg spin ladder in the strong-leg regime.