Two-leg Spin Research Articles

Structure and Magnetic Properties of a Family of Two-Leg Spin Ladder Compounds Ba2RE2Ge4O13 (RE = Pr, Nd, and Gd-Ho).

Compared with the intensive investigation on 3d transition metal (TM)-based spin ladder compounds, less attention has been paid to the ones constructed by rare earth (RE) ions. Herein, we report a family of RE-based spin ladder compounds Ba2RE2Ge4O13 (RE = Pr, Nd, Gd-Ho) crystallized into a monoclinic structure with the space group C2/c. The RE ions are arranged on a two-leg spin ladder motif along the b-axis, where the rung and leg exchange interactions are bridged via RE-O-RE pathways and RE-O-Ge-O-RE routes, respectively. Moreover, the much shorter rung distance in RE2O12 dimer units than the leg distance suggests that Ba2RE2Ge4O13 compounds are strong-rung spin ladder systems. All of the synthesized Ba2RE2Ge4O13 (RE = Pr, Nd, Gd-Ho) compounds exhibit dominant antiferromagnetic (AFM) interactions and the absence of magnetic order down to 1.8 K. Among the family members, Ba2Dy2Ge4O13 can be described by Jeff = 1/2 Kramers doublet states, and the low-temperature specific heat indicates the coexistence of the spin-dimerized state with a broad maximum at ∼2.4 K and long-range AFM order with TN = 0.81 K. This family of Ba2RE2Ge4O13 compounds thereby provides a rare platform to investigate the novel spin ladder physics constructed by 4f electrons.

Low-dimensional magnetic properties of the ladder-like polynuclear complex Cu2(naphac)2(OH)2 (naphac = 3-(1-naphthyl)acrylate)

The polynuclear complex Cu2(naphac)2(OH)2 consists of isolated Cu ladders in which square planar CuO4 and square-pyramidal CuO5 units are linked alternately along the crystalline a direction through their corners, and the resultant two adjacent Cu alternating chains connect each other through edges of the CuO5 units to form a ladder. The temperature dependence of the magnetic susceptibility above 50 K is reproduced by the calculation of the spin-1/2 two-leg honeycomb spin ladder model with almost zero exchange coupling between two legs of ladder. This is explained by the Jahn-Teller elongation of square-pyramidal CuO5 units. The absence of lambda-shaped peak in the specific heat down to 1.9 K suggests the existence of large quantum fluctuations of the spin owing to low-dimensional antiferromagnetic interactions.

Even-odd effects in the J1−J2 SU(N) Heisenberg spin chain

The zero-temperature phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N)$ antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general $N$. A fully gapped $\mathrm{SU}(N)$ valence bond solid made of $N$ sites is formed above a critical value of ${J}_{2}/{J}_{1}$ for all $N$. We find that the extension of this $N$-merized phase for larger values of ${J}_{2}$ strongly depends on the parity of $N$. For even $N$, the phase smoothly interpolates to the large ${J}_{2}$ regime where the model can be viewed as a zigzag $\mathrm{SU}(N)$ two-leg spin ladder. The phase exhibits both a $N$-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the $N$-merized phase with odd $N$ has only a finite extent with no incommensuration. A gapless phase in the $\mathrm{SU}{(N)}_{1}$ universality class is stabilized for larger ${J}_{2}$ that stems from the existence of a massless renormalization group flow from $\mathrm{SU}{(N)}_{2}$ to $\mathrm{SU}{(N)}_{1}$ conformal field theories when $N$ is odd.

The energy spectrum and low-temperature magnetic properties of the decorated two-leg mixed spin ladder

The energy spectra and low-temperature magnetic properties of two one-dimensional Heisenberg mixed spin (s = 1, 1/2) systems, namely decorated two-leg mixed spin ladders with the lattice topology of polyacene, are studied. The gapless character of the exact excitation energy spectra for both ladder models has been determined. We found numerically that the model with macroscopic ground state spin S0 has gapped excitations with the spin S > S0. This leads to the appearance of an intermediate plateau in field dependence of magnetization at low temperatures. We have shown that the ladder with equal coupling in legs has the maximal size of this plateau at the same coupling in rungs. For a mixed spin ladder model with Ising interactions in legs, the appearance of two intermediate magnetization plateaus at low temperatures and some values of coupling parameters was shown.

Partitioning the Two-Leg Spin Ladder in Ba2Cu1-x Zn x TeO6: From Magnetic Order through Spin-Freezing to Paramagnetism.

Ba2CuTeO6 has attracted significant attention as it contains a two-leg spin ladder of Cu2+ cations that lies in close proximity to a quantum critical point. Recently, Ba2CuTeO6 has been shown to accommodate chemical substitutions, which can significantly tune its magnetic behavior. Here, we investigate the effects of substitution for non-magnetic Zn2+ impurities at the Cu2+ site, partitioning the spin ladders. Results from bulk thermodynamic and local muon magnetic characterization on the Ba2Cu1-x Zn x TeO6 solid solution (0 ≤ x ≤ 0.6) indicate that Zn2+ partitions the Cu2+ spin ladders into clusters and can be considered using the percolation theory. As the average cluster size decreases with increasing Zn2+ substitution, there is an evolving transition from long-range order to spin-freezing as the critical cluster size is reached between x = 0.1 to x = 0.2, beyond which the behavior became paramagnetic. This demonstrates well-controlled tuning of the magnetic disorder, which is highly topical across a range of low-dimensional Cu2+-based materials. However, in many of these cases, the chemical disorder is also relatively strong in contrast to Ba2CuTeO6 and its derivatives. Therefore, Ba2Cu1-x Zn x TeO6 provides an ideal model system for isolating the effect of defects and segmentation in low-dimensional quantum magnets.

Quantum Phase Diagram of a Frustrated Spin-1/2 Ferro-Antiferromagnetic Normal Ladder.

In this work, we consider a frustrated two-leg spin-1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin-1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non-collinear ferrimagnetic (NCF), , antiferromagnetic and dimer phases. The quantum phase diagram is constructed for the Heisenberg spin-1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the stability of phase and calculate the pitch angle in the NCF phase.

Brane order and quantum magnetism in modulated anisotropic ladders

Two-leg spin-$1/2$ ladders with anisotropy and two different dimerization patterns are analyzed at zero temperature. This model is equivalent to a modulated interacting (Kitaev) ladder. The Hartree-Fock mean-field approximation reduces the model to a sum of two quadratic effective Majorana Hamiltonians, which are dual to two quantum transverse XY chains. The mapping between the effective Hamiltonian of the ladder and a pair of chains considerably simplifies calculations of the order parameters and analysis of the hidden symmetry breaking. The ground-state phase diagram of the staggered ladder contains nine phases, four of them are conventional antiferromagnets, while the other five possess nonlocal brane orders. Using the dualities and the newly found exact results for the local and string order parameters of the transverse XY chains, we were able to find analytically all the magnetizations and the brane order parameters for the staggered case, as functions of the renormalized couplings of the effective Hamiltonian. The columnar ladder has three ground-state phases and does not possess magnetic long-ranged order. The brane order parameters for these three phases are calculated numerically from the Toeplitz determinants. All brane-ordered phases are spin liquids with identified distinct order parameters, winding numbers, and sets of the Majorana edge modes. Disorder lines and the special points of disentanglement are found in both dimerization patterns. We expect this study to motivate the search for the real spin-Peierls anisotropic ladder compounds which manifest predicted properties.

Metastable magnetization plateaus in the S =1 organic spin ladder BIP-TENO induced by a microsecond-pulsed megagauss field

The entire magnetization process in the two-leg organic spin ladder BIP-TENO is studied with an ultrahigh magnetic field of up to 150 T. Nontrivial multiple magnetization plateaus are observed, indicating there exist strong quantum correlations between spins. In addition to the previously reported 1/4 plateau, another plateau appears at 1/3 magnetization only when spins are decoupled to the lattice degree of freedom in the adiabatic limit. Spontaneous symmetry breaking is expected to occur with the spin-lattice decoupling induced by a fast evolution of external magnetic fields in the range of $\ensuremath{\mu}$s. Under the adiabatic condition, five fractional (1/4, 1/3, 1/2, 2/3, and 3/4) magnetization plateaus are likely to appear with an assumption that the magnetization saturates at around 160 T.

Symmetry analysis of bond-alternating Kitaev spin chains and ladders

In this work, we analyze the nonsymmorphic symmetry-group structures for a variety of generalized Kitaev spin chains and ladders with bond alternations, including Kitaev-Gamma chain, Kitaev-Heisenberg-Gamma chain, beyond-nearest-neighbor interactions, and two-leg spin ladders. The symmetry analysis is applied to determine the symmetry-breaking patterns of several magnetically ordered phases in the bond-alternating Kitaev-Gamma spin chains, as well as the dimerization order parameters for spontaneous dimerizations. Our work is useful in understanding the magnetic phases in related models and may provide guidance for the symmetry classifications of mean field solutions in further investigations.

Absence of Spin Frustration in the Kagomé Layers of Cu2+ Ions in Volborthite Cu3V2O7(OH)2·2H2O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

We determined the spin exchanges between the Cu2+ ions in the kagomé layers of volborthite, Cu3V2O7(OH)2·2H2O, by performing the energy-mapping analysis based on DFT+U calculations, to find that the kagomé layers of Cu2+ ions are hardly spin-frustrated, and the magnetic properties of volborthite below ~75 K should be described by very weakly interacting antiferromagnetic uniform chains made up of effective S = 1/2 pseudospin units. This conclusion was verified by synthesizing single crystals of not only Cu3V2O7(OH)2·2H2O but also its deuterated analogue Cu3V2O7(OD)2·2D2O and then by investigating their magnetic susceptibilities and specific heats. Each kagomé layer consists of intertwined two-leg spin ladders with rungs of linear spin trimers. With the latter acting as S = 1/2 pseudospin units, each two-leg spin ladder behaves as a chain of S = 1/2 pseudospins. Adjacent two-leg spin ladders in each kagomé layer interact very weakly, so it is required that all nearest-neighbor spin exchange paths of every two-leg spin ladder remain antiferromagnetically coupled in all spin ladder arrangements of a kagomé layer. This constraint imposes three sets of entropy spectra with which each kagomé layer can exchange energy with the surrounding on lowering the temperature below ~1.5 K and on raising the external magnetic field B. We discovered that the specific heat anomalies of volborthite observed below ~1.5 K at B = 0 are suppressed by raising the magnetic field B to ~4.2 T, that a new specific heat anomaly occurs when B is increased above ~5.5 T, and that the imposed three sets of entropy spectra are responsible for the field-dependence of the specific heat anomalies.

Ising spin ladder with trimer rungs and next-nearest-neighbor coupling: frustration in physics and agent models

The extended model of two-leg Ising spin ladder with trimer rungs and next nearest neighbor interaction (NNN) in an external magnetic field is studied using the transfer matrix and linear renormalization group methods. In the standard version (with the same only nearest-neighbor interactions in both legs), such a ladder exhibits very interesting behavior—a frustration driven extremely sharp phase crossover at finite temperature that resembles a phase transition, impossible in one dimension. It is shown that in all considered cases with different interactions in each leg (asymmetric ladder), with NNN interactions and in the presence of small external field, such a crossover takes place when the point at which the effective interleg coupling vanishes coincides with the point at which the interleg correlation function exhibits an inflection point accompanied by the specific heat maximum. A hypothesis is formulated to describe an abrupt change in political view of the people where it is not necessary to resort to a concept of a phase transition, controversial for social systems. In some cases, this phenomenon can be understood as a phase crossover triggered by the level of frustration. The source of this frustration is proposed as an internal conflict between two areas of attitudes of the society members, personal and economic, which are shaped by personality traits possibly modified by life experience.

Quantum Phase Transitions and Finite Size Effects in Frustrated Two-Leg Spin Ladders

Quantum Phase Transitions and Finite Size Effects in Frustrated Two-Leg Spin Ladders

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

Multiple magnetization plateaus induced by farther neighbor interactions in an S=1 two-leg Heisenberg spin ladder

We study the magnetization process of the $S=1$ Heisenberg model on a two-leg ladder with farther neighbor spin-exchange interaction. We consider the interaction that couples up to the next-nearest neighbor rungs and find an exactly solvable regime where the ground states become product states. The next-nearest neighbor interaction tends to stabilize magnetization plateaus at multiples of 1/6. In most of the exactly solvable regime, a single magnetization curve shows two series of plateaus with different periodicities.

Quantum phases and thermodynamics of a frustrated spin-1/2 ladder with alternate Ising–Heisenberg rung interactions

We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropic S-type or discrete anisotropic σ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both S and σ-type of spins are anti-ferromagnetically aligned with each other, two nearest S spins along the rung form an anisotropic singlet bond whereas two nearest σ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heat C v (T), magnetic susceptibility χ(T) and thermal entropy S(T) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed from χ(T) and C v (T) curves.

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.

The Synthesis of a Quasi-One-Dimensional Iron-Based Telluride with Antiferromagnetic Chains and a Spin Glass State.

The report on the superconductivity of the two-legged spin ladders BaFe2S3 and BaFe2Se3 has established 123-type iron chalcogenides as a novel subgroup in the iron-based superconductor family and has stimulated the continuous exploration of other iron-based materials with new structures and potentially novel properties. In this paper, we report the systematic study of a new quasi-one-dimensional (1D) iron-based compound, Ba9Fe3Te15, including its synthesis and magnetic properties. The high-pressure synthesized Ba9Fe3Te15 crystallized in a hexagonal structure that mainly consisted of face-sharing FeTe6 octahedral chains running along the c axis, with a lattice constant of a = 10.23668 Å; this led to weak interchain coupling and an enhanced one-dimensionality. The systematic static and dynamic magnetic properties were comprehensively studied experimentally. The dc magnetic susceptibility showed typical 1D antiferromagnetic characteristics, with a Tmax at 190 K followed by a spin glass (SG) state with freezing at Tf ≈ 6.0 K, which were also unambiguously proved by ac susceptibility measurements. Additionally, X-ray magnetic circular dichroism (XMCD) experiments revealed an unexpected orbital moment for Fe2+, i.e., 0.84 μB per Fe in Ba9Fe3Te15. The transport property is electrically insulating, with a thermal activation gap of 0.32 eV. These features mark Ba9Fe3Te15 as an alternative type of iron-based compound, providing a diverse candidate for high-pressure studies in order to pursue some emerging physics.

Spin Gap in β-TeVO4: a Quantum Monte Carlo Study

In this paper, we proposed a two-leg spin ladder model for the description of magnetic properties of the β-TeVO4 compound. Quantum Monte Carlo (QMC) simulation was applied to describe the temperature-dependent magnetic susceptibility data for low temperatures. The two-leg spin ladder model presents a spin gap, and we suggests that β-TeVO4 compound presents such a spin gap also, and therefore, the model proposed here can be experimentally tested by measuring the spin gap of the compound. The susceptibility phase diagram has a rounded peak in the vicinity of T ≈ 12.2 K and obeys Troyer’s law for low temperatures and Curie’s law for high temperatures. We also study the susceptibility diagram in low temperatures and found the spin gap Δ = 8.06 K. The linearization of the equation for susceptibility in low temperatures allows us to obtain the spin gap value, and such a linearization was made with the data from the QMC simulation. In all the results, there is a very good agreement with the experimental data. We also show that the spin gap is null and the susceptibility is proportional to T for low temperatures when relatively high values of the ladders’ coupling is considered. The theoretical results are compared with other studies as well as applied to describe the susceptibility phase diagram of consolidated spin ladder compound, C9H18N2CuBr4.

Topological phases in two-legged Heisenberg ladders with alternating interactions

We analyze the possible existence of topological phases in two-legged spin ladders considering a staggered interaction in both chains. When the staggered interaction in one chain is shifted by one site with respect to the other chain, the model can be mapped, in the continuum limit, into a non linear sigma model NL$\sigma$M plus a topological term which is nonvanishing when the number of legs is two. This implies the existence of a critical point which distinguishes two phases. We perform a numerical analysis of energy levels, parity and string non-local order parameters, correlation functions between $x,y,z$ components of spins at the edges of an open ladder, the degeneracy of the entanglement spectrum and the entanglement entropy in order to characterize these two different phases. Finally, we identify one phase with a Mott insulator and the other one with a Haldane insulator.

Iron-Based Chalcogenide Spin Ladder BaFe2X3 (X = Se,S)

The relevance of magnetic, structural, orbital, and charge degrees of freedom in the iron-based superconductors (FeSCs) and related materials occupies a central focus in condensed matter physics. While the majority of iron-based materials exhibit the same two-dimensional iron square lattice structural motif, a family of AFe2X3 (X = Se,S) compounds introduces a quasi-one-dimensional (1D) ladder motif, which resembles the two-legged spin ladder copper oxide materials. Furthermore, unlike most parent compounds of FeSCs, the members of this spin ladder family are insulators. Recently, a superconducting transition has been observed under pressure with Tc up to 24 K, similar to the pressure-induced superconductivity in the copper oxide ladder Sr14−xCaxCu24O41 material, stimulating much interest. Here, we review the magnetic, structural, and electronic properties in this family, particularly in the BaFe2X3 series tuned by pressure and by chemical substitution. The established pressure-temperature (P-T) and carrier concentration-temperature (x-T) phase diagrams in related materials provide useful information to extend the variety of high-temperature superconductors and compare with other FeSCs. We also review some essential information about analogous square lattice FeSCs.