Ladder Material Research Articles

Confinement of fractional quantum number particles in a condensed-matter system

The concept of confinement states that in certain systems the constituent particles are bound together by an interaction for which the strength increases with increasing particle separation. One of the consequences of this is that these individual particles cannot be observed directly. The most famous example of confinement is found in particle physics where baryons and mesons are produced by the confinement of quarks. However, similar phenomena can occur in condensed-matter physics systems such as spin ladders that consist of two spin-1/2 antiferromagnetic chains coupled together by spin exchange interactions. Excitations of individual chains (spinons) carrying spin S=1/2, are confined by even an infinitesimal interchain coupling. Most ladders studied so far cannot illustrate this process because the large strength of their interchain coupling suppresses the spinon excitations at all energy scales. Here we present neutron scattering experiments for a weakly coupled ladder material. At high energies the behaviour of this system approaches that of individual chains, but at low energies it is dominated by the integral spin excitations of strongly coupled chains. The composition of integral quantum number particles such as protons and neutrons from the strong confinement of fractional quantum number particles such as quarks is well known in high-energy physics. Now, similar behaviour has been found in condensed-matter physics, in the excitation spectra of a weakly coupled spin-ladder compound.

Thermodynamics of the Spin Luttinger Liquid in a Model Ladder Material

The phase diagram in temperature and magnetic field of the metal-organic, two-leg, spin-ladder compound (C5H12N)2CuBr4 is studied by measurements of the specific heat and the magnetocaloric effect. We demonstrate the presence of an extended spin Luttinger-liquid phase between two field-induced quantum critical points and over a broad range of temperature. Based on an ideal spin-ladder Hamiltonian, comprehensive numerical modeling of the ladder specific heat yields excellent quantitative agreement with the experimental data across the entire phase diagram.

Muon Spin Relaxation Measurements on a Spin–Ladder Material Na2Co2(C2O4)3(H2O)2

Positive muon spin-relaxation (µ + SR) measurements on a spin–ladder material Na 2 Co 2 (C 2 O 4 ) 3 (H 2 O) 2 are reported. We find that the relaxation rate, λ, under a longitudinal field of 3950 Oe increases with decreasing temperature, T , and is a maximum at T peak ≃18 K. Below T peak , λ decreases with decreasing T . This finding implies the observation of a spin gap formation by µ + SR technique. The approach of the exponent β in the relaxation function to 0.5 with decreasing T suggests a freezing of dilute moments. Below about 5 K, we observe a sinusoidal oscillation in the time spectrum in zero applied field, which indicates an onset of long-range magnetic order. All these observations give microscopic evidence that the spin–ladder material is close to a quantum critical point.

Linear Temperature Dependence of the Magnetic Heat Conductivity inCaCu2O3

We present experimental results for the thermal conductivity kappa of the pseudo-two-leg ladder material CaCu2O3. The strong buckling of the ladder rungs renders this material a good approximation to a S=1/2 Heisenberg chain. Despite a strong suppression of the thermal conductivity of this material in all crystal directions due to inherent disorder, we find a dominant magnetic contribution kappa mag along the chain direction. kappa mag is linear in temperature, resembling the low-temperature limit of the thermal Drude weight D th of the S=1/2 Heisenberg chain. The comparison of kappamag and Dth yields a magnetic mean-free path of l mag approximately 22+/-5 A, in good agreement with magnetic measurements.

The Magnetic Property of a Uniaxial Spin–Ladder Material Na2Fe2(C2O4)3(H2O)2

Magnetic susceptibility, magnetization and heat capacity measurements are made on a single crystal sample of a spin–ladder material, Na 2 Fe 2 (C 2 O 4 ) 3 (H 2 O) 2 . The susceptibilities show a broad maximum at a temperature of about 25 K and 20 K parallel (χ || ) and perpendicular (χ ⊥ ) to the ladder direction, respectively. The maximum value of χ || is about three times larger than that of χ ⊥ . Both χ || and χ ⊥ decrease steeply at low temperatures down to about 5 K, at which χ || shows an upturn. We find a broad peak in the temperature dependence of the heat capacity. Susceptibility, magnetization and heat capacity data are used to construct the magnetic field versus temperature phase diagram of this compound. Quantum fluctuations are not strong enough to form a singlet ground-state, probably due to the presence of Ising anisotropy. The actual ground state is expected to be close to the quantum critical-point between the spin-gapped and a Néel ordered phases with the help of the inter-ladder interaction.

Thermal conductivity in the doped two-leg ladder antiferromagnet Sr 14− xCa xCu 24O 41

Within the t– J model, the heat transport of the doped two-leg ladder material Sr 14− x Ca x Cu 24O 41 is studied in the doped regime where superconductivity appears under pressure in low temperatures. The energy dependence of the thermal conductivity κ c ( ω ) shows a low-energy peak, while the temperature dependence of the thermal conductivity κ c ( T ) is characterized by a broad band. In particular, κ c ( T ) increases monotonously with increasing temperature at low temperatures T < 0.05 J , and is weakly temperature-dependent in the temperature range 0.05 J < T < 0.1 J , then decreases for temperatures T > 0.1 J , in qualitative agreement with experiments. Our result also shows that although both dressed holons and spinons are responsible for the thermal conductivity, the contribution from the dressed spinons dominates the heat transport of Sr 14− x Ca x Cu 24O 41.

Optical absorption of S= two-leg spin ladder systems

Abstract We calculate the optical absorption spectrums for the S= 1 2 two-leg spin ladder systems using continued fraction method based on Lanczos algorithm. We use two sets of parameters suggested for an S= 1 2 two-leg spin ladder material SrCu2O3. We find that due to a cyclic four-spin interaction the dispersion curve becomes flatter and hence, the large peak structure appears in the optical absorption spectrums.

Role of Umklapp processes in the conductivity of doped two-leg ladders

Recent conductivity measurements performed on the hole-doped two-leg ladder material ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ reveal an approximately linear power law regime in the c-axis dc resistivity as a function of temperature for $x=11.$ In this work, we employ a bosonic model to argue that Umklapp processes are responsible for this feature and for the high spectral weight in the optical conductivity which occurs beyond the finite frequency Drude-like peak. Including quenched disorder in our model allows us to reproduce experimental conductivity and resistivity curves over a wide range of energies.

NMR observation of charge fluctuations in quasi-one-dimensional cuprates

Results of the Cu NMR/NQR experiments are presented for the nearly quarter-filled zigzag chain compound PrBa 2Cu 4O 8 and the hole-doped two-leg ladder material Sr 14− x Ca x Cu 24O 41. A pronounced peak is found in the temperature dependence of the nuclear spin–lattice and the nuclear spin–spin relaxation rates in PrBa 2Cu 4O 8. The ratio of these rates for 63Cu and 65Cu indicates that the relaxation at the peak is caused by fluctuations of electric field gradient. Similar behavior was observed in Sr 14− x Ca x Cu 24O 41 for x>3. We propose that gradual slowing down of electronic charge fluctuations and partial charge freezing occur in these materials.

RETRACTED: Field-induced superconductivity in a spin-ladder cuprate.

We report on the modulation of the transport properties of thin films, grown by molecular beam epitaxy, of the spin-ladder compound [CaCu2O3]4, using the field effect in a gated structure. At high hole-doping levels, superconductivity is induced in the nominally insulating ladder material without the use of high-pressure or chemical substitution. The observation of superconductivity is in agreement with the theoretical prediction that holes doped into spin ladders could pair and possibly superconduct.

The electronic properties of cuprate ladder materials

We review the electronic properties of cuprate ladder materials, with a focus on so called ‘telephone number compound’ (Sr, Ca)14Cu24O41. This is the only ladder material which allows carrier doping and growth of single crystals. These features made investigations possible of transport anisotropy and frequency-dependent (optical) conductivity. One of the remarkable discoveries is the realization of superconductivity under high-pressure; however, analysis of transport dimensionality has suggested that the superconductivity is not due to Bose–Einstein condensation of singlet preformed pairs on the rungs, but due to cross-over from one- to two-dimensional electronic transport under pressure. This characterizes the superconductivity of 14-24-41 compound to be ‘anisotropic 2–d’, an extension of the category where high Tc cuprates belong to.

Conductivity of doped two-leg ladders.

Recently, conductivity measurements were performed on the hole-doped two-leg ladder material S(r14-x)Ca(x)Cu(24)O(41). In this work, we calculate the conductivity for doped two-leg ladders using a model of hole pairs forming a strongly correlated liquid. Quantum interference effects are handled using renormalization group methods. We find that our model can account for the low-energy features of the experiments. However, at higher energies there are deviations from the predictions of this model. Using the results of our calculations as well as results on the ground state of doped two-leg ladders, we suggest a scenario to explain the experimental results.

Paramagnetic resonance evidence for a spin gap in ladder material MgCu 2O 3

The electron paramagnetic resonance of Co 2+ doped into the ladder material MgCu 2O 3 shows a pronounced decrease in intensity as the temperature is lowered below room temperature, indicative of the opening of a spin gap. In the same temperature range, there is a marked increase in the parallel component, g ||, of the axially symmetric g tensor with decreasing temperatures, suggestive of the existence of antiferromagnetic spin ordering fluctuations. The gap is estimated from the data to be 40–50 meV.

Field-dependent thermodynamic properties of spin-ladder and bilayer systems

Field-dependent thermodynamic properties of two gapped spin systems, two-leg spin-ladder and square-lattice bilayer, are studied using finite-temperature perturbation theory in the strong-coupling limit. The treatment gives reasonable description of the gapped disordered phase of the systems. The free energy $F(H,T)$, susceptibility $\ensuremath{\chi}(H,T)$ and specific heat $C(H,T)$ are calculated. The susceptibility displays a maximum depending strongly on the external field, while it is insensitive to H at higher temperature. With the external field close to the lower critical value, the specific heat exhibits two-round-peak structure. These results agree quite well with the recent experimental measurements on the strongly coupled ladder material ${\mathrm{Cu}}_{2}({\mathrm{C}}_{5}{\mathrm{H}}_{12}{\mathrm{N}}_{2}{)}_{2}{\mathrm{Cl}}_{4}$ by Hammar et al.

Magnetic and superconducting properties of doped (Sr,Ca) 10Cu 17O 29-type single crystals

Magnetization, resistivity and electron spin resonance (ESR) measurements have been performed on single crystals of A 10Cu 17O 29 (A=Ca 5.9, Sr 3.5, Bi 0.3, Pb 0.1, Y 0.1, Al 0.1) of the S=1/2 quasi-one-dimensional system, which has both simple chains and two-leg ladders of copper ions. Substantial hole doping has been achieved in the studied crystals, which led to superconductivity with a high critical temperature ( T c≈80 K). The values of the penetration depth have been estimated for temperatures in the range 30–60 K using the reversible magnetization data. A rough estimation of the Ginzburg–Landau parameter, κ, indicates that the superconductivity in the investigated ladder material should be described as an extreme type-II limit. It has been suggested that the superconductivity in the studied system should be related to the two-leg ladders rather than to the chains.

The spin dynamics of (VO) 2P 2O 7: A Heisenberg spin ladder

Heisenberg spin ladders offer valuable insight into the behaviour of low dimensional magnetic systems, representing an intermediate stage between one dimensional spin chains and two dimensional lattices. We have studied the spin dynamics of the spin ladder material (VO) 2P 2O 7 by inelastic neutron scattering and have found that the observed scattering is broadly consistent with the excitation spectrum predicted by theoretical studies.

Appearance of magnetic long range order in the spin ladder compound LaCuO 2.5

We report here the two current topics in the ladder compounds. 1. The new ladder compound LaCuO2.5 recently discovered by Hiroi and Takano shows a clear sign of magnetic long range order at around 125 K observed by μ+SR technique. This result demonstrates that the ground state of LaCuO2.5 is not a spin liquid state, but a magnetically ordered state. 2. Superconductivity has been found in the ladder material (Sr,Ca)14Cu24O41 under high pressure between 3 GPa and 4.5 GPa. The superconducting transition temperatures Tc (onset) are 12 K and 9 K at 3 GPa and 4.5 GPa, respectively.

Superconductivity in the Ladder Material Sr0.4Ca13.6Cu24O41.84

We have observed superconductivity in the ladder material Sr 0.4 Ca 13.6 Cu 24 O 41.84 under pressures of 3 GPa and 4.5 GPa by means of electrical measurements. The superconducting transition temperatures T c (onset) are 12 K and 9 K at 3 and 4.5 GPa, respectively. The superconducting volume fraction was obtained to be about 5% from magnetization measurement under 3.5 GPa at 4.2 K, indicating the bulk nature of the superconductivity in this system.

Observation of a spin gap in SrCu2O3 comprising Ssin-12 quasi-1D two-leg ladders.

Magnetic properties of Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{Sr}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{5}$, containing two-leg and three-leg $S=\frac{1}{2}$ ladders made of antiferromagnetic Cu-O-Cu linear bonds, were investigated. The susceptibility of the two-leg ladder material, Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$, is characteristic of thermal excitation from a nonmagnetic ground state with a spin gap of about 420 K, while the susceptibility of ${\mathrm{Sr}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{5}$, containing three-leg ladders, reflects a gapless spin excitation spectrum. The temperature dependence of the nuclear-spin lattice relaxation rate, $\frac{1}{{T}_{1}}$, of $^{63}\mathrm{Cu}$ NMR also indicates the existence of a spin gap only for Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$. The spin gap we observed for Sr${\mathrm{Cu}}_{2}$${\mathrm{O}}_{3}$ confirms a recent theoretical prediction for the magnetic behavior of spin = \textonehalf{} antiferromagnetically coupled Heisenberg chains.