Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: high-order coupled-cluster calculations

We investigate the ground-state magnetic long-range order of quasi-one-dimensional quantum Heisenberg antiferromagnets for spin quantum numbers s = 1/2 and s = 1. We use the coupled cluster method to calculate the sublattice magnetization and its dependence on the inter-chain coupling J_⊥. We find that for the unfrustrated spin-1/2 system, an infinitesimal inter-chain coupling is sufficient to stabilize magnetic long-range order, in agreement with results obtained by other methods. For s = 1, we find that a finite inter-chain coupling is necessary to stabilize magnetic long-range order. Furthermore, we consider a quasi one-dimensional spin-1/2 system, where a frustrating next-nearest neighbor in-chain coupling is included. We find that for stronger frustration as well, a finite inter-chain coupling is necessary to have magnetic long-range order in the ground state, and that the strength of the inter-chain coupling necessary to establish magnetic long-range order is related to the size of the spin gap of the isolated chain.     

Magnetic properties of undoped YBa 2 Cu 3 O 6 + x system

In the present paper, we study the magnetic properties of bilayer cuprate antiferromagnets. In order to evaluate the expressions for spin-wave dispersion, sublattice magnetization, Néel temperature and the magnetic contribution to the specific heat, the double time Green's function technique has been employed in the random phase approximation (RPA). The spin wave dispersion curve for a bilayer antiferromagnetic system is found to consist of one acoustic and one optic branch. The “optical magnon gap” has been attributed solely to the intra-bilayer exchange coupling (J _⊥ ) as its magnitude does not change significantly with the inter-bilayer exchange coupling (J_z). However J_z is essential to obtain the acoustic mode contribution to the magnetization. The numerical calculations show that the Néel temperature (T _N ) of the bilayer antiferromagnetic system increases with the J_z and a small change in J_z gives rise to a large change in the Néel temperature of the system. The magnetic specific heat of the system follows a T² behaviour but in the presence of J_z it varies faster than T². Received 13 July 2000 and Received in final form 14 May 2001     

Second- to first-order transition in two coupled antiferromagnetic rings

We numerically investigate an S=1/2 spin model, in which two dimerized antiferromagnetic rings interact with each other ferromagnetically. It is shown that the order of the magnetoelastic transition is strongly affected by the interring coupling J_⊥ and there may exist a critical J_⊥^* dividing the first-order transition and the continuous transition.     

Scaling behaviour of the energy gap of spin-1/2 AF-Heisenberg chains in both uniform and staggered fields

The energy gap of the 1D AF-Heisenberg model in the presence of both uniform (H) and staggered (h) magnetic fields is investigated using the exact diagonalization technique. The opening of the gap in the presence of a staggered field is found to scale with h^ν, where ν=ν(H) is the critical exponent, and depends on the uniform field. With respect to the range of the staggered magnetic field, two regimes are identified through which the dependence of the real critical exponent ν(H) on H can be calculated numerically. Our numerical results are in good agreement with the results obtained by other theoretical approaches.     

Quantum Phase Diagram of an Exactly Solved Mixed Spin Ladder

We investigate the quantum phase diagram of the exactly solved mixed spin-(1/2,1) ladder via the thermodynamic Bethe ansatz (TBA). In the absence of a magnetic field the model exhibits three quantum phases associated with su(2), su(4), and su(6) symmetries. In the presence of a strong magnetic field, there is a third and full saturation magnetization plateaux within the strong antiferromagnetic rung coupling regime. Gapless and gapped phases appear in turn as the magnetic field increases. For weak rung coupling, the fractional magnetization plateau vanishs and the model undergoes new quantum phase transitions. However, in the ferromagnetic coupling regime, the system does not have a third saturation magnetization plateau. The critical behaviour in the vicinity of the critical points is also derived systematically using the TBA.     

Charge density waves and bond order waves in a quarter filled extended Hubbard ladder

We investigate the phase diagram of a quarter filled Hubbard ladder with nearest-neighbor Coulomb repulsion using bosonization and renormalization group approach. Focusing on the strong-repulsion regime, we discuss the effect of an interchain exchange interaction J and interchain repulsion V on the possible ground states of the system and charge order configurations. Since the spin excitations always possess a gap, we find competing bond-order wave and charge density wave phases as possible ground states of the ladder model. We discuss the elementary excitations in these various phases and point an analogy between the excitations on some of these phases and those of a Kondo-Heisenberg insulator. We also study the order of the quantum phase transitions between the different ground states of the system. We obtain second order transitions in the Ising or SU(2)₂ universality class or first order transitions. We map the complete phase diagram in the J –V plane by integrating perturbative renormalization-group equations. Finally, we discuss the effect of doping away from half-filling and the effect of an applied magnetic field.     

Phase diagram for a t-J bilayer: role of interlayer couplings

The phase diagram for a t-J bilayer as a function of interplanar hopping, t_⊥ and hole concentration, x is presented for a few different values of interplanar exchange, J_⊥ using variational Monte Carlo calculations. The phase diagram shows rich features, such as a coexistence of antiferromagnetism and superconductivity at underdoping, planar (d-wave) and interplanar (d_z-wave) superconducting correlations for small and large J_⊥, respectively at optimal and overdoping. Another unusual feature appears in the form of a dome shaped structure in the phase diagram where the superconducting correlations are initially assisted as interplanar hopping is enhanced for small t_⊥, while larger t_⊥ is found to be detrimental to superconductivity.     

Magnetic properties of zig-zag ladders

We analyze the phase diagram of a system of spin-1/2 Heisenberg antiferromagnetic chains interacting through a zig-zag coupling, also called zig-zag ladders. Using bosonization techniques we study how a spin-gap or more generally plateaux in magnetization curves arise in different situations. While for coupled XXZchains, one has to deal with a recently discovered chiral perturbation, the coupling term which is present for normal ladders is restored by an external magnetic field, dimerization or the presence of charge carriers. We then proceed with a numerical investigation of the phase diagram of two coupled Heisenberg chains in the presence of a magnetic field. Unusual behaviour is found for ferromagnetic coupled antiferromagnetic chains. Finally, for three (and more) legs one can choose different inequivalent types of coupling between the chains. We find that the three-leg ladder can exhibit a spin-gap and/or non-trivial plateaux in the magnetization curve whose appearance strongly depends on the choice of coupling. Received 11 February 1999 and Received in final form 16 June 1999     

Structure determination, valence, and superexchange in the dimerized low temperature phase of α ′ - NaV 2 O 5

We report results of a new analysis for the low-temperature structure of α ^′ -NaV₂O₅ from synchrotron X-ray diffraction experiments. We confirm the existence of two inequivalent ladder structures in each vanadium layer. Based on our structural data we perform a bond-valence calculation for the vanadium sites in the low temperature state. Due to an asymmetric charge ordering we obtain only two different vanadium valences despite the three inequivalent sites. This explains the ⁵¹V-NMR observation of only two resonant peaks in the charge ordered phase. By use of a Slater-Koster method to obtain hopping matrix elements and cluster calculations we obtain effective vanadium-vanadium hoppings which compare well to LDA results. Using these in a cluster calculation we obtain a superexchange of 0.047 eV between electrons on neighbouring rungs of the same ladder for the undistorted phase. For the distorted phase we find a significant alternation in the shifts of the oxygen atoms along the legs of one of the two ladder types which leads to a significant exchange dimerisation δ _J ≈ 0.25. Received 24 November 2000     

Electrical and magnetic properties of hot extruded Bi-2223/Ag concentric tapes

Summary In this work we report on the anisotropic physical properties of silver-sheathed Bi-2223 tapes fabricated by means of hot extrusion and repeated pressing and sintering processes. The obtained Bi-2223/Ag short tapes, having critical current densitiesJ _c of 20–30 kA/cm² at 77 K, 0 T, were measured in external magnetic fields up to 0.5T applied in two different orientations (i.e. μ₀H‖(a,b)-planes and μ₀H ⊥(a,b)-planes). The magnetic characterizations were performed in a wide range of temperatures and magnetic fields to study the first magnetization curve of tapes evaluating the lower critical fields μ₀H_c1⊥ab and ⊥₀H_c1#x2016;ab and their dependences on temperature. TheJ _c values at different fields in the temperature range 4.6–90 K, calculated from the magnetization data by the critical state model, are also presented. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Quenching of the Haldane gap in LiVSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and related compounds

We report results of susceptibility χ and ⁷Li NMR measurements on LiVSi₂O₆. The temperature dependence of the magnetic susceptibility χ(T) exhibits a broad maximum, typical for low-dimensional magnetic systems. Quantitatively it is in agreement with the expectation for an S=1 spin chain, represented by the structural arrangement of V ions. The NMR results indicate antiferromagnetic ordering below T_N=24 K. The intra- and interchain coupling J and J_p for LiVSi₂O₆, and also for its sister compounds LiVGe₂O₆, NaVSi₂O₆ and NaVGe₂O₆, are obtained via a modified random phase approximation which takes into account results of quantum Monte Carlo calculations. While J_p is almost constant across the series, J varies by a factor of 5, decreasing with increasing lattice constant along the chain direction. The comparison between experimental and theoretical susceptibility data suggests the presence of an easy-axis magnetic anisotropy, which explains the formation of an energy gap in the magnetic excitation spectrum below T_N, indicated by the variation of the NMR spin-lattice relaxation rate at T≪T_N.     

Gap-behavior in the vicinity of a saturation transverse field

We have studied the behavior of the energy gap of the 1D AF spin- XXZ model in a transverse magnetic field (h) using the exact diagonalization technique. The ground state phase diagram consists of two spin-flop and paramagnetic phases. Using a modified finite-size scaling approach, we have computed the critical exponent of the energy gap in the vicinity of the critical transverse field h_c(Δ). Our numerical results confirm that the continuous phase transition from the spin-flop phase to the paramagnetic one is in the universality class of the Ising model in the transverse field (ITF). By applying conformal estimates of a small perturbation (h≪1), we have also justified our numerical results.     

Ladders in a magnetic field: a strong coupling approach

We show that non-frustrated and frustrated ladders in a magnetic field can be systematically mapped onto an XXZ Heisenberg model in a longitudinal magnetic field in the limit where the rung coupling is the dominant one. This mapping is valid in the critical region where the magnetization goes from zero to saturation. It allows one to relate the properties of the critical phase (H _c ¹, H _c ², the critical exponents) to the exchange integrals and provide quantitative estimates of the frustration needed to create a plateau at half the saturation value for different models of frustration. Received: 7 May 1998 / Revised and Accepted: 10 July 1998     

Phase diagram of the Ising square lattice with competing interactions

We restudy the phase diagram of the 2D-Ising model with competing interactions J₁ on nearest neighbour and J₂ on next-nearest neighbour bonds via Monte-Carlo simulations. We present the finite temperature phase diagram and introduce computational methods which allow us to calculate transition temperatures close to the criticalpoint at J₂ = J₁/2. Further on we investigate the character of the different phase boundariesand find that the transition is weakly first order formoderate J₂ > J₁/2.     

Magnetization plateau in the S=1/2 XXZ spin chain with period 3 magnetic field

We investigate the S=1/2 XXZ spin chain with period 3 magnetic field term. The magnetization plateau-nonplateau transition at m=±1/6 is expected to be of the Berezinski–Kosterlitz–Thouless type from the bosonization argument. By examining the level crossing of low-lying excitations numerically, we precisely determine the plateau phase diagram.     

Ground state phase diagrams and the tricritical behaviors of Ising metamagnet in both external longitudinal and transverse field

The ground state magnetic properties of a two-sublattice Ising metamegnet in both external longitudinal and transverse fields are studied within the mean-field approach. A parameter α=(Z₁J₁+Z₂J₂)/(Z₁J₁−Z₂J₂) which reflects the strength ratio of spin coupling in the plane and in adjacent planes is introduced. The ground state energy, the longitudinal staggered magnetization, the longitudinal total magnetization and the transverse total magnetization are calculated. The ground state phase diagrams in Ω−h and Ω−α plane are presented. The results show that when Ω is given, the longitudinal critical magnetic field increases when α decreases; the phase transition changes always from first order to second order with increase in the longitudinal magnetic field h or decrease in α. The reentrant phenomenon occurs in the range α?−0.66, Ω?0.21, h?0.78.     

Bilayer exchange coupling and neel temperature of YBa2Cu3O6.2

The present paper attempts to study the Neel temperature of bilayer antiferromagnetic cuprate YBa₂Cu₃O_6.2 within anisotropic Heisenberg model. The double time Green’s function formalism within random phase approximation (RPA) has been used to obtain various correlation functions. The magnetization and the Neel temperature (T _N) are evaluated. It is observed that the ratio of intrabilayer to inplane exchange coupling (r=J⊥/J‖) plays an important role in the magnetic dynamics of bilayer systems. The recent experimental data of bilayer system YBa₂Cu₃O_6.2 have been used to estimate the ratio r from the expression for Neel temperature. The estimated values of spin gap and the ratio of hopping matrix elements t⊥/t‖ are found to be in fairly good agreement with the existing experimental results.     

Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)     

Breakdown of an intermediate plateau in the magnetization process of anisotropic spin-1 Heisenberg dimer: Theory vs. experiment

The magnetization process of the spin-1 Heisenberg dimer model with the uniaxial or biaxial single-ion anisotropy is particularly investigated in connection with recent experimental high-field measurements performed on the single-crystal sample of the homodinuclear nickel(II) compound [Ni₂(Medpt)₂(μ-ox)(H₂O)₂](ClO₄)₂·2H₂O (Medpt=methyl-bis(3-aminopropyl)amine). The results obtained from the exact numerical diagonalization indicate a striking magnetization process with a marked spatial dependence on the applied magnetic field for arbitrary but finite single-ion anisotropy. It is demonstrated that the field range, which corresponds to an intermediate magnetization plateau emerging at a half of the saturation magnetization, basically depends on a single-ion anisotropy strength as well as a spatial orientation of the applied field. The breakdown of the intermediate magnetization plateau is discussed at length in relation to the single-ion anisotropy strength.     

Crystallographic anisotropy and distortions in helicoidal magnetic structure

The appearance and development of aperiodic distortions in a helicoidal, layered magnetic structure with increasing crystallographic magnetic anisotropy in the magnetization rotation plane have been theoretically studied. A simple phase diagram for this system is proposed. It is established that, at a weak anisotropy, the spiral splits into regions of various lengths with an approximately uniform rotation of the magnetization in each region and a deviation from uniformity at the boundaries; the stronger the anisotropy, the shorter the regions and the greater the deviations. In the limit of high anisotropy, the minimum energy of the system corresponds (depending on the ratio of interlayer exchange integrals J ₁ and J ₂) to either a spiral with constant angular pitch (a multiple of the angle between easy axes) or a double antiferromagnetic structure with a four-layer period. In the case of sixth-order anisotropy with |J ₁| = −J ₂, the energies of phases with different periods (four and six layers for J ₁ > 0; four and three layers for J ₁ < 0) coincide and the excess boundary energy vanishes. In the case of a fourth- and second-order anisotropy, the analogous anomalies appear at |J ₁| = −2J ₂. As a result, the magnetic structure at these points becomes unstable and the phase diagram exhibits the corresponding singularities.