Antiferromagnetic Spin Chain Research Articles

Permutation-symmetric multicritical points in random antiferromagnetic spin chains.

We present a general theory of a class of multicritical points in the phase diagrams of random antiferromagnetic spin chains. We show that low-energy properties of these points are almost completely determined by a permutation symmetry of the effective theory not shared by the microscopic Hamiltonian. One case provides an analytic theory of the quantum critical point in the random spin-3/2 chain, studied in a recent work by Refael, Kehrein, and Fisher.

Non-Fermi-liquid behavior: Exact results for ensembles of magnetic impurities

In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.

The Effects of Zn 2+ doping on Spin-Peierls transition in CuGeO 3

Electron spin resonance (ESR) measurements on CuGeO 3 doped with Zn 2+ ions have been performed in the temperature range of 3–300 K. The ESR spectra of Cu 2+ ions have been observed to be strongly temperature dependent for both pure and doped samples. The ESR line intensity exponentially vanishes below a critical temperature, T c=14 K, for pure CuGeO 3. However, the replacement of magnetic Cu 2+ by non-magnetic Zn 2+ ion causes a drastic shift of T c to lower values, as well as significant increase in ESR signal intensity as the temperature is further decreased. The one-dimensional antiferromagnetic spin chain formed by Cu 2+ ions is broken by Zn 2+ ion, giving uncoupled spins at the end of the chains which result in an extra contribution to the spectra at lower temperatures. It is shown that the ground state of dimerized spins is singlet.

Dynamics of twists on antiferromagnetic spin chains: Theory

The equation of motion of twists on classical antiferromagnetic Heisenberg spin chains are derived. It is shown that twists interact via position- and velocity-dependent long-range two-body forces. A quiescent regime is identified wherein the system conserves momentum. With increasing kinetic energy the system exits this regime and momentum conservation is violated due to walls annihilation. A bitwist system is shown to be integrable and its exact solution is analysed. Many-twist systems are discussed and novel periodic twist lattice solutions are found on closed chains. The stability of these solutions is discussed.

SPIN CORRELATIONS IN MAGNETIZED HALDANE CHAINS

Neutron scattering experiments have been carried out in high magnetic fields to understand the magnetized state of the uniform spin-1 antiferromagnetic chain. In zero field this system has a cooperative singlet ground state with a gap to a propagating triplet excitation. The quasi-one-dimensional uniform spin-1 antiferromagnets NENP (Ni(C2D8N2)2NO2CIO4) and NDMAP (Ni(C5D14N2)2N3PF6) were examined. NENP has an alternating g-tensor such that staggered magnetization is induced for arbitrarily small fields and there is no finite field phase transition. In the high field phase the lowest energy mode has a field dependent gap and an unusually small effective spin wave velocity. NDMAP has only one spin per unit cell and hence a uniform g-tensor. This system has a critical transition at a finite field. Surprisingly the high field phase has quasi-two-dimensional or three-dimensional long-range order depending on the direction of the applied field. In the paramagnetic high field phase immediately above the ordering transition of NDMAP, there are gapless magnetic excitations that are broader in Q than the higher energy gap mode. The data is compared to theoretical predictions of a gapless incommensurate phase above the critical field.

Phase diagram of the random Heisenberg antiferromagnetic spin-1 chain.

We present a new perturbative real space renormalization group (RG) to study random quantum spin chains and other one-dimensional disordered quantum systems. The method overcomes problems of the original approach which fails for quantum random chains with spins larger than S=1/2. Since it works even for weak disorder, we are able to obtain the zero temperature phase diagram of the random antiferromagnetic Heisenberg spin-1 chain as a function of disorder. We find a random singlet phase for strong disorder. As the disorder decreases, the system shows a crossover from a Griffiths to a disordered Haldane phase.

The XXZ spin chain at Δ=−1/2: Bethe roots, symmetric functions, and determinants

A number of conjectures have been given recently concerning the connection between the antiferromagnetic XXZ spin chain at Δ=−1/2 and various symmetry classes of alternating sign matrices. Here we use the integrability of the XXZ chain to gain further insight into these developments. In doing so we obtain a number of new results using Baxter’s Q function for the XXZ chain for periodic, twisted and open boundary conditions. These include expressions for the elementary symmetric functions evaluated at the ground state solution of the Bethe roots. In this approach Schur functions play a central role and enable us to derive determinant expressions which appear in certain natural double products over the Bethe roots. When evaluated these give rise to the numbers counting different symmetry classes of alternating sign matrices.

Properties of Haldane excitations and multiparticle states in the antiferromagnetic spin-1 chain compoundCsNiCl3

We report inelastic time-of-flight and triple-axis neutron scattering measurements of the excitation spectrum of the coupled antiferromagnetic spin-1 Heisenberg chain system ${\mathrm{CsNiCl}}_{3}.$ Measurements over a wide range of wave-vector transfers along the chain confirm that above ${T}_{N} {\mathrm{CsNiCl}}_{3}$ is in a quantum-disordered phase with an energy gap in the excitation spectrum. The spin correlations fall off exponentially with increasing distance with a correlation length $\ensuremath{\xi}=4.0(2)$ sites at $T=6.2\mathrm{K}.$ This is shorter than the correlation length for an antiferromagnetic spin-1 Heisenberg chain at this temperature, suggesting that the correlations perpendicular to the chain direction and associated with the interchain coupling lower the single-chain correlation length. A multiparticle continuum is observed in the quantum-disordered phase in the region in reciprocal space where antiferromagnetic fluctuations are strongest, extending in energy up to twice the maximum of the dispersion of the well-defined triplet excitations. We show that the continuum satisfies the Hohenberg-Brinkman sum rule. The dependence of the multiparticle continuum on the chain wave vector resembles that of the two-spinon continuum in antiferromagnetic spin-1/2 Heisenberg chains. This suggests the presence of spin-1/2 degrees of freedom in ${\mathrm{CsNiCl}}_{3}$ for $T<~12 \mathrm{K},$ possibly caused by multiply frustrated interchain interactions.

µSR Study of Cu Benzoate at Very Low Temperature – Existence or Nonexistence of Long Range Order in Coupled Chains –

Zero-, longitudinal- and transverse-field µSR experiments are performed for a linear chain antiferromagnet Cu benzoate, Cu(C 6 H 5 COO)·3H 2 O, and no long range order (LRO) is found down to 20 mK. The upper limit of the ratio of the Neel temperature to the exchange coupling, k B T N / J <0.002, is even better than that of Sr 2 CuO 3 , which is known as the best candidate of S =1/2 antiferromagnetic Heisenberg quantum spin chain. Significance of our findings is discussed in view of whether there is a non-zero critical coupling ratio necessary for LRO in coupled Heisenberg chains.

Elementary Excitations in Quantum Antiferromagnetic Chains: Dyons, Spinons and Breathers

Considering experimental results obtained on three prototype compounds, TMMC, CsCoCl 3 (or CsCoBr 3 ), and Cu Benzoate, we discuss the importance of non-linear excitations in the physics of quantum (and classical) antiferromagnetic spin chains. soliton dyons spinons breathers

Large-SApproach to Chiral Phases in Frustrated Spin Chains

A large-S approach to the description of chiral phases in frustrated antiferromagnetic spin-S chains with easy-plane anisotropy is proposed. The approach is valid in the vicinity of the classical Lifshitz point j=1/4, where j is the relative strength of the frustrating next-nearest-neighbor coupling. The effective theory turns out to be the nonlinear sigma-model with the additional fourth-order term in spatial derivatives. The topological term persists for j>1/4, which leads to disappearance of the chiral gapped phase for half-integer S, in accordance with the recent numerical results.

Spectral and transport properties of quantum wires with bond disorder

Systems with bond disorder are defined through lattice Hamiltonians that are of pure nearest neighbour hopping type, i.e., do not contain on-site contributions. They stand representative for the general family of disordered systems with chiral symmetries. Application of the Dorokhov–Mello–Pereyra–Kumar transfer matrix technique P.W. Brouwer et al. [Phys. Rev. Lett 81 (1998) 862; Phys. Rev. Lett. 84 (2000) 1913] has shown that both spectral and transport properties of quasi one-dimensional systems belonging to this category are highly unusual. Most notably, regimes with absence of exponential Anderson localization are observed, the single particle density of states exhibits singular structure in the vicinity of the band centre, and the manifestation of these phenomena depends in an apparently topological manner on the even- or oddness of the channel number. In this paper we re-consider the problem from the complementary perspective of the nonlinear σ -model. Relying on the standard analogy between one-dimensional statistical field theories and zero-dimensional quantum mechanics, we will relate the problem to the behaviour of a quantum point particle subject to an Aharonov–Bohm flux. We will build on this analogy to re-derive earlier DMPK results, identify a new class of even/odd staggering phenomena (now dependent on the total number of sites in the system) and trace back the anomalous behaviour of the bond disordered system to a simple physical mechanism, viz. the flux periodicity of the quantum Aharonov–Bohm system. We will also touch upon connections to the low energy physics of other lattice systems, notably disordered chiral systems in 0 and 2 dimensions and antiferromagnetic spin chains.

Thermodynamics of the random antiferromagnetic spin-1 chain

The random exchange antiferromagnetic Heisenberg spin-1 chain at finite temperature is studied using a renormalization-group method. We follow the evolution of the bond probability distribution and calculate the free energy of the system. The spurious results found for the free energy shows that the standard renormalization group approach used for spin- 1 2 chains does not guarantee the existence of the random singlet phase in the random spin-1 chain even in the presence of strong disorder.

G-factor and linewidth of the quasi-one-dimensional Heisenberg antiferromagnet copper benzoate

The principal values and axes of the anisotropic exchange tensor in the antiferromagnetic spin chain compound Cu-benzoate are determined by electron spin resonance (ESR) at 9.5 GHz from an analysis of the temperature-dependent shift of the g-factor and the anisotropy of linewidth.

Phase diagram of an impurity in the spin-1/2 chain: two-channel Kondo effect versus Curie law.

We consider a magnetic S = 1/2 impurity in the antiferromagnetic spin chain as a function of two coupling parameters: the symmetric coupling of the impurity to two sites in the chain J1 and the coupling between the two sites J2. By using field theory arguments and numerical calculations we can identify all possible fixed points and classify the renormalization flow between them, which leads to a nontrivial phase diagram. Depending on the detailed choice of the two (frustrating) coupling strengths, the stable phases correspond either to a decoupled spin with Curie law behavior or to a non-Fermi-liquid fixed point with a logarithmically diverging impurity susceptibility as in the two-channel Kondo effect. Our results resolve a controversy about the renormalization flow.

ONE KIND OF THE GAUGE FIELD THEORY OF SPIN LADDERS

We consider a massless fermion interacting with the gauge field by Pauli interaction in which the coupling constant is dimensionless. The model is equivalent to the s=1/2 antiferromagnetic XXZ spin chain. The two flavours massless fermion of such model can describe the two-leg spin ladder system qualitatively, and there is no gapless exitation in such a system.

Helimagnetic structure ofYMn2 observed by means of nuclear magnetic resonance and neutrondiffraction

We approach the helimagnetic structure of the itinerant-electronmagnet YMn2, in which the Mn sublattice forms a geometricallyfrustrated corner-sharing tetrahedral lattice, by means of bothlow-energy neutron diffraction and precise nuclear magneticresonance (NMR) experiments, by modifying the magnetic state by Tbsubstitution (the introduction of lattice inhomogeneity), and byconsidering the origin of the tetragonal lattice distortion detectedbelow TN. The spin reorientation induced by the Tbsubstitution from the helical state with the propagation vectorQ⃗ = [τ01] (τ = 0.018) and with spins lying in the{100} plane to that with Q⃗ = [ττ1] (τ = 0.015) and {111}-plane rotation is interpreted as symmetrylowering from a coherent proper screw state with a high magneticsymmetry to an asymmetric but locally preferable configuration withthe easy-plane anisotropy perpendicular to the local symmetry axis.Treating the magnetic state as a weakly coupled assembly ofone-dimensional antiferromagnetic spin chains, which is realized asa result of the partial release of the frustration, and taking intoconsideration the lattice symmetry, the possibility of double-axialhelical structures arises and is discussed. In this study, all theinconsistency among previously reported NMR spectra is removed, andthe strong frequency dependence of the spin-echo decay time T2found unexpectedly is explained in terms of a phenomenological modeltaking into consideration the dynamic motion of electron spins inthe locally anisotropic magnetic system.

Magnetization profiles and NMR spectra of doped Haldane chains at finite temperatures

Open segments of S=1 antiferromagnetic spin chains are studied at finite temperatures and fields using continuous time Quantum Monte Carlo techniques. By calculating the resulting magnetization profiles for a large range of chain lengths with fixed field and temperature we reconstruct the experimentally measured NMR spectrum of impurity doped Y$_2$BaNi$_{1-x}$Mg$_x$O$_5$. For temperatures above the gap the calculated NMR spectra are in excellent agreement with the experimental results, confirming the existence of $S=1/2$ excitations at the end of open S=1 chain segments. At temperatures below the gap, neglecting inter chain couplings, we still find well defined peaks in the calculated NMR spectra corresponding to the $S=1/2$ chain end excitations. At low temperatures, inter chain couplings could be important, resulting in a more complicated phase.

One-Dimensional Mixed-Spin Heisenberg Antiferromagnet with Single-Ion Anisotropy in a Magnetic Field: Thermodynamics

The S = 1 and S = ½ alternating Heisenberg antiferromagnetic spin chain with single-ion anisotropy in the presence of an applied magnetic field is investigated on the basis of the Schwinger boson mean-field theory. The specific heat, the susceptibility and the magnetization as functions of temperature, the anisotropy as well as the applied field are discussed, respectively. The energy spectrum as a function of both the external field and the anisotropy is obtained. The results indicate that the single-ion anisotropy does not change so much the features of the specific heat, while the susceptibility, the magnetization and the energy gaps are remarkably affected by the external field and the anisotropy. It is observed that with varying the external field a magnetization plateau exists at very low temperature. The system appears to exhibit a ferrimagnetic longe-range order for both h ≠ 0 and D1 ≠ 0 in the ground state. Our results are compared with those obtained by other methods.

Quantum phase transition in the random antiferromagnetic spin-1 chain

We study the random antiferromagnetic spin-1 chain following the evolution of the bond probability distributions under a renormalization group transformation. We use a mapping of the spin-1 chain into an effective spin-1/2 chain with both ferromagnetic (odd bonds) and antiferromagnetic (even and odd bonds) interactions. We obtain a recursion relation for the coupling constants, solving exactly up to a four-spin cluster. Our improved perturbation treatment on these larger clusters shows that the random singlet phase in the spin-1 chain, differently from previous results, is obtained only when $100%$ of the odd bonds are strong ferromagnetic, i.e., larger than the even antiferromagnetic bonds. Otherwise the ground state is that of a dimerized spin-1/2 chain.