Low-lying excitations in the S = 1 antiferromagnetic Heisenberg chain

In order to confirm the picture of domain-wall excitations in the hidden antiferromagnetic order of the Haldane phase, the structure of the low-lying excitations in the S = 1 antiferromagnetic Heisenberg chain is studied by a quantum Monte Carlo method. It is confirmed that there exists a finite energy gap between the first- and the second-excited states at k = π as well as between the ground state and the first-excited state at k = π. In the thermodynamic limit, the second-excited state at k = π is separated from the ground state by the gap which is three times as large as the Haldane gap. From the size dependences of the low-lying-excitation energies, the interactions between the elementary excitations in the excited states are concluded to be repulsive.     

Two-dimensional Heisenberg model with spin s=1/2 and antiferromagnetic exchange treated as a spin liquid

The spin system of the Heisenberg model (s=1/2) on a square lattice with antiferromagnetic (AFM) exchange between nearest neighbors (in which there is no long-range magnetic order at any T≠0) is treated as a spatially homogeneous isotropic spin liquid. The double-time temperature Green’s function method is used in the framework of a second-step decoupling scheme. It is shown that, as T → 0, the spin liquid goes over (without any change in symmetry) to a singlet state with energy (per bond) ?₀=?0.352 and the correlation length diverges as ξ ∝ T ^?1 exp(T ₀/T). The spatial spin correlators oscillate in sign with distance, as in the AFM state. The theory allows one to calculate the main characteristics of the system in all temperature ranges.     

Ground state properties of S = 1 antiferromagnetic chain systems studied by ESR

Electron spin resonance (ESR) was used to study the ground state properties of two kinds of spin (S) one Heisenberg antiferromagnetic chain systems, namely a uniform chain system (HAUC), which is well known as the Haldane system, and a bond alternating chain system (HABA). To investigate and compare the features of the ground state, two nickel chain compounds doped with non-magnetic Zn²⁺ impurities were studied. The HAUC was modelled with Ni(1,3-pn)₂(μ-NO₂)(ClO₄)(1,3-pn = 1,3-propanediamine), abbreviated as NINO, while the HABA was modelled with Ni(333-tet)(μ-NO₂)(ClO₄) (333-tet = bis-(3-aminopropyl)-1,3-propanediamine), abbreviated as NTENP. Both systems have a singlet ground state with an excitation gap. The ground state of NINO approximates well to the valence bond solid state, thus producing S = 1/2 spins at the sites neighbouring the impurities. The angular dependence of the ESR signals of NINO:Zn is explained by the anisotropy of the g tensor for spin 1/2. On the other hand, the ground state of NTENP is expected to be in the singlet dimer phase based on the ratio of alternating bond strengths. In this case, it is expected that the S = 1 spins will appear at the sites neighbouring the impurities without forming the singlet dimer. From ESR studies of NTENP:Zn was observed the triplet state (S = 1), induced by the impurity doping, which is consistent with the above picture.     

Theory of muon spin relaxation by critical fluctuations in antiferromagnetic salts

Relaxation rates for positive muons implanted in antiferromagnetic salts are predicted on the basis of calculations performed with a coupled-mode theory of critical fluctuations in isotropic and uniaxial magnets. Anisotropy suppresses fluctuations transmitted by the isotropic (hyperfine) relaxation mechanism. The dipolar mechanism leads to a relaxation rate which increases on lowering the temperature to the critical point; the predicted form, proportional to the critical correlation length, yields the same temperature dependence as for the NMR linewidth. For a magnet with isotropic spin interactions, both contributions (hyperfine and dipolar) to the relaxation rate diverge with a temperature dependence given by the square-root of the correlation length.     

New polarization effect and collective excitation in S = 1/2 quasi-one-dimensional antiferromagnetic quantum spin chain

Anomalous polarization characteristics of magnetic resonance in CuGeO₃ doped with 2% Co impurity are reported. For the Faraday geometry, this mode is damped for the microwave field B _ω aligned along a certain crystallographic direction, showing that the character of magnetic oscillation differs from the standard spin precession. The observed resonance coexists with the ESR on Cu²⁺ chains; it is argued not to be caused by “impurity” EPR, as previously claimed, but to correspond to a previously unknown collective mode of magnetic oscillations in an S = 1/2 AF quantum spin chain. The text was submitted by the authors in English.     

Elementary spin excitations in a Heisenberg S=1/2 antiferromagnet with Skyrmions

The elementary spin excitations in two-dimensional Heisenberg antiferromagnets with spin S=1/2 in a metastable, spatially inhomogeneous state are investigated. The energy spectrum of the excitations, the local order parameter, and the temperature dependence of the spin correlation length are found. It is shown that the results obtained can be used to explain the experimental data on neutron scattering in La₂CuO₄ at temperatures T>T _N. Fiz. Tverd. Tela (St. Petersburg) 39, 656–659 (April 1997)     

Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.     

Low-temperature spin dynamics of a classical compressible Heisenberg chain

The dynamic spin correlation function of a classical compressible Heisenberg chain is investigated in the low temperature limit. Anharmonic processes, arising from the nonlinearity of the spin equations of motion and from the coupling of the spins to translational degrees of freedom, are taken into account to lowest order. Two-magnon processes and magnon-phonon processes contribute to the spectra. They can give rise to additional resonances but mostly their weight is very small. The main influence of the spin-phonon coupling lies in a change of the width and position of the spin-wave resonance. Comparison is made with previous work.Research assistant of the Belgian National Fund for Scientific Research (N.F.W.O.)     

The spin-1/2 antiferromagnetic Heisenberg chain with competing interactions

We investigate the thermodynamical and magnetic properties of the one dimensional spin-1/2 antiferromagnetic Heisenberg model with competing interactions near the transition between the "dimer phase" and the "frustrated phase".