Quasi One-dimensional Antiferromagnets Research Articles

Quasiparticle interactions in frustrated Heisenberg chains

Interactions between elementary excitations in quasi-one dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wavefunctions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (non integrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasi-particle excitations are bound states of topological solitons. The spin structure factor involving two quasi-particle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.

Haldane gap in the quasi-one-dimensional nonlinear σ model

This work studies the appearance of a Haldane gap in quasi one-dimensional antiferromagnets in the long wavelength limit, via the nonlinear $\sigma$-model. The mapping from the three-dimensional, integer spin Heisenberg model to the nonlinear $\sigma$-model is explained, taking into account two antiferromagnetic couplings: one along the chain axis ($J$) and one along the perpendicular planes ($J_\bot$) of a cubic lattice. An implicit equation for the Haldane gap is derived, as a function of temperature and coupling ratio $J_\bot/J$. Solutions to these equations show the existence of a critical coupling ratio beyond which a gap exists only above a transition temperature $T_N$. The cut-off dependence of these results is discussed.

Zero-point fluctuation in quasi one-dimensional antiferromagnets: theory and experiment

A systematic comparison is given of the quantum reduction in the ordered spin of quasi one-dimensional Heisenberg antiferromagnets as predicted by spin-wave theory and as measured in ionic systems with known spin-wave parameters. Simple linear theory yields a leading term (1/(2 pi ))ln(C mod J/J' mod )-1/2 where further terms can be neglected for practical purposes if mod J'/J mod <10-2; such expressions are listed for ferromagnetic and antiferromagnetic square and triangular lattices of antiferromagnetic chains with zero anisotropy. For half-integer-spin systems with 1/2<or=S<or=5/2, excellent agreement with experiment is found over the range 10-2> mod J'/J mod >10-4 when a known correction for 'kinematical interactions' is applied. It should thus be possible to identify covalency reductions in excess of 10%. For the S=1 system CsNiCl3, however, the measured spin reduction may indicate extra quantum fluctuations related to the Haldane effect. From the susceptibility behaviour, the quantum ground state for progressively smaller mod J'/J mod is argued to increasingly resemble a singlet separated from other states by an energy gap.

Finite segments, “free spins” and random exchange in spin S=1 quasi one-dimensional antiferromagnets

Magnetic susceptibility of representative examples of S=1 Heisenberg antiferromagnetic chains, AgVP 2S 6 and NENP, has a divergent low temperature contribution, in spite of the fact that the bulk susceptibility should vanish due to the presence of the Haldane gap. The divergence follows a power law T -α with α≈0.6 that is quite different from free spin paramagnetism. We propose that this contribution is due to finite segments that weakly interact to form a Random Exchange system.

Magnetic excitations in quasi one-dimensional antiferromagnets

Neutron scattering experiments have been making considerable contributions in understanding the quantum many-body problem of the one-dimensional antiferromagnet. Advanced techniques like the neutron polarization analysis and high energy chopper spectroscopy combined with the conventional triple axis spectroscopy are able to shed more light on this old, but still topical, problem. To illustrate this point the neutron scattering experiments on quasi one-dimensional antiferromagnets of ABX 3 type are described.

μSR study of hexagonal ABX 3

To elucidate the magnetic ordering process in quasi one-dimensional antiferromagnets, hexagonal ABX 3 compounds which have spin frustration among the magnetic chains on the triangular lattice, μ +SR experiments were performed on a typical Ising spin system CsCoCl 3. Below T N2 = 9 K, precession component was observed with the precession frequency extrapolated to 4.2 MHz at 0 K. In the partially disordered phase below T N1 = 21 K, a relaxation component of muon polarization is superimposed on the precession spectra due to static magnetic dipolar field indicating remarkable spin fluctuations despite of long range ordering. In the paramagnetic phase, only the relaxation component was observed. The results are interpreted in terms of domain wall solitons which propagate along the magnetic chains. The missing signal and its temperature dependence are future problems.

Neutron Scattering Study of Magnetic Excitations in a One-Dimensional Heisenberg Antiferromagnet CsVCl3

We report a high energy-resolution neutron scattering study of magnetic excitations in a one-dimensional Heisenberg antiferromagnet CsVCl 3 with S =3/2. Because of the weak antiferromagnetic coupling J '/ J ∼10 -4 in the hexagonal basal plane, the spin direction rotates by 120° with respect to the nearest neighbor spins, and the spin-wave dispersion in the basal plane consists of three branches. In the present experiment we observed an almost dispersionless mode and an acoustic branch in neutron profiles which are in good agreement with the previous studies. Accurate absolute cross-section measurements revealed, however, that the intensity of the acoustic branch could be accounted for neither by the linear spin-wave theory (the observed intensity is weaker by a factor 33) nor by the magneto-vibrational scattering (stronger by two orders of magnitude). Quantum effects, which cause large corrections in quasi-one dimensional antiferromagnets, are also discussed on the basis of the 1/ S expansion, but also fa...

Theory of the Field Dependence of the Néel Temperature in Quasi One-Dimensional Antiferromagnets

The field dependence of the Neel temperature T N of an antiferromagnet is explained by use of the Oguchi first mean field theory. It is shown that T N increases in a uniform magnetic field of appropriate magnitude when the spin entropy at T N is large. The latter condition occurs when the antiferromagnet is quasi one-dimensional with small anisotropy energy.