A full description of a series of spin-wave measurements in
CsNiCl3 in the three-dimensional (3D) and one-dimensional (1D) phases and their analysis to provide the first experimental evidence for the Haldane gap is presented. Neutron scattering experiments were performed on a single crystal of
CsNiCl3 with both (h,0,l) and (h,h,l) as the scattering plane. The order parameter in both 3D phases was measured and the spin-wave dispersion determined in the lower phase. The spin-wave spectrum calculated from a dynamic susceptibility method was compared with the experimental response in the lower 3D phase to obtain the following values for the exchange and anisotropy constants: J=0.345\ifmmode\pm\else\textpm\fi{}0.008 THz, J'=0.0060\ifmmode\pm\else\textpm\fi{}0.005 THz, and D=-0.0130\ifmmode\pm\else\textpm\fi{}0.0015 THz. These parameters confirm that
CsNiCl3 in its disordered phase is a good approximation to a one-dimensional Heisenberg antiferromagnet. In the 1D phase the gap frequency for an isolated chain of
Ni2+ ions is found to be 0.32 THz close to the gap estimated in finite-chain calculations. The results constitute experimental support for the Haldane conjecture that the excitations of integer-spin chains, unlike half-integer--spin chains, exhibit an apparent anisotropy that arises not from the underlying isotropic Hamiltonian, but from many-body effects.
Two quasi-one-dimensional
S=1 quantum antiferromagnetic materials,
PbNi2V2O8 and
SrNi2V2O8, are studied by inelastic neutron scattering on powder samples. A simple model Hamiltonian is proposed for the two systems and used to analyze the data. Quantitative information on in-chain and interchain interactions obtained from this analysis is discussed in the context of qualitatively different ground-state properties: magnetic long-range order in
SrNi2V2O8 and disordered ``spin liquid'' Haldane-gap state in
PbNi2V2O8.We investigate the zero-temperature and the finite-temperature properties of the two-dimensional antiferromagnetic quantum spin system composed of the
s=1/2 and
s=1 spins. The spin excitation spectrum as well as the thermodynamic quantities are computed by means of the Schwinger-boson mean-field theory. We discuss how the magnetic double structure with the gapful and the gapless excitations is generated, and apply the results systematically to the Haldane gap system in a staggered magnetic field and also to the weakly coupled ferrimagnetic mixed-spin chains. It is confirmed that the results obtained are consistent with the experiments for the quasi-one-dimensional Haldane compounds
R2BaNiO5.The quantum phases of one-dimensional spin
s=1/2 chains are discussed for models with two parameters, frustrating exchange
g=J2>0 between second neighbors and normalized nonfrustrating power-law exchange with exponent $\ensuremath{\alpha}$ and distance dependence ${r}^{\ensuremath{-}\ensuremath{\alpha}}$. The ground state (GS) at
g=0 has a long-range order (LRO) for $\ensuremath{\alpha}<2$ and long-range spin fluctuations for $\ensuremath{\alpha}>2$. The models conserve total spin
S=SA+SB, have singlet GS for any
g, $\ensuremath{\alpha}\ensuremath{\ge}0$ and decouple at
1/g=0 to linear Heisenberg antiferromagnets on sublattices
A and
B of odd- and even-numbered sites. Exact diagonalization of finite chains gives the sublattice spin $\ensuremath{\langle}{S}_{A}^{2}\ensuremath{\rangle}$, the magnetic gap
Em to the lowest triplet state, and the excitation ${E}_{\ensuremath{\sigma}}$ to the lowest singlet with opposite inversion symmetry to the GS. An analytical model that conserves sublattice spin has a first-order quantum transition at
gc=1/4ln2 from a GS with perfect LRO to a decoupled phase with
SA=SB=0 for $g\ensuremath{\ge}4/{\ensuremath{\pi}}^{2}$ and no correlation between spins in different sublattices. The model with $\ensuremath{\alpha}=1$ has a first-order transition to a decoupled phase that closely resembles the analytical model. The bond order wave (BOW) phase and continuous quantum phase transitions of finite models with $\ensuremath{\alpha}\ensuremath{\ge}2$ are discussed in terms of GS degeneracy where ${E}_{\ensuremath{\sigma}}(g)=0$, excited state degeneracy where ${E}_{\ensuremath{\sigma}}(g)={E}_{m}(g)$, and $\ensuremath{\langle}{S}_{A}^{2}\ensuremath{\rangle}$. The decoupled phase at large frustration has nondegenerate GS for any exponent $\ensuremath{\alpha}$ and excited states related to sublattice excitations.
Mixed-spin systems composed of quantum spin chains with gapped magnetic excitations interacting through `auxiliary' magnetic ions show an effective separation between low-frequency classical and high-frequency quantum spin correlations. This phenomenon is realized in a family of rare-earth nickelates. Studies of these materials enable experimental measurements of some previously inaccessible fundamental properties of quantum spin chains to be made. The non-trivial intrinsic dynamics of the auxiliary spins gives rise to peculiar excitations of a mixed nature, and in certain cases may play a key role in long-range magnetic ordering.
In 1983, F. Duncan M. Haldane predicted a singlet ground state for isolated integer-spin one-dimensional antiferromagnets with low single-ion anisotropy D. Since then, a lot of species containing chains of integer spin ions were tested to check the basic conjecture on an energy gap separating the continuum of the excited states from the ground state. As a result of these studies, it has been established that there are numerous states competing with the Haldane phase, namely long-range ordered, dimerized, and large-D phases. The long-range magnetic order takes place due to sufficiently strong exchange interactions between adjacent chains. Dimerization results from the alternation of the exchange interactions within the chains. Both uniaxial and rhombic single-ion anisotropies can suppress the Haldane phase, which is robust only until some critical values. The choice between the competing phases depends also on exchange anisotropy. Excellent reviews on the basic results obtained during the first 20 years of investigation of these phenomena provided solid background for the future studies. Here, we present some developments in this field obtained over the next two decades of research on spin-1 chain systems.