Consequences of critical interchain couplings and anisotropy on a Haldane chain

Abstract

Effects of interchain couplings and anisotropy on a Haldane chain have been investigated by single-crystal inelastic neutron scattering and density functional theory (DFT) calculations on the model compound ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$. Significant effects on low-energy excitation spectra are found where the Haldane gap (${\ensuremath{\Delta}}_{0}\ensuremath{\approx}0.41J$, where $J$ is the intrachain exchange interaction) is replaced by three energy minima at different antiferromagnetic zone centers due to the complex interchain couplings. Further, the triplet states are split into two branches by single-ion anisotropy. Quantitative information on the intrachain and interchain interactions as well as on the single-ion anisotropy is obtained from the analyses of the neutron scattering spectra by the random-phase approximation method. The presence of multiple competing interchain interactions is found from the analysis of the experimental spectra and is also confirmed by the DFT calculations. The interchain interactions are two orders of magnitude weaker than the nearest-neighbor intrachain interaction $J=8.7$ meV. The DFT calculations reveal that the dominant intrachain nearest-neighbor interaction occurs via nontrivial extended superexchange pathways Ni-O-V-O-Ni involving the empty $d$ orbital of V ions. The present single-crystal study also allows us to correctly position ${\mathrm{SrNi}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$ in the theoretical $D\text{\ensuremath{-}}{J}_{\ensuremath{\perp}}$ phase diagram [T. Sakai and M. Takahashi, Phys. Rev. B 42, 4537 (1990)], showing where it lies within the spin-liquid phase.