A Near-Ideal Molecule-Based Haldane Spin-Chain.

Abstract

The molecular coordination complex NiI$_2$(3,5-lut)$_4$ [where (3,5-lut) $=$ (3,5-lutidine) $=$ (C$_7$H$_9$N)] has been synthesized and characterized by several techniques including synchrotron X-ray diffraction, ESR, SQUID magnetometry, pulsed-field magnetization, inelastic neutron scattering and muon spin relaxation. Templated by the configuration of 3,5-lut ligands the molecules pack in-registry with the Ni--I$\\cdots$I--Ni chains aligned along the $c$--axis. This arrangement leads to through-space I$\\cdots$I magnetic coupling which is directly measured for the first time in this work. The net result is a near-ideal realization of the $S = 1$ Haldane chain with $J = 17.5~\\rm{K}$ and energy gaps of $\\Delta^{\\parallel} = 5.3~{\\rm K}$ $\\Delta^{\\perp} =7.7~{\\rm K}$, split by the easy-axis single-ion anisotropy $D=-1.2~{\\rm K}$. The ratio $D/J = -0.07$ affords one of the most isotropic Haldane systems yet discovered, while the ratio $\\Delta_0/J = 0.40(1)$ (where $\\Delta_0$ is the average gap size) is close to its ideal theoretical value, suggesting a very high degree of magnetic isolation of the spin chains in this material. The Haldane gap is closed by orientation-dependent critical fields $\\mu_0H_{\\rm c}^{\\parallel} = 5.3~\\rm{T}$ and $\\mu_0H_{\\rm c}^{\\perp} = 4.3~\\rm{T}$, which are readily accessible experimentally and permit investigations across the entirety of the Haldane phase, with the fully polarized state occurring at $\\mu_0 H_{\\rm s}^{\\parallel}=46.0~\\rm{T}$ and $\\mu_0 H_{\\rm s}^{\\perp}=50.7~\\rm{T}$. The results are explicable within the so-called fermion model, in contrast to other reported easy-axis Haldane systems. Zero-field magnetic order is absent down to $20~{\\rm mK}$ and emergent end-chain effects are observed in the gapped state, as evidenced by detailed low-temperature measurements.