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 $J=17.5\mathrm{K}$ and energy gaps of ${\Delta }^{\parallel }=5.3\mathrm{K}$ ${\Delta }^{\perp }=7.7\mathrm{K}$, split by the easy-axis single-ion anisotropy $D=-1.2\mathrm{K}$. 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 ${\mu }_0{H}_{\mathrm{c}}^{\parallel }=5.3\mathrm{T}$ and ${\mu }_0{H}_{\mathrm{c}}^{\perp }=4.3\mathrm{T}$, which are readily accessible experimentally and permit investigations across the entirety of the Haldane phase, with the fully polarized state occurring at ${\mu }_0{H}_{\mathrm{s}}^{\parallel }=46.0\mathrm{T}$ and ${\mu }_0{H}_{\mathrm{s}}^{\perp }=50.7\mathrm{T}$. 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 $20\mathrm{mK}$ and emergent end-chain effects are observed in the gapped state, as evidenced by detailed low-temperature measurements.

13 pages, 8 figures plus supporting information