S=12ferromagnetic-antiferromagnetic alternating Heisenberg chain in a zinc-verdazyl complex

Abstract

We successfully synthesized the zinc-verdazyl complex $[{\text{Zn(hfac)}}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}(o\ensuremath{-}\mathrm{Py}\ensuremath{-}V)$ [hfac = 1,1,1,5,5,5-hexafluoroacetylacetonate; $o$-Py-V = 3-(2-pyridyl)-1,5-diphenylverdazyl], which is an ideal model compound with an $S=\frac{1}{2}$ ferromagnetic-antiferromagnetic alternating Heisenberg chain (F-AF AHC). Ab initio molecular-orbital (MO) calculations indicate that two dominant interactions ${J}_{\mathrm{F}}$ and ${J}_{\mathrm{AF}}$ form the $S=\frac{1}{2}$ F-AF AHC in this compound. The magnetic susceptibility and magnetic specific heat of the compound exhibit thermally activated behavior below approximately 1 K. Furthermore, its magnetization curve is observed up to the saturation field and directly indicates a zero-field excitation gap of 0.5 T. These experimental results provide evidence for the existence of a Haldane gap. We successfully explain the results in terms of the $S=\frac{1}{2}$ F-AF AHC through quantum Monte Carlo calculations with $|{J}_{\mathrm{AF}}/{J}_{\mathrm{F}}|=0.22$. The ab initio MO calculations also indicate a weak AF interchain interaction ${J}^{\ensuremath{'}}$ and that the coupled F-AF AHCs form a honeycomb lattice. The ${J}^{\ensuremath{'}}$ dependence of the Haldane gap is calculated, and the actual value of ${J}^{\ensuremath{'}}$ is determined to be less than $0.01|{J}_{\mathrm{F}}|$.