$S=\frac{1}{2}$ ferromagnetic-antiferromagnetic alternating Heisenberg chain in a zinc-verdazyl complex

We successfully synthesized the zinc-verdazyl complex $\left[{\text{Zn(hfac)}}_2\right]·(o-\mathrm{Py}-V)$ [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 $J^{\prime }$ and that the coupled F-AF AHCs form a honeycomb lattice. The $J^{\prime }$ dependence of the Haldane gap is calculated, and the actual value of $J^{\prime }$ is determined to be less than $0.01|J_{\mathrm{F}}|$.

Figure 1

(a) Molecular structure of [Zn(hfac)${}_2]·(o$-Py-V). Molecular packing of neighboring (b) $M_0-M_1$, (c) $M_0-M_2$, and (d) $M_0-M_3$ molecular pairs, which are associated with $J_{\mathrm{F}}$, $J_{\mathrm{AF}}$, and $J^{\prime }$, respectively. Broken lines indicate C-C and N-C short contacts. Hydrogen atoms are omitted for clarity. (e) Crystal structure forming an alternating chain consisting of $J_{\mathrm{F}}$ and $J_{\mathrm{AF}}$ along the $c$ axis, and (f) the corresponding $S=\frac{1}{2}$ F-AF AHC.

Figure 2

Temperature dependence of magnetic susceptibility ($\chi =M/H$) of [Zn(hfac)${}_2]·(o$-Py-V) at 0.1 T. The open circles denote raw data, and the open triangles are corrected for the paramagnetic term due to the impurity. The inset shows the temperature dependence of $\chi T$. The solid lines with open triangles, squares, and circles represent the calculated results for the $S=\frac{1}{2}$ F-AF AHC with $\alpha =|J_{\mathrm{AF}}/J_{\mathrm{F}}|=0.10$, 0.22, and 0.40, respectively.

Figure 3

Magnetization curve of [Zn(hfac)${}_2]·(o$-Py-V) at 0.13 K. The open triangles denote raw data, and the values of the vertical axis have been shifted by $0.1{\mu }_B/\text{f.u.}$ for clarity. The closed circles are corrected for the paramagnetic term due to the impurity. The solid line with open squares represents the calculated result for the $S=\frac{1}{2}$ F-AF AHC with $\alpha =|J_{\mathrm{AF}}/J_{\mathrm{F}}|=0.22$. The upper and the lower insets show the expansion of the low-field region and field derivative $dM/dB$, respectively.

Figure 4

Temperature dependence of magnetic specific heat of [Zn(hfac)${}_2]·(o$-Py-V) at 0 and 1.0 T. The solid lines with open circles and triangles represent the calculated results for the $S=\frac{1}{2}$ F-AF AHC with $\alpha =|J_{\mathrm{AF}}/J_{\mathrm{F}}|=0.22$ at 0 and 1.0 T, respectively. The inset shows the total specific heat.

Figure 5

$\beta =|J^{\prime }/J_{\mathrm{F}}|$ dependence of the energy gap $\Delta$ for the weakly coupled $S=\frac{1}{2}$ F-AF AHCs with $\alpha =|J_{\mathrm{AF}}/J_{\mathrm{F}}|=0.22$ and $J_{\mathrm{F}}/k_{\mathrm{B}}=-12.8$ K. The inset shows the $1/N$ dependence of $|\Delta /J_{\mathrm{F}}|$ for each $\beta$. The broken lines are fitting curves described in the text. The illustration shows the $S=\frac{1}{2}$ honeycomb lattice consisting of $J_{\mathrm{F}}$, $J_{\mathrm{AF}}$, and $J^{\prime }$.