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

We present a model compound for the $S=1/2$ ferromagnetic Heisenberg chain composed of the verdazyl-based complex $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right][4-\mathrm{Cl}-o-\mathrm{Py}-\mathrm{V}-{(4-\mathrm{F})}_2]$. $Abinitio$ MO calculations indicate a predominant ferromagnetic interaction forming an $S=1/2$ ferromagnetic chain. The magnetic susceptibility and specific heat indicate a phase transition to an antiferromagnetic (AF) order due to the finite interchain couplings. We explain the magnetic susceptibility and magnetization curve above the phase-transition temperature based on the $S=1/2$ ferromagnetic Heisenberg chain. The magnetization curve in the ordered phase is described by a conventional AF two-sublattice model. Furthermore, the obtained magnetic specific heat reproduces the almost temperature-independent behavior of the $S=1/2$ ferromagnetic Heisenberg chain. In the low-temperature region, the magnetic specific heat exhibits a $\sqrt{T}$ dependence, which is attributed to the energy dispersion in the ferromagnetic chain.

Figure 1

(a) Molecular structure of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right][4-\mathrm{Cl}-o-\mathrm{Py}-\mathrm{V}-{(4-\mathrm{F})}_2]$. (b) Molecular pair associated with the dominant ferromagnetic interaction $J$. Hydrogen atoms are omitted for clarity. The broken line indicates N-C short contact. (c) Crystal structure forming a 1D chain along the $a$-axis, and (d) the corresponding $S=1/2$ ferromagnetic chain. (e) Crystal structure viewed parallel to the chain direction. The broken line encloses molecules comprising each chain structure.

Figure 2

Temperature dependence of magnetic susceptibility ($\chi =M/H$) of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right][4-\mathrm{Cl}-o-\mathrm{Py}-\mathrm{V}-{(4-\mathrm{F})}_2]$ at 0.05 T. The upper inset shows the temperature dependence of $\chi T$. The solid lines with open circles and open squares represent the calculated results for the isolated ferromagnetic chain and the ferromagnetic chain with the AF mean field, respectively. The lower inset shows $\chi$ in the vicinity of the phase-transition temperature at 0.05 and 0.1 T.

Figure 3

Magnetization curve of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right][4-\mathrm{Cl}-o-\mathrm{Py}-\mathrm{V}-{(4-\mathrm{F})}_2]$ at (a) 1.8 K and (b) 0.08 K. The broken line represents the Brillouin function for $S=1/2$ at 1.8 K. The solid lines represent the calculated results for (a) the $S=1/2$ ferromagnetic chain at 1.8 K by using QMC method and for (b) the AF two-sublattice model at zero temperature by using the mean-field approximation.

Figure 4

Specific heat of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right][4-\mathrm{Cl}-o-\mathrm{Py}-\mathrm{V}-{(4-\mathrm{F})}_2]$. (a) Total specific heat $C_{\mathrm{p}}$ and its magnetic contribution $C_{\mathrm{m}}$ at 0 T. The solid line with squares represents the calculated result for the $S=1/2$ ferromagnetic Heisenberg chain. (b) Low-temperature region of $C_{\mathrm{m}}$ at 0, 0.01, 0.03, and 0.1 T. The inset shows the $\sqrt{T}$ dependence of the low-temperature $C_{\mathrm{m}}$ at 0.03 and 0.1 T.