Effective $S=2$ antiferromagnetic spin chain in the salt ($o$-MePy-V)${\mathrm{FeCl}}_4$

We present a model compound for the $S=2$ antiferromagnetic (AF) spin chain composed of the salt ($o$-MePy-$\mathrm{V}){\mathrm{FeCl}}_4$. Ab initio molecular-orbital calculations indicate the formation of a partially stacked two-dimensional (2D) spin model comprising five types of exchange interactions between $S=1/2$ and $S=5/2$ spins, which locate on verdazyl radical and Fe ion, respectively. The magnetic properties of the synthesized crystals indicate that the dominant interaction between the $S=1/2$ and $S=5/2$ spins stabilizes an $S=2$ spin in the low-temperature region, and an effective $S=2$ AF chain is formed for $T\ll 10$ K and $H<4$ T. We explain the magnetization curve and electron-spin-resonance modes quantitatively based on the $S=2$ AF chain. At higher fields above quantitatively 4 T, the magnetization curve assumes two-thirds of the full saturation value for fields between 4 and 20 T, and approaches saturation at $\sim 40$ T. The spin model in the high-field region can be considered as a quasi-2D $S=1/2$ honeycomb lattice under an effective internal field caused by the fully polarized $S=5/2$ spin.

Figure 1

(a) Molecular structure of ($o$-MePy-$\mathrm{V}){\mathrm{FeCl}}_4$. Molecular pairs associated with exchange interactions (b) $J_1$, (c) $J_2$, (d) $J_3$, (e) $J_4$, and (f) $J_5$. Hydrogen atoms are omitted for clarity. The broken lines indicate short contact related to the rings with high spin-density distributions. Crystal structure in the (g) $bc$ and (h) $ab$ planes. The broken lines represent the honeycomb lattice composed of $J_3$ and $J_4$.

Figure 2

(a) 2D spin model composed of $J_i$ ($i=1$–4) with $S_{\mathrm{V}}=1/2$ and $S_{\mathrm{Fe}}=5/2$. (b) 1D chain composed of exchange path of $S_{\mathrm{Fe}}-S_{\mathrm{V}}-S_{\mathrm{Fe}}$ ($J_1-J_2$) and effective $S_{\mathrm{hy}}=2$ AF chain.

Figure 3

Temperature dependence of magnetic susceptibility ($\chi =M/H$) of ($o$-MePy-$\mathrm{V}){\mathrm{FeCl}}_4$ at 0.1 and 1.0 T. The inset shows the temperature dependence of $\chi T$. The solid line represents the calculated result for the $S_{\mathrm{V}}-S_{\mathrm{Fe}}$ dimer coupled by $J_1$.

Figure 4

Specific heat of ($o$-MePy-$\mathrm{V}){\mathrm{FeCl}}_4$ at 0, 2, 4, 7 T. The arrows indicate the phase-transition temperatures. For clarity, the values for 2, 4, and 7 T have been shifted up by 8.5, 16, 21 $\text{J}{\mathrm{mol}}^{-1}$ K, respectively.

Figure 5

Magnetization curve of ($o$-MePy-$\mathrm{V}){\mathrm{FeCl}}_4$ (a) below 5 T at 1.8 K and (b) up to 53 T at 1.4 K. The broken and solid lines represent the calculated result for the $S=2$ AF chain with $J_{AF}/k_{\mathrm{B}}=0.52$ K at 0 and 1.8 K, respectively. The arrow indicates sharp peak of $dM/dH$ associated with the spin-flop transition at $H_{\mathrm{SF}}$. The horizontal lines indicate full saturation $M_{\mathrm{s}}$ and $\text{2/3}{M}_{\mathrm{s}}$ considering the sample purity of $96\%$.

Figure 6

Frequency dependence of ESR absorption spectra of ($o$-MePy-$\mathrm{V}){\mathrm{FeCl}}_4$ at 1.8 K for (a) directly detected high frequencies and (b) low frequencies measured by cylindrical high-sensitivity cavities. The arrows indicate resonance signals.

Figure 7

Frequency-field plot of the ESR resonance fields at 1.8 K. The solid and broken lines are calculated AF resonance modes for the principal axes with high and low transition probabilities, respectively. The discontinuous changes of the lines correspond to the spin-flop transition at $H_s$.