Various regimes of quantum behavior in an $S=\frac{1}{2}$ Heisenberg antiferromagnetic chain with fourfold periodicity

We have succeeded in synthesizing single crystals of the verdazyl radical $\beta$-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl. The $ab$ $initio$ molecular orbital calculation indicates the formation of an $S=1/2$ Heisenberg antiferromagnetic chain with fourfold magnetic periodicity consisting of three types of exchange interactions. We successfully explain the magnetic and thermodynamic properties based on the expected spin model by using the quantum Monte Carlo method. Furthermore, we reveal that the alternating and unique Ising ferromagnetic chains become effective in the specific field regions and observe a cooperative phenomenon caused by the magnetic order and quantum fluctuations. These results demonstrate that the verdazyl radical could form an unconventional spin model with interesting quantum behavior and provide a way to study a variety of quantum spin systems.

Figure 1

(a) The molecular structure of $\beta$-2,6-Cl${}_2$-V. (b) Crystal structure forming a chain along the $a$ axis, and (c) corresponding $S=1/2$ HAFC with fourfold magnetic periodicity. (d) Molecular packing associated with the interchain interaction $J^{\prime }$. Broken lines indicate C-C and N-C short contacts. Hydrogen atoms are omitted for clarity.

Figure 2

Temperature dependence of magnetic susceptibility ($\chi =M/H$) and $\chi T$ of $\beta$-2,6-Cl${}_2$-V at 0.5 T. The solid lines represent the calculated results for the $S=1/2$ HAFC with fourfold periodicity.

Figure 3

Magnetization curves of $\beta$-2,6-Cl${}_2$-V at 1.3 K in high-magnetic fields. The lower inset shows those at 0.15, 0.30, and 0.60 K in the low-field region; the upper inset shows their field derivative $dM/dH$. The arrows indicate phase transition fields. For clarity, the values of the vertical axes have been shifted arbitrarily. The solid lines with open squares represent the calculated results for the $S=1/2$ HAFC with fourfold periodicity.

Figure 4

Temperature dependence of (a) magnetic susceptibility $\chi$ and (b) $C_{\mathrm{m}}/T$ of $\beta$-2,6-Cl${}_2$-V at various magnetic fields. For clarity, $C_{\mathrm{m}}/T$ for 4.0, 5.0, 6.0, 7.0, 8.0, and 8.5 T have been shifted up by 0.15, 0.25, 0.35, 0.45, 0.55, and 0.70 J/mol K${}^2$, respectively. The arrows indicate phase transition temperatures. The inset shows magnetic entropy at 0 and 8.0 T. (c) Magnetic field versus temperature phase diagram of $\beta$-2,6-Cl${}_2$-V.

Figure 5

Effective magnetic models in $\beta$-2,6-Cl${}_2$-V at $T\ll J_3/k_{\mathrm{B}}$. (a) The $S=1/2$ HAF alternating chain formed by $J_1$ and $J_{\mathrm{eff}}$ below $H_{1/2}$. Broken ellipses indicate singlet pairs connected by $J_3$. (b) The Ising ferromagnetic chain formed by $J_z$ with a weak $XY$ AF interaction in terms of the effective spin ${\mathit{S}}_{\mathrm{eff}}$ near the saturation field. The arrows indicate fully polarized spins connected by $J_1$.