Magnetic properties of the $S=\frac{1}{2}$ honeycomb lattice antiferromagnet $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$

We successfully synthesized single crystals of the verdazyl radical $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$ [=3-(2-chloro-3,6-difluorophenyl)-1,5-diphenylverdazyl], which is a rare model compound with an $S=\frac{1}{2}$ Heisenberg antiferromagnetic (HAF) honeycomb lattice. Ab initio molecular orbital calculations indicate two dominant AF interactions, forming a slightly distorted honeycomb lattice. We explain the magnetic susceptibility and the magnetization curve up to the saturation field based on the expected spin model using the quantum Monte Carlo method. In the low-temperature regions, we found a phase transition to an AF ordered state at about 0.77 K for the zero field and obtained the magnetic field-temperature phase diagram from the magnetic susceptibility and the specific heat for various magnetic fields. Through the analysis considering the effect of lattice distortion on magnetic behavior, we confirm that the lattice distortion of the present model is small enough that it does not affect the intrinsic behavior of the uniform $S=\frac{1}{2}$ HAF honeycomb lattice.

Figure 1

(a) Molecular structure of $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$. (b) Crystal structure of $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$. The broken lines indicate two types of C-C short contacts associated with $J_1$ and $J_2$. Hydrogen atoms are omitted for clarity. The thick transparent hexagon represents a part of the honeycomb lattice composed of nearby six molecules. (c) Honeycomb lattice formed by intermolecular interactions $J_1$ and $J_2$.

Figure 2

Temperature dependence of magnetic susceptibility ($\chi =M/H$) of $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$ at 0.1 T. The insets shows temperature dependence of $d\chi /dT$ in the low-temperature regions. The arrow indicates the phase transition temperature. The solid line with squares represents the calculated results for the $S=\frac{1}{2}$ HAF honeycomb lattice with $\alpha =J_2/J_1=0.76$.

Figure 3

Temperature dependence of magnetic susceptibility ($\chi =M/H$) of $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$ in the low-temperature regions at various magnetic fields. For clarity, the values of the vertical axes for 1.5, 2.0, 2.5, and 3.0 T have been shifted up by 0.0028, 0.0062, 0.0098, and 0.013 emu/mol, respectively. The inset shows temperature dependence of $d\chi /dT$ at 1.0 T. The arrows indicate the phase transition temperatures.

Figure 4

Magnetization curve and its field derivative of $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$ at 0.5 K. The solid line with squares represents the calculated results for the $S=\frac{1}{2}$ HAF honeycomb lattice with $\alpha =J_2/J_1=0.76$.

Figure 5

Specific heat $C/T$ of $2\text{−}\mathrm{Cl}\text{−}3,6\text{−}{\mathrm{F}}_2\text{−}\mathrm{V}$ in the low-temperature regions at various magnetic fields. The arrow indicate the phase transition temperatures. The inset shows the entropy at 0 T. For clarity, $C/T$ for 1.0, 2.0, 3.0, 3.5, and 3.7 T have been shifted up by 5.3, 9.0, 16, 21, and 26 J/mol ${\mathrm{K}}^2$, respectively.

Figure 6

Magnetic field vs temperature phase diagram showing AF ordered phase. The circles, triangles, and square indicate the phase boundaries determined from the magnetic susceptibility, the specific heat, and the magnetization curve, respectively.

Figure 7

Calculated magnetic susceptibilities (a) and magnetization curves at 0.05 K (b) of $S=1/2$ HAF honeycomb lattice for various values of $\alpha =J_2/J_1$. The insets show the expansion of the low-temperature region of the magnetic susceptibility and the vicinity of saturation of the magnetization curves.