Antiferromagnetic Mott insulating state in single crystals of the honeycomb lattice material ${\text{Na}}_2{\text{IrO}}_3$

We have synthesized single crystals of ${\text{Na}}_2{\text{IrO}}_3$ and studied their structure, transport, magnetic, and thermal properties using powder x-ray diffraction, electrical resistivity, isothermal magnetization $M$ versus magnetic field $H$, magnetic susceptibility $\chi$ versus temperature $T$, and heat capacity $C$ versus $T$ measurements. ${\text{Na}}_2{\text{IrO}}_3$ crystallizes in the monoclinic $C2/c$ (No. 15) type structure which is made up of Na and ${\text{NaIr}}_2{\text{O}}_6$ layers alternately stacked along the $c$ axis. The $\chi \left(T\right)$ data show Curie-Weiss behavior at high $T>200\text{K}$ with an effective moment ${\mu }_{\text{eff}}=1.82\left(1\right){\mu }_{\text{B}}$ indicating an effective spin $S_{\text{eff}}=1/2$ on the ${\text{Ir}}^{4+}$ moments. A large Weiss temperature $\theta =-116\left(3\right)\text{K}$ indicates substantial antiferromagnetic interactions between these $S_{\text{eff}}=1/2$, ${\text{Ir}}^{4+}$ moments. Anomalies in $\chi \left(T\right)$ and $C\left(T\right)$ data indicate that ${\text{Na}}_2{\text{IrO}}_3$ undergoes a transition into a long-range antiferromagnetically ordered state below $T_{\text{N}}=15\text{K}$. The magnetic entropy at $T_{\text{N}}$ is only about 20% of what is expected for $S_{\text{eff}}=1/2$ moment ordering. The reduced entropy and the large ratio $\theta /T_N\approx 8$ suggest geometrical magnetic frustration and/or low-dimensional magnetic interactions in ${\text{Na}}_2{\text{IrO}}_3$. In plane resistivity measurements show insulating behavior. This behavior together with the local-moment magnetism indicates that bulk ${\text{Na}}_2{\text{IrO}}_3$ is a Mott insulator.

Figure 1

(Color online) The crystallographic structure of ${\text{Na}}_2{\text{IrO}}_3$. The Na, Ir, and O atoms are shown as blue (black), red (dark gray), and yellow (light gray) spheres, respectively. (a) The view perpendicular to the $c$ axis showing the layered structure with layers containing only Na atoms alternating slabs of ${\text{NaIr}}_2{\text{O}}_6$ stacked along the $c$ axis. The ${\text{IrO}}_6$ octahedra are shown in pink with the (red) Ir atoms sitting in the middle. (b) One of the ${\text{NaIr}}_2{\text{O}}_6$ slabs viewed down the $c$ axis to highlight the honeycomb lattice of Ir atoms within the layer. The Na atoms occupy voids between the ${\text{IrO}}_6$ octahedra.

Figure 2

(Color online) (a) Rietveld refinement of the x-ray diffraction data of polycrystalline ${\text{Na}}_2{\text{IrO}}_3$ synthesized at $900°\text{C}$. The closed symbols represent the observed data, the solid lines represent the fitted pattern, the dotted lines represent the difference between the observed and calculated intensities, and the vertical bars represent the peak positions. (b) X-ray diffraction of $c$ axis oriented single crystals of ${\text{Na}}_2{\text{IrO}}_3$. The inset shows the powder x-ray diffraction of crushed single crystals on a semi-log plot.

Figure 3

(Color online) The in-plane electrical resistivity $\rho$ versus temperatures $T$ for a single crystal of ${\text{Na}}_2{\text{IrO}}_3$. The inset (a) shows the $\rho$ versus $1/T$ data on a semi-log scale. The inset (b) shows the $\rho$ versus $1/T^{1/4}$ data on a semi-log scale.

Figure 4

(Color online) Isothermal magnetization $M$ versus magnetic field $H$ at various temperatures $T$ for a collection of randomly oriented single crystals of ${\text{Na}}_2{\text{IrO}}_3$. The inset shows the $M/H$ versus $H$ data at $T=100\text{T}$.

Figure 5

(Color online) (a) Inverse magnetic susceptibility $1/\chi =H/M$ versus temperature $T$ for a collection of randomly oriented single crystals of ${\text{Na}}_2{\text{IrO}}_3$ in a magnetic field $H=2\text{T}$. The solid curve through the data is a fit by the expression $\chi ={\chi }_0+C/\left(T-\theta \right)$ and the dashed curve is an extrapolation to $T=0$. (b) The anisotropic magnetic susceptibilities ${\chi }_c$ and ${\chi }_{ab}$ versus $T$. The powder average susceptibility $\left({\chi }_c+2{\chi }_{ab}\right)/3$ and the polycrystalline susceptibility ${\chi }_{\text{poly}}$ are also shown. The solid curve through the ${\chi }_{\text{poly}}$ data is the Curie-Weiss fit. The inset shows the ${\chi }_c\left(T\right)$ data at low $T$ to highlight the broad maximum at $T\approx 23\text{K}$. The arrow indicates the onset temperature $T_{\text{N}}=15\text{K}$ for the long-ranged antiferromagnetic ordering.

Figure 6

(Color online) (a) The heat capacity divided by temperature $C/T$ versus $T$ data between $T=1.8\text{K}$ and 40 K for single crystals of ${\text{Na}}_2{\text{IrO}}_3$ and the heat capacity of ${\text{Na}}_2{\text{SnO}}_3$ as the lattice contribution $C_{\text{lattice}}/T$ versus $T$. The inset shows the $C/T$ versus $T$ data in $H=0$ and 7 T applied magnetic field. (b) The difference heat capacity $\Delta C$ and difference entropy $\Delta S$ versus $T$ data between $T=1.8$ and 40 K.