Evolution of magnetism in the single-crystal honeycomb iridates $({\text{Na}}_{1-x}$Li${}_x{)}_2\text{Ir}{\text{O}}_3$

We report the successful synthesis of single crystals of the layered iridate (Na${}_{1-x}$Li${}_x$)${}_2$IrO${}_3$, $0\le x\le 0.9$, and a thorough study of its structural, magnetic, thermal, and transport properties. This compound allows a controlled interpolation between Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$, while maintaining the quantum magnetism of the honeycomb Ir${}^{4+}$ planes. The measured phase diagram demonstrates a suppression of the Néel temperature $T_N$ at an intermediate $x$, indicating that the magnetic orders in Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$ are distinct. X-ray data show that for $x\approx 0.7$, when $T_N$ is suppressed the most, the honeycomb structure is least distorted, leading to the speculation that at this intermediate doping of the material is closest to the spin liquid that has been sought after in Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$. By analyzing our magnetic data with a single-ion theoretical model we also show that the trigonal splitting on the Ir${}^{4+}$ ions changes sign from Na${}_2$IrO${}_3$ to Li${}_2$IrO${}_3$.

Figure 1

Synthesis and structure of (Na${}_{1-x}{A}_x$)${}_2$IrO${}_3$ (with $A=\text{Li}$ or K). (a) The lattice parameters $a$ and $c$ (left scale) and the $b$ (right scale) as a function of $x$. Note that the green data points for Li${}_2$IrO${}_3$ ($x=1.0$) are obtained from Ref. [10]. Inset: An illustration of the crystal structure of Na${}_2$IrO${}_3$. (b) The evolution of distortion of the honeycomb lattice of Ir${}^{4+}$ ions from $L_2>L_1$ for $x=0$ to $L_1>L_2$ for $x=1$. At $x\approx 0.7$, the system is a near perfect honeycomb.

Figure 2

Study of the Néel transition as a function of $x$ in (Na${}_{1-x}$Li${}_x$)${}_2$IrO${}_3$ in the specific heat and in-plane susceptibility. (a) The specific heat for different $x$. We have plotted $C\left(T\right)/T$ for presentation purposes. (b) The in-plane magnetic susceptibility ${\chi }_{\parallel }\left(T\right)$ at ${\mu }_{0}H=0.1$ T. Inset: Zoom-in of the ${\chi }_{\parallel }$ data to show kinks at the phase transitions.

Figure 3

Ordering and interaction scales of (Na${}_{1-x}{A}_x$)${}_2$IrO${}_3$ ($A=\text{Li}$ or K) as a function of $x$. (a) The Néel temperature $T_N$, and (b) the Curie-Weiss temperature ${\theta }_{\mathrm{CW}}$ (left scale) and the frustration parameter (right scale) as a function of $x$. Note that K doping increases $T_N$, in sharp contrast to Li doping, and that the green data points for Li${}_2$IrO${}_3$ ($x=1.0$) are obtained from Ref. [10].

Figure 4

Comparisons between $x=0$ and $0.90$: The temperature dependence of (a) the in-plane and perpendicular-to-plane magnetic susceptibility ${\chi }_{\parallel }\left(T\right)$ and ${\chi }_{\perp }\left(T\right)$ at ${\mu }_{0}H=0.1$ T for $x=0$ and $0.9$. Inset: The enlarged low-temperature ${\chi }_{\parallel }\left(T\right)$ (left scale) and ${\chi }_{\perp }\left(T\right)$ (right scale). (b) The angular dependence of magnetization M at ${\mu }_{0}H=1\text{T}$ for $x=0$ and $0.90$ of (Na${}_{1-x}$Li${}_x$)${}_2$IrO${}_3$ in the $a$-$c$ plane (solid circles) and for $x=0$ in the $a$-$b$ plane (open squares). Inset: A schematic of the sample orientation relative to the $a$ and $c$ axis and the magnetic field $H$. A detailed interpretation of the anisotropies of $\chi$ and its relation to the trigonal field $\Delta$ is given in the text. Data for other dopings are shown in the SM (Ref. [24]).

Figure 5

(a) Curie constants ${\mathcal{A}}_{\parallel }$ and ${\mathcal{A}}_{\perp }$ as a function of the parameter $\Delta /\lambda$ calculated from the model Eq. (1). (b) An extrapolation of the experimental ${\chi }_{\perp }\left(T\right)/{\chi }_{\parallel }\left(T\right)$ in the high-temperature limit. At $T=\infty$ this ratio should be simply ${\mathcal{A}}_{\perp }/{\mathcal{A}}_{\parallel }$. Note that Na${}_2$IrO${}_3$ has ${\mathcal{A}}_{\perp }/{\mathcal{A}}_{\parallel }>1$ and hence $\Delta <0$, and based on the shown extrapolation for $x=0.9$, Li${}_2$IrO${}_3$ will extrapolate to ${\mathcal{A}}_{\perp }/{\mathcal{A}}_{\parallel }<1$ with $\Delta >0$. In both cases, clearly $\lambda \gg \left|\Delta \right|$.