Hyperhoneycomb Iridate $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ as a Platform for Kitaev Magnetism

A complex iridium oxide $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ crystallizes in a hyperhoneycomb structure, a three-dimensional analogue of honeycomb lattice, and is found to be a spin-orbital Mott insulator with $J_{\text{eff}}=1/2$ moment. Ir ions are connected to the three neighboring Ir ions via $\mathrm{Ir}\text{−}{\mathrm{O}}_2\text{−}\mathrm{Ir}$ bonding planes, which very likely gives rise to bond-dependent ferromagnetic interactions between the $J_{\text{eff}}=1/2$ moments, an essential ingredient of Kitaev model with a spin liquid ground state. Dominant ferromagnetic interaction between $J_{\text{eff}}=1/2$ moments is indeed confirmed by the temperature dependence of magnetic susceptibility $\chi (T)$ which shows a positive Curie-Weiss temperature ${\theta }_{\mathrm{CW}}\sim +40\mathrm{K}$. A magnetic ordering with a very small entropy change, likely associated with a noncollinear arrangement of $J_{\text{eff}}=1/2$ moments, is observed at $T_c=38\mathrm{K}$. With the application of magnetic field to the ordered state, a large moment of more than $0.35{\mu }_B/\mathrm{Ir}$ is induced above 3 T, a substantially polarized $J_{\text{eff}}=1/2$ state. We argue that the close proximity to ferromagnetism and the presence of large fluctuations evidence that the ground state of hyperhoneycomb $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ is located in close proximity of a Kitaev spin liquid.

Figure 1

(a) Crystal structure of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$. Green, gray, and blue spheres represent lithium, iridium, and oxygen atoms, respectively. (b) Local lattice network of ${\mathrm{IrO}}_6$ octahedra in $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ [24], displaying Ir-O bond lengths and two different Ir-O-Ir angles obtained from the single crystal analysis [16]. (c) Hyperhoneycomb lattice of Ir ions in $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$. The pink and blue lines show the twisted zigzag chains alternating along the $c$ axis. The black dotted lines are the bond bridging the zigzag chains. The numbers indicated are Ir-Ir distances and the angles between Ir atoms.

Figure 2

(a) Temperature dependence of magnetic susceptibility for $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ under 1 T. The inset shows the temperature dependence of the inverse of magnetic susceptibility. The red solid line delineates the Curie-Weiss fit at high temperatures between 200 and 350 K. (b) Temperature dependence of specific heat divided by temperature recorded at 0 and 7 T.

Figure 3

Magnetization curve of $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$. The blue and red dots are data taken at 5 and 50 K, respectively. The inset shows the temperature dependence of magnetization under a magnetic field of 1 and 4 T.

Figure 4

(a) XMCD spectra at the Ir $L_{2,3}$ edges for $\beta \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$. The data are collected at $T=5\mathrm{K}$, ${\mu }_{0}H=4\mathrm{T}$. The spectra at the $L_3$ edge were also measured under high pressures. The inset shows the temperature dependence of the XMCD signal measure at 1 T under ambient pressure and 1–1.5 GPa. The uncertainty of pressure derives from the pressure change with temperature. (b) Pressure dependence of the XMCD signal of the $L_3$ edge at $T=5\mathrm{K}$, ${\mu }_{0}H=4\mathrm{T}$. The inset shows the temperature dependence of resistivity measured at 0, 0.3, 0.9, 1.2, 1.8, 2.4, and 3.0 GPa.