Li${}_2$RhO${}_3$: A spin-glassy relativistic Mott insulator

Motivated by the rich interplay among electronic correlation, spin-orbit coupling (SOC), crystal-field splitting, and geometric frustrations in the honeycomblike lattice, we systematically investigated the electronic and magnetic properties of Li${}_2$RhO${}_3$. The material is semiconducting with a narrow band gap of $\Delta \sim 78$ meV, and its temperature dependence of resistivity conforms to a three-dimensional variable range hopping mechanism. No long-range magnetic ordering was found down to 0.5 K, due to the geometric frustrations. Instead, single atomic spin-glass behavior below the spin-freezing temperature ($\sim$6 K) was observed and its spin dynamics obeys the universal critical slowing down scaling law. A first-principles calculation suggested it to be a relativistic Mott insulator mediated by both electronic correlation and SOC. With moderate strength of electronic correlation and SOC, our results shed light on the research of the Heisenberg-Kitaev model in realistic materials.

Figure 1

(a) The crystalline structure of Li${}_2$RhO${}_3$, which is stacked by alternating Li and LiRh${}_2$O${}_6$ layers. (b) Within the LiRh${}_2$O${}_6$ layer, the RhO${}_6$ octahedra form a honeycomblike lattice.

Figure 2

Electrical resistivity of Li${}_2$RhO${}_3$. The inset shows resistivity in the Arrhenius plot and 3D-VRH plot. The dashed lines are guides to eyes. The thermal activating gap $\Delta \sim 78$ meV is estimated in the Arrhenius plot.

Figure 3

Temperature dependent magnetic susceptibility of Li${}_2$RhO${}_3$. (a), (b) $\chi \left(T\right)$ of S1 and S2 measured under various fields, respectively, in both ZFC and FC processes. The inset of (a) displays a Curie-Weiss fit of $1/\chi \left(T\right)$ in the high $T$ region, while the inset of (b) shows a hysteretic loop in $M\left(H\right)$ below $T_g$. (c) ac susceptibility measurement of S1. Inset of (c): Scaling plot of $\log \left(f\right)$ vs $\log [(T_f/T_g)-1]$ for S1 (solid) and S2 (open), with the best fitted parameters ${\tau }_0\sim {10}^{-11.9\left(2\right)}$ s, $z\nu =8.2\left(3\right)$, $T_{g1}=5.30$ K, and $T_{g2}=5.97$ K. The solid line is a guide to the eyes of this fitting.

Figure 4

Main frame: Specific heat divided by $T$ of Li${}_2$RhO${}_3$ (red), compared to the lattice contribution (black), which was derived by correcting its nonmagnetic reference Li${}_2$SnO${}_3$. The solid (open) symbols represent data measured under ${\mu }_{0}H=0$ (9 T). Lower inset: $C/T$ of Li${}_2$RhO${}_3$ and Li${}_2$SnO${}_3$ plot in the $T^2$ scale. Upper inset: Magnetic contribution to specific heat in Li${}_2$RhO${}_3$; also shown is the magnetic entropy gain $S_m$ as a function of $T$.

Figure 5

The calculated density of states (DOS) and band structure of Li${}_2$RhO${}_3$, based on (a) LDA, (b) LDA+$U$ ($U=3$ eV), and (c) LDA+$U$+SOC ($U=3$ eV). The calculations were performed with stripy-AFM structure.