Thermodynamic Evidence of Proximity to a Kitaev Spin Liquid in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$

Kitaev magnets are materials with bond-dependent Ising interactions between localized spins on a honeycomb lattice. Such interactions could lead to a quantum spin-liquid (QSL) ground state at zero temperature. Recent theoretical studies suggest two potential signatures of a QSL at finite temperatures, namely, a scaling behavior of thermodynamic quantities in the presence of quenched disorder, and a two-step release of the magnetic entropy. Here, we present both signatures in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ which is synthesized from $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ by replacing the interlayer Li atoms with Ag atoms. In addition, the dc susceptibility data confirm the absence of a long-range order, and the ac susceptibility data rule out a spin-glass transition. These observations suggest a closer proximity to the QSL in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ compared to its parent compound $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ that orders at 15 K. We discuss an enhanced spin-orbit coupling due to a mixing between silver $d$ and oxygen $p$ orbitals as a potential underlying mechanism.

Figure 1

(a) Honeycomb lattice of edge-sharing ${\mathrm{IrO}}_6$ octahedra in both $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ and ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$. (b) Heisenberg exchange paths between neighboring octahedra. (c) Octahedral coordination of Li atoms between the layers of $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$. (d) Linear (dumbbell) coordination of Ag atoms between the layers of ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ which leads to increasing the interlayer separation. (e) Rietveld analysis with a magnified view of the Warren line shape due to stacking faults (See also Figs. S1 and S3 [17]).

Figure 2

(a) dc magnetic susceptibility as a function of temperature in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ (red) and $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ (black) with a magnified view below 30 K in the inset. The yellow line is a Curie-Weiss fit. (b) Heat capacity per mole Ir as a function of temperature in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ (red) and $\alpha \text{−}{\mathrm{Li}}_2{\mathrm{IrO}}_3$ (black data from Ref. [36]). (c) A small splitting in the dc susceptibility data under ZFC and FC conditions appears below 10 K. It disappears at higher fields. The curves are slightly shifted for visibility. (d) The real part of the ac susceptibility ${\chi }_{\mathrm{ac}}^{\prime }$ as a function of temperature. (e) Data collapse for $H^{\alpha }{\chi }_{\mathrm{ac}}^{\prime }$ as a function of $T/H$ on a semilog scale with $\alpha =0.17$. (f) Data collapse for $T^{\alpha -1}M$ as a function of $H/T$ on a log-log scale.

Figure 3

(a) Heat capacity ($C/T$ per mole Ir or Sn) plotted as a function of temperature in ${\mathrm{Ag}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ and its lattice model ${\mathrm{Ag}}_3{\mathrm{LiSn}}_2{\mathrm{O}}_6$. (b) Magnetic heat capacity ($C_m$) and entropy ($S_m$) plotted in units of $R\ln (2)$ as a function of temperature. Two broad features are revealed at $T_H\approx 75$ and $T_L=13\mathrm{K}$.

Figure 4

Density of states calculated at three levels of DFT with (a) local density approximation (LDA), (b) $\mathrm{LDA}+\mathrm{SOC}$, and (c) $\mathrm{LDA}+\mathrm{SOC}+U$, where $U$ is the exchange potential.