Effect of nonmagnetic dilution in the honeycomb-lattice iridates ${\mathrm{Na}}_2$${\mathrm{IrO}}_3$ and ${\mathrm{Li}}_2$${\mathrm{IrO}}_3$

We have synthesized single crystals of ${\mathrm{Na}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ and polycrystals of ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ and studied the effect of magnetic depletion on the magnetic properties by measurements of the magnetic susceptibility, specific heat, and magnetocaloric effect at temperatures down to 0.1 K. In both systems, the nonmagnetic substitution rapidly changes the magnetically ordered ground state into a spin glass, indicating strong frustration. While for the Li system the Weiss temperature ${\Theta }_{\mathrm{W}}$ remains unchanged up to $x=0.55$, a strong decrease $|{\Theta }_{\mathrm{W}}|$ is found for the Na system. This suggests that only for the former system magnetic exchange beyond nearest neighbors is dominating. This is also corroborated by the observation of a smeared quantum phase transition in ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ near $x=0.5$, i.e., much beyond the site percolation threshold of the honeycomb lattice.

Figure 1

Field-cooled (FC) and zero-field-cooled (ZFC) susceptibility vs temperature as indicated by filled and open symbols, respectively, for ${\mathrm{Na}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ with $x=0.05$, $0.11$ (top) and $0.17$, $0.26$ (bottom). Vertical arrows mark ${\mathrm{T}}_g$. Respective insets display $1/\Delta \chi$ (with $\Delta \chi =\chi -{\chi }_0$) vs $T$. Solid lines indicate Curie-Weiss behavior.

Figure 2

FC and ZFC susceptibility (represented by filled and open symbols, respectively) for ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ with $x=0.09$ and $0.22$, measured at $H=0.01$ T. Vertical arrows mark $T_{\mathrm{g}}$. The inset displays $1/\Delta \chi$ vs $T$ for all investigated $x$. Solid lines illustrate CW behavior.

Figure 3

Specific heat as $C/T$ vs $T$ for various ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ samples. The inset displays the low-$T$ data for $x=0.51$ and 0.55 on a $ln\left(T\right)$ axis. Broad maxima indicate $T_{\mathrm{g}}$, above which a logarithmic temperature dependence is found (see lines).

Figure 4

(Top) Specific heat as $C/T$ vs $T$ (on logarithmic scale) at various fields for ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$, $x=0.55$. The inset displays zero field data together with respective thermal expansion data as $\alpha /T$. (Bottom) Magnetic Grüneisen parameter ${\Gamma }_{\mathrm{H}}=T^{-1}{(dT/dH)}_S$ at different magnetic fields vs $T$ (on log-log scale). The solid line indicates the $T^{-1.7}$ divergence at 0.2 T. The inset displays scaling behavior ${\Gamma }_{\mathrm{H}}h$ vs $T/h^{\epsilon }$ with $\epsilon =0.86$ and $h=(H-0.2$ T).

Figure 5

Evolution of normalized spin glass ordering temperatures (top) and Curie Weiss temperatures (bottom) for ${\mathrm{Na}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$ and ${\mathrm{Li}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$. The vertical dotted line at $x=0.3$ indicates the percolation threshold in the honeycomb lattice. The dashed black line in the upper panel indicates the linear suppression of $T_{\mathrm{g}}$ for ${\mathrm{Na}}_2$(${\mathrm{Ir}}_{1-x}$${\mathrm{Ti}}_x$)${\mathrm{O}}_3$.