Putative spin liquid in the triangle-based iridate ${\mathrm{Ba}}_3{\mathrm{IrTi}}_2{\mathrm{O}}_9$

We report on thermodynamic, magnetization, and muon spin relaxation measurements of the strong spin-orbit coupled iridate ${\mathrm{Ba}}_3{\mathrm{IrTi}}_2{\mathrm{O}}_9$, which constitutes a distinct frustration motif made up of a mixture of edge- and corner-sharing triangles. In spite of a strong antiferromagnetic exchange interaction of the order of 100 K, we find no hint for long-range magnetic order down to 23 mK. The magnetic specific heat data unveil $T$-linear and $T$-squared dependences at low temperatures below 1 K. At the respective temperatures, the zero-field muon spin relaxation features a persistent spin dynamics, indicative of unconventional low-energy excitations. A comparison to the $4d$ isostructural compound ${\mathrm{Ba}}_3{\mathrm{RuTi}}_2{\mathrm{O}}_9$ suggests that a concerted interplay of compasslike magnetic interactions and frustrated geometry promotes a dynamically fluctuating state in a triangle-based iridate.

Figure 1

(a) Triangular bilayers of $\mathrm{Ir}{\left(1\right)}^{4+}/\mathrm{Ti}{\left(2\right)}^{4+}$ which are separated by a nonmagnetic triangular layer of $\mathrm{Ti}{\left(3\right)}^{4+}$ and are stacked along the $c$ axis. The blue, green, and red balls stand for Ir, Ti, and O atoms, respectively. The barium atoms are omitted for clarity. The gray solid lines depict the superexchange paths Ir-O-O-Ir. In the presence of the ${\mathrm{Ti}}^{4+}/{\mathrm{Ir}}^{4+}$ cation disorders within the $\mathrm{Ir}\left(1\right)\mathrm{Ti}\left(2\right){\mathrm{O}}_9$ dimers, a nearly isotropic tetrahedron ($J_1\approx J_2$) is created. (b) Temperature dependence of resistivity of ${\mathrm{Ba}}_{3}M{\mathrm{Ti}}_2{\mathrm{O}}_9$ plotted on a log-log scale. The solid lines are fits to a power law $\rho \left(T\right)\sim T^{-n}$. (c) Temperature dependence of the magnetic susceptibility of ${\mathrm{Ba}}_{3}M{\mathrm{Ti}}_2{\mathrm{O}}_9$ measured at $H=500$ Oe in zero-field-cooled and field-cooled processes. The solid lines represent the intrinsic magnetic susceptibility ${\chi }_{\mathrm{intr}}\left(T\right)$ obtained by subtracting the contribution from orphan spins. The inset plots the inverse magnetic susceptibility. The Curie-Weiss fits are shown in the temperature range $T=100–320$ K with solid lines.

Figure 2

Magnetization curve $M\left(H\right)$ of ${\mathrm{Ba}}_3{\mathrm{IrTi}}_2{\mathrm{O}}_9$ and ${\mathrm{Ba}}_3{\mathrm{RuTi}}_2{\mathrm{O}}_9$ measured at $T=1.5$ K. The black circles are the experimental data and the red solid lines are fits of $M\left(H\right)$ to the equation described in the text. The blue dashed lines are the contribution of orphan spins to magnetization, $M_{\mathrm{imp}}\left(H\right)$, and the green open circles represent the residual magnetization intrinsic to the system obtained by subtracting the orphan-spin contribution from the raw data.

Figure 3

(a) Temperature dependence of specific heat of the ${\mathrm{Ba}}_{3}M{\mathrm{Ti}}_2{\mathrm{O}}_9$ polycrystalline samples plotted on a log-log scale together with the nonmagnetic counterpart ${\mathrm{Ba}}_3{\mathrm{ZnSb}}_2{\mathrm{O}}_9$ (thick solid line). The specific heat measurements were performed for temperatures below 4 K and at zero magnetic field. (b) The magnetic specific heat $C_m$ of ${\mathrm{Ba}}_{3}M{\mathrm{Ti}}_2{\mathrm{O}}_9$, obtained by subtracting the nonmagnetic contribution. The solid lines are the fits of the $C_m$ data to a power law $\gamma T^{\alpha }$.

Figure 4

(a), (b) Zero-field muon spin depolarization $P\left(t\right)$ of ${\mathrm{Ba}}_{3}M{\mathrm{Ti}}_2{\mathrm{O}}_9$, measured in the temperature range $T=0.02–125$ K. The solid lines are fitted to the stretched exponential function. (c), (d) Temperature dependence of the muon spin relaxation rate ${\lambda }_{\mathrm{ZF}}$ and stretching exponent $\beta$ extracted from the zero-field data. (e), (f) Longitudinal-field dependence of the muon spin depolarization measured at $T=23$ (50) mK for the Ru (Ir) compound in a magnetic field $H=0–200$ G.