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Frustrated transition metal compounds in which spin-orbit coupling (SOC) andelectron correlation work together have attracted much attention recently. Inthe case of 5$d$ transition metals, where SOC is large, $j_\text{eff}=1/2$bands near the Fermi level are thought to encompass the essential physics ofthe material, potentially leading to a concrete realization of exotic magneticphases such as the Kitaev spin liquid. Here we derive a spin model on atriangular lattice based on $j_\text{eff} = 1/2$ pseudospins that interact viaantiferromagnetic Heisenberg ($J$) and Kitaev ($K$) exchanges, and crucially,an anisotropic $(\Gamma)$ exchange. Our classical analysis of the spin modelreveals that, in addition to small regions of 120$^\circ$, $\mathbb{Z}_2$ /dual-$\mathbb{Z}_2$ vortex crystal and nematic phases, the stripy andferromagnetic phases dominate the $J$-$K$-$\Gamma$ phase diagram. We apply ourmodel to the 5$d$ transition metal compound, Ba$_3$IrTi$_2$O$_9$, in which theIr$^{4+}$ ions form layered two-dimensional triangular lattices. We compute theband structure and nearest-neighbor hopping parameters using ab-initiocalculations. By combining our ab-initio and classical analyses, we predictthat Ba$_3$IrTi$_2$O$_9$ has a stripy ordered magnetic ground state.

Magnetic Orders Proximal to the Kitaev Limit in Frustrated Triangular Systems: Application to Ba$_3$IrTi$_2$O$_9$