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We report the structural and magnetic properties of the4}\textit{\textcolor{black}{d }}\textcolor{black}{(M = Rh) based and5}\textit{\textcolor{black}{d }}\textcolor{black}{(M = Ir) based systemsBa$_{3}$M$_{x}$Ti$_{3-x}$O$_{9}$ (nominally $x$ = 0.5, 1). The studiedcompositions were found to crystallize in a hexagonal structure with thecentrosymmetric space group }$P6_{3}/mmc$.\textcolor{black}{{} The structurescomprise of A$_{2}$O$_{9}$ polyhedra (with the A site (possibly) statisticallyoccupied by M and Ti) in which pairs of transition metal ions are stacked alongthe crystallographic }\textit{\textcolor{black}{c}}\textcolor{black}{-axis.These pairs form triangular bilayers in the $ab$-plane. The magnetic Rh and Irions occupy these bilayers, diluted by Ti ions even for $x$ = 1. These bilayersare separated by a triangular layer which is dominantly occupied by Ti ions.From magnetization measurements we infer strong antiferromagnetic couplings forall of the materials but the absence of any spin-freezing or spin-ordering downto 2~K. Further, specific heat measurements down to 0.35~K show no sign of aphase transition for any of the compounds. Based on these thermodynamicmeasurements we propose the emergence of a quantum spin liquid ground state forBa$_{3}$Rh$_{0.5}$Ti$_{2.5}$O$_{9}$, and Ba$_{3}$Ir$_{0.5}$Ti$_{2.5}$O$_{9}$,in addition to the already reported Ba$_{3}$IrTi$_{2}$O$_{9}$. }

physical review. b./physical review. b

Ba$_{3}$M$_{x}$Ti$_{3-x}$O$_{9}$(M = Ir, Rh): A family of  5\textit{\textcolor{black}{d}}/4\textit{\textcolor{black}{d}}-based, diluted  quantum spin liquids