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The 6H-perovskites Ba$_3$RRu$_2$O$_9$ (R = rare earth element) demonstratethe magnetodielectric (MD) coupling as a manifestation of $4d - 4f$ magneticinteractions. Here, we have reported a detailed study of the structural,magnetic, heat capacity, and MD properties of the 6H-perovskiteBa$_3$GdRu$_2$O$_9$. The signature of long-range antiferromagnetic (AFM)ordering $\sim$ 14.8 K ($T_N$) is evident from the magnetization and heatcapacity studies. The $T_N$ shifts towards the lower temperature side, apartfrom splitting in two with the application of the magnetic field.Field-dependent magnetization at 1.8 K shows three metamagnetic transitionswith the opening of small hysteresis in different regions. A new transition at$T_1$ emerges after the onset of the first metamagnetic transition. Complexmagnetic behavior is observed in different magnetic field regions whereas thesefield regions themselves vary with the temperature. Dielectric responserecorded at zero and 80 kOe field exhibits the development of MD coupling wellabove $T_N$. The MD coupling ($\sim$ 4.5 \% at 10 K) is enhanced by 25 \% ascompared to the Dy counterpart. Effect of complex magnetic behavior is alsoconveyed in the MD results where the maximum value of MD coupling is observedin the vicinity of 10 K (onset of $T_1$) and near the second metamagnetictransition. Our investigation suggests that both Gd and Ru moments alignsimultaneously at $T_N$. Short-range magnetic correlations are possiblyresponsible for MD coupling above $T_N$.

Large magnetodielectric coupling in the vicinity of metamagnetic transition in $6H-$perovskite Ba$_3$GdRu$_2$O$_9$