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

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