Tuning of magnetic frustration in S=1/2 Kagom\'{e} lattices {[Cu₃(CO₃)₂(bpe)₃](ClO₄)₂}_(n) and {[Cu₃(CO₃)₂(bpy)₃](ClO₄)₂}_(n) through rigid and flexible ligands

Single crystalline and polycrystalline samples of $S=1/2$ Kagom\'{e} lattices {[Cu$_{3}$(CO$_{3}$)$_{2}$$(bpe)_{3}$](ClO$_{4}$)$_2$}$_{n}$ and {[Cu$_{3}$(CO$_{3}$)$_{2}$$(bpy)_{3}$](ClO$_{4}$)$_2$}$_{n}$, respectively were synthesized. Their structural and magnetic properties were characterized by means of x-ray diffraction and magnetization measurements. Both compounds crystalize in a hexagonal structure (space group $P-6$) consisting of CuO$_4$ Kagom\'{e} layers in the $ab$-plane but linked along $c$ direction through either rigid $bpy$ or flexible $bpe$ ligands to form 3D frame works. Magnetic measurements reveal that both the compounds undergo ferromagnetic ordering ($T_{\rm C}$) at low temperatures and the $T_{\rm C}$ and the extent of frustration could be tuned by changing the nature of the pillar ligands. {[Cu$_{3}$(CO$_{3}$)$_{2}$$(bpe)_{3}$](ClO$_{4}$)$_2$}$_{n}$ which is made up of flexible $bpe$ ligands has a $T_{\rm C}$ of 5.7 K and a Curie-Weiss temperature ($\theta_{\rm CW}$) of -39.7 K giving rise to a frustration parameter of $\frac{|\theta_{\rm CW}|}{T_{\rm C}} \simeq$ 6.96. But the replacement of $bpe$ by a more rigid and electronically delocalized $bpy$ ligand leads to an enhanced $T_{\rm C} \simeq$ 9.3 K and a reduced frustration parameter of $\frac{|\theta_{\rm CW}|}{T_{\rm C}} \simeq$ 3.54.