The quasi-one-dimensional diamond spin chain systems have attracted significant research attention for unveiling novel quantum magnetic phenomena driven by low dimensionality and magnetic frustration. Even though several $3d$ transition-metal (TM)-based diamond chain magnets have been studied, rare-earth (RE) counterparts are still rare. Herein, we report a family of rare-earth diamond chain compounds, $\mathrm{NaB}{\mathrm{a}}_3\mathrm{R}{\mathrm{E}}_3\mathrm{S}{\mathrm{i}}_6{\mathrm{O}}_{20}$ ($\mathrm{RE}=\mathrm{Nd}$, Gd-Dy), which crystallize in an orthorhombic structure with the Ama2 space group. The structural analysis reveals that the edge-sharing ${\mathrm{REO}}_8/{\mathrm{REO}}_7$ polyhedra form an infinite diamond chain along the $c$ axis with well separation by the nonmagnetic ${\mathrm{SiO}}_4$ tetrahedra and ${\mathrm{BaO}}_7/{\mathrm{BaO}}_8$ polyhedra perpendicular to the $c$-axis, in which the nearest neighboring (NN) intra-chain RE-RE distance $d_{\mathrm{intra}}\sim 3.818-3.916\AA$ is significantly shorter than the NN inter-chain distance $d_{\mathrm{inter}}\sim 6.471-6.763\AA$. Magnetic measurements indicate no magnetic order down to 1.8 K for all family members. Specific heat characterizations on ${\mathrm{NaBa}}_3{\mathrm{Nd}}_3{\mathrm{Si}}_6{\mathrm{O}}_{20}$ and ${\mathrm{NaBa}}_3{\mathrm{Gd}}_3{\mathrm{Si}}_6{\mathrm{O}}_{20}$ reveal the formation of long-range magnetic order at $T_{\mathrm{N}}\sim 0.20$ K and $T_{\mathrm{N}}\sim 0.42$ K with large spin fluctuations at low temperatures. Furthermore, ${\mathrm{NaBa}}_3{\mathrm{Gd}}_3{\mathrm{Si}}_6{\mathrm{O}}_{20}$ exhibits a large magnetocaloric effect at temperatures below 1 K, making it an attractive candidate for sub-Kelvin magnetic refrigeration. The serial family compounds $\mathrm{NaB}{\mathrm{a}}_3\mathrm{R}{\mathrm{E}}_3\mathrm{S}{\mathrm{i}}_6{\mathrm{O}}_{20}$ provide an ideal platform for exploring novel diamond spin chain physics involving $4f$ electrons.

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• Antiferromagnetism
• Magnetism
• Magnetocaloric effect