Structural and magnetic characterization of rare-earth antiferromagnets <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>LiBa</mml:mi> <mml:msub> <mml:mi mathvariant="normal">RE</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml

Geometrically frustrated spin systems continue to serve as a fertile ground for realizing nontrivial quantum states, making the exploration of new materials in this category a central pursuit. In this work, we report the synthesis and investigation of a new family of antiferromagnets, $\mathrm{LiBa}{\mathrm{RE}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{3}$ (RE = Pr, Nd, Sm--Tb). These compounds crystallize in the trigonal $P\overline{3}m1$ space group, where neighboring $\mathrm{RE}{\mathrm{O}}_{9}$ polyhedra share faces to form spatially confined ${\mathrm{RE}}_{6}$ spin hexamers. These hexamers interconnect within the $ab$ plane to construct a two-dimensional frustrated triangular spin-hexamer lattice, featuring hierarchical spin interactions with strong intracluster and weak intercluster couplings. Magnetic susceptibility measurements down to 1.8 K reveal no signs of long-range magnetic order or spin freezing across the entire series, despite the presence of dominant antiferromagnetic interactions. Further magnetization studies on a representative member $\mathrm{LiBaG}{\mathrm{d}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{3}$ down to 0.4 K uncover a long-range antiferromagnetic transition at \ensuremath{\sim}0.91 K. Quasi-adiabatic demagnetization experiments on this material demonstrate outstanding cooling effect, reaching a pronounced temperature minimum at \ensuremath{\sim}146 mK near the antiferromagnetic critical field ${\ensuremath{\mu}}_{0}{H}_{c}\ensuremath{\sim}0.75$ T. Notably, this temperature valley is markedly broadened over an extended field interval, indicating the presence of a quantum critical state near ${\ensuremath{\mu}}_{0}{H}_{c}$ with persistent spin fluctuations. Altogether, $\mathrm{LiBa}{\mathrm{RE}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{3}$ represents a versatile platform of frustrated spin clusters, offering new possibilities for exploring unconventional magnetic ground states and potential cryogenic cooling applications.