A Spin Frustrated Hourglass {Gd$_9$} Molecular Nanomagnet with Unusual Magnetocaloric Properties

We report a highly symmetric {Gd$_9$} molecular nanocage with the formula [Gd$_9$(BA)$_{16}$(OH)$_{10}$]Cl·3(C$_2$H$_5$OH)·4(H$_2$O), which crystallizes in the cubic space group Pn3̅n. The structure features two crystallographically distinct Gd$^{3+}$ ions, forming highly regular triangular Gd$^{3+}$ arrangements leading to a geometrically frustrated magnetic network. Magnetization measurements at 2 K reveal a broad plateau between 1.5 and 4 T, while zero-field heat capacity shows a Schottky anomaly centered at 0.6 K─indicative of low-lying excited states and competing magnetic interactions. The magnetocaloric effect, evaluated through both direct and indirect methods, exhibits a re-entrant profile in the isentropic curves, pointing to a nontrivial evolution of magnetic entropy under applied fields. To probe the origin of this behavior, we employed the finite-temperature Lanczos method on a model spin Hamiltonian. The results reveal that the antiferromagnetic exchange between Gd$^{3+}$ ions, combined with the frustration inherent to the {Gd$_9$} geometry, leads to a degenerate ground state. An external field lifts this degeneracy, producing a regime with a sharply reduced density of states between 1.5 and 4 K, which underlies the unconventional magnetocaloric response. ... mehrThe {Gd$_9$} cage thus represents a rare example of a spin-frustrated arrangement arising from competing antiferromagnetic interactions between the Gd$^{3+}$. These findings demonstrate how frustrated topologies and tunable low-energy excitations can be exploited to modulate the magnetothermal properties, with potential implications for cryogenic magnetic cooling technologies.