Quantum paramagnetism in the decorated square-kagome antiferromagnet Na6Cu7BiO4(PO4)4Cl3

The square-kagome lattice Heisenberg antiferromagnet is a highly frustrated Hamiltonian whose material realizations have been scarce. We theoretically investigate the recently synthesized ${\mathrm{Na}}₆{\mathrm{Cu}}₇{\mathrm{BiO}}₄{(\mathrm{PO})}₄{)}₄{\mathrm{Cl}}₃$ where a ${\mathrm{Cu}}²⁺$ spin-$1/2$ square-kagome lattice (with a six site unit cell) is decorated by a seventh magnetic site alternatingly above and below the layers. The material does not show any sign of long-range magnetic order down to 50 mK despite a Curie-Weiss temperature of $\ensuremath{-}212\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ indicating a quantum paramagnetic phase. Our DFT energy mapping elicits a purely antiferromagnetic Hamiltonian that features longer range exchange interactions beyond the pure square-kagome model and, importantly, we find the seventh site to be strongly coupled to the plane. We combine two variational Monte Carlo approaches, pseudofermion/Majorana functional renormalization group and Schwinger-Boson mean field calculations to show that the complex Hamiltonian of ${\mathrm{Na}}₆{\mathrm{Cu}}₇{\mathrm{BiO}}₄{(\mathrm{PO})}₄{)}₄{\mathrm{Cl}}₃$ still features a nonmagnetic ground state. We explain how the seventh ${\mathrm{Cu}}²⁺$ site actually aids the stabilization of the disordered state. We predict static and dynamic spin structure factors to guide future neutron scattering experiments.