The square-kagome lattice Heisenberg antiferromagnet is a highly frustrated Hamiltonian whose material realizations have been scarce. We theoretically investigate the recently synthesized Na6Cu7BiO4(PO)4)4Cl3 where a Cu2+ 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 −212K 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 Na6Cu7BiO4(PO)4)4Cl3 still features a nonmagnetic ground state. We explain how the seventh Cu2+ site actually aids the stabilization of the disordered state. We predict static and dynamic spin structure factors to guide future neutron scattering experiments.
