Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu$_7$TeO$_4$(SO$_4$)$_5$Cl

Quantum antiferromagnets based on the square-kagome lattice are proving to be a fertile platform for realizing nontrivial phenomena in frustrated magnetism. Recently, several decorated square-kagome compounds of the nabokoite family have been synthesized, allowing for experimental exploration of model Hamiltonians. Here, we carry out a theoretical analysis of KCu$_7$TeO$_4$(SO$_4$)$_5$Cl nabokoite using a Heisenberg Hamiltonian derived from density functional theory energy mapping. We employ classical Monte Carlo simulations to explain the two transitions experimentally observed in the low-temperature magnetization curve. Interestingly, the intermediate-field phase is also found in a purely two-dimensional model and is described by a spin liquid featuring subextensive degeneracy with a ferrimagnetic component. We show that this phase can be approximated by a checkerboard lattice in a magnetic field. Finally, we assess the effects of quantum fluctuations in zero fields using the pseudo-Majorana functional renormalization group method.