$\require{mhchem}$Quantum paramagnetism in the decorated square-kagome antiferromagnet $\ce{Na6Cu7BiO4(PO4)4Cl3}$

TL;DR

This study investigates the quantum paramagnetic behavior of a decorated square-kagome antiferromagnet material, revealing a nonmagnetic ground state stabilized by complex interactions and the seventh magnetic site, supported by advanced computational methods.

Contribution

It introduces a detailed theoretical analysis of the complex Hamiltonian of Na6Cu7BiO4(PO4)4Cl3, showing how the seventh site stabilizes a nonmagnetic quantum paramagnetic phase.

Findings

Material exhibits no long-range magnetic order down to 50 mK.

Complex Hamiltonian includes longer-range interactions beyond the pure square-kagome model.

The seventh magnetic site strongly couples to the plane and aids in stabilizing the disordered state.

Abstract

$\require{mhchem}$The square-kagome lattice Heisenberg antiferromagnet is a highly frustrated Hamiltonian whose material realizations have been scarce. We theoretically investigate the recently synthesized $\ce{Na6Cu7BiO4(PO4)4Cl3}$ where a Cu$^{2+}$ spin-$1/2$ square-kagome lattice (with 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 $-212$ 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, pseudo-fermion/Majorana functional renormalization group and Schwinger-Boson mean field calculations to show that the complex Hamiltonian of $\ce{Na6Cu7BiO4(PO4)4Cl3}$ still features a nonmagnetic ground state. We explain how the seventh 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.