Low-spin ground state of the giant single-molecule magnets {Mn$_{70}$} and {Mn$_{84}$}

The single-molecule magnets {Mn$_{70}$} and {Mn$_{84}$} are characterized by a 14-site unit cell with $S=2$ spin sites arranged in a circular geometry. Experimentally, these systems exhibit a magnetic ground state with a notably low total spin $S_{\text{tot}}=5-7$. Up to now, this low-spin ground state has been up difficult to describe theoretically due to the complexity of the quantum Heisenberg model for such a large system. In this work, we fill this gap and demonstrate that the ground state of {Mn$_{70}$} and {Mn$_{84}$} is in fact governed by a small, finite $S_{\text{tot}}$ in quantitative agreement with the experiment. We employ accurate, large-scale SU(2)-symmetric density-matrix renormalization group calculations for a quantum Heisenberg model with previously published exchange parameters obtained by density-functional theory. We do not find a low-spin state for the same parameters and $S=1$ and thus propose that frustrated systems with $S\geq2$ are inherently prone to weak ferromagnetic interactions. This could account for the prevalence of similar low-spin Mn-based single-molecule magnets. Finally, we compute the full magnetization curve and find wide plateaus at 10/14, 11/14, 12/14 and 13/14 of the saturation, which can be traced back to nearly-independent 3-site clusters with broken inter-cluster bonds.