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The single-molecule magnets (SMMs) {Mn$_{70}$} and {Mn$_{84}$} arecharacterized by a 14-site unit cell with $S=2$ spin sites, arranged in acircular geometry. Experimentally, these SMMs exhibit a magnetic ground statewith a notably low total spin, $S_{\text{tot}}=5-7$. This low-spin ground statehas been up to now difficult to describe theoretically due to the complexity ofthe quantum Heisenberg model for this large system. In this work, we are infact able to quantitatively reproduce the low-spin energy minimum by employinglarge-scale SU(2)-symmetric density-matrix renormalization group (DMRG)calculations using previously published exchange parameters obtained bydensity-functional theory. We do not find a low-spin state for the sameparameters and $S=1$, which leads us to propose that frustrated systems with$S\geq2$ are inherently prone to weak ferromagnetic interactions. This couldaccount for the prevalence of similar low-spin Mn-based SMMs. Finally, bycomputing the full magnetization curve, we find wide plateaus at 10/14, 11/14,12/14 and 13/14 of the saturation. This can be explained by independent 3-siteclusters with broken inter-cluster bonds.

The low-spin ground state of the giant Mn wheels