Using hyper-optimized tensor networks and first-principles electronic structure to simulate experimental properties of the giant {Mn84} torus

The single-molecule magnet {Mn84} is a challenge to theory due to its high nuclearity. Building on our prior work which characterized the structure of the spectrum of this magnet, we directly compute two experimentally accessible observables, the field-dependent magnetization up to 75 T and the temperature-dependent heat capacity, using parameter free theory. In particular, we use first principles calculations to derive short- and long-range exchange interactions, while we compute the exact partition function of the resulting classical Potts and Ising spin models for all 84 Mn $S=2$ spins to obtain the observables. The latter computation is possible because of a simulation methodology that uses hyper-optimized tensor network contraction, borrowing from recent techniques developed to simulate quantum supremacy circuits. We also synthesize the magnet and measure its heat capacity and field-dependent magnetization. We observe good qualitative agreement between theory and experiment, identifying an unusual peak in the heat capacity in both, as well as a plateau in the magnetization. Our work also identifies some limitations of current theoretical modeling in large magnets, such as the sensitivity to small, long-range, exchange couplings.