Magnetism of transition-metal-doped tetrel nanoclusters: multi-reference character and spin–orbit effects in Sn ₁₂ TM (TM = Cr, Mn, Fe)

The magnetic behavior of endohedrally transition-metal-doped tetrel clusters Sn₁₂TM (TM = Cr, Mn, Fe) was investigated using a combined experimental and theoretical approach. Based on an improved experimental setup, the magnetic deflection was measured over a wide temperature range of T_nozzle = 16-240 K. From a Curie analysis of the experimentally observed single-sided shift at high nozzle temperatures, the spin multiplicities and g-factors were determined. It was observed that all three nanoclusters analyzed are paramagnetic, with Sn₁₂Mn being a sextet with g = 2.1 ± 0.1, while Sn₁₂Cr is a quintet with the same g-factor and Sn₁₂Fe is also a quintet but with a higher g-factor of 2.4 ± 0.1. In order to better understand the interplay between geometric and electronic structures and their influence on magnetism, a global geometry optimization was carried out, followed by a quantum-chemical analysis of the electronic structure using density functional theory (DFT) and wavefunction methods. The multi-reference calculations proved particularly important for Sn₁₂Fe because DFT fails to correctly predict the value of the g-factor. To describe the electronic ground state of Sn₁₂Fe, two reference configurations must be taken into account. A charge transfer from the Sn ligands to Fe manifests in very low-lying electronic excitations. These charge transfer excitations lead to a significant increase in the g-factor compared to the value of the free electron due to the large spin-orbit coupling constant of Sn. As a result, in contrast to Sn₁₂Mn and Sn₁₂Cr, the spin density of Sn₁₂Fe is strongly delocalized over the entire cluster framework.