Vibrational bottleneck of magnetic relaxation in single-ion endohedral fullerenes

Endohedral fullerene-based molecular magnets have been shown to exhibit remarkable magnetic properties. Notably, azafullerene complexes with a single lanthanide ion demonstrate high blocking temperature and long magnetic relaxation time despite their weak crystal field anisotropy when compared to traditional double-decker lanthanide complexes. This work presents a comprehensive ab initio investigation of the spin-vibrational couplings responsible for the unique magnetic properties of endohedral fullerenes with a single magnetic ion, focusing on the Dy@C81N complex as an example. The study reveals that only two vibrational modes, characterized by translational motion of the Dy ion along the interior surface of the fullerene cage, drive high-temperature magnetic relaxation. These low-frequency quasi-translational modes represent a vibrational bottleneck for magnetic relaxation, similar to the one previously identified in the single-atom magnets with magnetic ions placed on metal oxide or graphene surfaces. Taking advantage of this vibrational bottleneck by eliminating the resonances between the spin transitions and the vibrational transitions involving two quasi-translational modes could lead to endohedral fullerenes with even higher blocking temperature and longer magnetic relaxation time.