Vibrational Bottleneck of Magnetic Relaxation in Single-Ion Endohedral Fullerenes

Endohedral-fullerene-based molecular magnets containing a single lanthanide ion demonstrate high blocking temperature and long magnetic relaxation time despite their weak crystal field anisotropy. This work presents a comprehensive <i>ab initio</i> 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 molecular vibrations, characterized by translational motion of the ion along the interior surface of the fullerene cage, drive high-temperature magnetic relaxation. These low-frequency modes represent a vibrational bottleneck for magnetic relaxation, similar to the one identified in the single-atom magnets with magnetic ions placed on metal oxide or graphene surfaces. However, the translational motions of the ion inside the fullerene cage can hybridize with the internal rotation of fullerenes in the molecular crystal, resulting in more vibrations strongly coupled to electron spin.