  To design molecular spin qubits with enhanced quantum coherence, a control of
the coupling between the local vibrations and the spin states is crucial, which
could be realized in principle by engineering molecular structures via
coordination chemistry. To this end, understanding the underlying structural
factors that govern the spin relaxation is a central topic. Here, we report the
investigation of the spin dynamics in a series of chemically-designed
europium(II)-based endohedral metallofullerenes (EMFs). By introducing a unique
structural difference, i.e. metal-cage binding site, while keeping other
molecular parameters constant between different complexes, these manifest the
key role of the three low energy metal-based vibrations in mediating the
spin-lattice relaxation times (T1). The temperature dependence of T1 can thus
be normalized by the frequencies of these low energy vibrations to show an
unprecedentedly universal behavior for EMFs in frozen CS2 solution. Our
theoretical analysis indicates that this structural difference determines not
only the vibrational rigidity but also spin-vibration coupling in these
EMF-based qubit candidates.
