Binding Sites, Vibrations and Spin‐Lattice Relaxation Times in Europium(II)‐Based Metallofullerene Spin Qubits

Abstract

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-displacing vibrations in mediating the spinlattice relaxation times (T 1 ). The temperature dependence of T 1 can thus be normalized by the frequencies of these low energy vibrations to show an unprecedentedly universal behavior for EMFs in frozen CS 2 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.

Endohedral metallofullerene molecular nanomagnets

“…In this line, it is the carbon ring motifs coordinating to the metal inside the cage that are of significance to the single-ion anisotropy and ligand fields, which include various binding sites such as a hexagon, pyracylene, and a fused-pentagon in a cage violating the isolated pentagon rule (IPR). 82,83 However, the number of mixed-metal NCFs based on fullerene cages instead of I h (7)-C 80 is rather limited, partly due to the exceptional stability and high yield of C 80 6− and also associated with the synthetic difficulty in HPLC separation of NCFs with different metallic clusters inside the same cage. Popov et al reported the synthesis of DySc 2 N nitride clusterfullerenes with different carbon cages, including D 3 (6140)-C 68 and D 5h (6)-C 80 as well as the well-studied I h (7)-C 80 .…”

“…In this line, it is the carbon ring motifs coordinating to the metal inside the cage that are of significance to the single-ion anisotropy and ligand fields, which include various binding sites such as a hexagon, pyracylene, and a fused-pentagon in a cage violating the isolated pentagon rule (IPR). 82,83 However, the number of mixed-metal NCFs based on fullerene cages instead of I h (7)-C 80 is rather limited, partly due to the exceptional stability and high yield of C The possibility to construct NCF-based SIMs using other anisotropic Ln 3+ ions, instead of Dy 3+ , has also been explored. AC measurements of HoSc 2 N@I h (7)-C 80 reveal that it is a fieldinduced SMM, that is, slow relaxation of magnetization is only shown in the presence of an applied DC field.…”

“…Only three vibrational modes are present in mono-EMFs in which the metal ion oscillates along the x-, y-and z-axes. 83 This extraordinarily low-coordination environment, being inaccessible via conventional synthetic strategies since Ln ions always tend to have large coordination numbers, resembles the cases where single Ln atoms (Ho and Dy) are attached on graphene or metallic surfaces. [175][176][177] Thanks to the reduced spin-phonon coupling as a result of low coordination, these single-atom magnets display magnetic bistability at an atomic level despite the large strength difference of ligand fields imposed by distinct surfaces.…”

The impact of spin-vibrational coupling on magnetic relaxation of a Co(ii) single-molecule magnet

“…97 A plethora of stimulating reports appeared recently, interpreting the impact of lattice vibrations coupled with electronic spins on magnetization relaxation. 18,[98][99][100] Here, we have probed complex 1, with strong axial magnetic anisotropy, for spin-vibrational dynamics to predict the corresponding relaxation mechanism. The vibrational modes energetically closer to the barrier height are expected to couple with the spin and provide a relaxation pathway.…”

Impact of Spin-Phonon Coupling on Magnetic Relaxation of a Co(II) Single-Molecule Magnet

“…15,[87][88][89] Here, we have probed complex 1, with strong axial magnetic anisotropy, for spin-vibrational dynamics to predict the corresponding relaxation mechanism. The vibrational modes energetically closer to the barrier height are expected to couple with the spin and provide the relaxation pathway 90.…”