# Orientationally Resolved Electron-Spin Relaxation and Coherence in Fullerene-Encapsulated Rare-Earth Dimers with a Single-Electron Metal–Metal Bond

## TL;DR

This study explores the spin dynamics of rare-earth dimers inside carbon cages, revealing how their structure affects quantum properties.

## Contribution

The paper introduces a systematic EPR study of dimetallofullerenes with varying metal compositions and cage isomers.

## Key findings

- Fullerene isomerism significantly impacts the spin dynamics of metal dimers.
- Spin-lattice relaxation times differ between Ih and D5h cage isomers due to spin-phonon coupling.
- Substituting Y with Gd accelerates spin-lattice relaxation and decoherence.

## Abstract

Rare-earth dimers with single-electron metal–metal
bonds
feature strong hyperfine and exchange interactions between metal atoms
and an unpaired valence electron. Their stabilization inside carbon
cages opens the possibility for applications in quantum information
processing and sensing but requires investigation of their unusual
spin states and dynamics. Herein, we present a systematic EPR study
of dimetallofullerenes M2@C80(CH2Ph) with M2
5+ dimers, whose composition varied
from Y2 (S = 1/2) through YGd (S = 4) to Gd2 (S = 15/2). High-field
W-band EPR spectroscopy facilitated the analysis of different molecular
orientations and T
1 anisotropy and allowed
resolution of individual |m
S⟩ →
|m
S + 1⟩ transitions in high-spin
Gd dimetallofullerenes. For Y2@C80(CH2Ph), we demonstrated that fullerene isomerism strongly influences
the molecular and spin dynamics of metal dimers. The pronounced difference
in spin-lattice relaxation times T
1 was
found for the Ih
and D
5h
cage isomers and rationalized by Raman
spectroscopic study and calculations of spin-phonon couplings. Lateral
metal modes, which play the main role in the spin-lattice relaxation
of endohedral metallofullerenes, were found at higher frequencies
in the D
5h
isomer, in
line with its longer T
1. The orientational
dependence of spin decoherence was ascribed to the rotational motion
of the Y2@C80(CH2Ph) molecules in
glassy toluene. Substitution of Y with Gd accelerated spin-lattice
relaxation and decoherence. A similar T
1 and phase-memory relaxation time (T
m) of YGd@C80(CH2Ph) and Gd2@C80(CH2Ph) proved that the effect does not scale
with the number of Gd atoms. While the Rabi frequency is constant
across the whole spectrum in Y2@C80(CH2Ph), YGd@C80(CH2Ph) and Gd2@C80(CH2Ph) exhibit variations in the Rabi frequencies
for their |m
S⟩ → |m
S + 1⟩ transitions.