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Single-molecule magnets are among the most promising platforms for achievingmolecular-scale data storage and processing. Their magnetisation dynamics aredetermined by the interplay between electronic and vibrational degrees offreedom, which can couple coherently, leading to complex vibronic dynamics.Building on an ab initio description of the electronic and vibrationalHamiltonians, we formulate a non-perturbative vibronic model of the low-energymagnetic degrees of freedom in monometallic single-molecule magnets. Describingtheir low-temperature magnetism in terms of magnetic polarons, we are able toquantify the vibronic contribution to the quantum tunnelling of themagnetisation, a process that is commonly assumed to be independent ofspin-phonon coupling. We find that the formation of magnetic polarons lowersthe tunnelling probability in both amorphous and crystalline systems bystabilising the low-lying spin states. This work, thus, shows that spin-phononcoupling subtly influences magnetic relaxation in single-molecule magnets evenat extremely low temperatures where no vibrational excitations are present.

Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets