The use of single molecule magnets in mainstream electronics requires their magnetic moment to be stable over long times. One can achieve such a goal by designing compounds with spin-reversal barriers exceeding room temperature, namely with large uniaxial anisotropies. Such strategy, however, has been defeated by several recent experiments demonstrating under-barrier relaxation at high temperature, a behaviour today unexplained. Here we propose spin–phonon coupling to be responsible for such anomaly. With a combination of electronic structure theory and master equations we show that, in the presence of phonon dissipation, the relevant energy scale for the spin relaxation is given by the lower-lying phonon modes interacting with the local spins. These open a channel for spin reversal at energies lower than that set by the magnetic anisotropy, producing fast under-barrier spin relaxation. Our findings rationalize a significant body of experimental work and suggest a possible strategy for engineering room temperature single molecule magnets.

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion’s first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

We perform a systematic investigation of the spin-phonon coupling leading to spin relaxation in the prototypical mononuclear single molecule magnet [(tpa^Ph)Fe]⁻. In particular we analyze in detail the nature of the most relevant vibrational modes giving rise to the relaxation. Our fully ab initio calculations, where the phonon modes are evaluated at the level of density functional theory and the spin-phonon coupling by mapping post-Hartree–Fock electronic structures onto an effective spin Hamiltonian, reveal that acoustic phonons are not active in the spin-phonon relaxation process of dilute SMMs crystals. Furthermore, we find that intra-molecular vibrational modes produce anisotropy tensor modulations orders of magnitude higher than those associated to rotations. In light of these results we are able to suggest new designing rules for spin-long-living SMMs which go beyond the tailoring of static molecular features but fully take into account dynamical features of the vibrational thermal bath evidencing those internal molecular distortions more relevant to the spin dynamics.

The intramolecular components of acoustic phonons and the Zeeman interaction make electronic spins relax in an external field.

Spin-phonon coupling is the main driver of spin relaxation and decoherence in solid-state semiconductors at finite temperature. Controlling this interaction is a central problem for many disciplines, ranging from magnetic resonance to quantum technologies. Spin relaxation theories have been developed for almost a century but often use a phenomenological description of phonons and their coupling to spin, resulting in a nonpredictive tool and hindering our detailed understanding of spin dynamics. Here, we combine time-local master equations up to the fourth order with advanced electronic structure methods and perform predictions of spin-phonon relaxation time for a series of solid-state coordination compounds based on both transition metals and lanthanide Kramers ions. The agreement between experiments and simulations demonstrates that an accurate, universal, and fully ab initio implementation of spin relaxation theory is possible, thus paving the way to a systematic study of spin-phonon relaxation in solid-state materials.

Here we report the investigation of the magnetization dynamics of a vanadyl complex with diethyldithiocarbamate (Et₂dtc^–) ligands, namely [VO(Et₂dtc)₂] (1), in both solid-state and frozen solution. This showed an anomalous and unprecedentedly observed field dependence of the relaxation time, which was modeled with three contributions to the relaxation mechanism. The temperature dependence of the weight of the two processes dominating at low fields was found to well correlate with the low energy vibrations as determined by THz spectroscopy. This detailed experimental comparative study represents a fundamental step to understand the spin dynamics of potential molecular quantum bits, and enriches the guidelines to design molecule-based systems with enhanced quantum coherence.