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 design of slow relaxing magnetic molecules requires the optimization of internal molecular vibrations to reduce spin-phonon coupling.

The coupling between electronic spins and lattice vibrations is fundamental for driving relaxation in magnetic materials. The debate over the nature of spin-phonon coupling dates back to the 1940s, but the role of spin-spin, spin-orbit, and hyperfine interactions has never been fully established. Here, we present a comprehensive study of the spin dynamics of a crystal of Vanadyl-based molecular qubits by means of first-order perturbation theory and first-principles calculations. We quantitatively determine the role of the Zeeman, hyperfine, and electronic spin dipolar interactions in the direct mechanism of spin relaxation. We show that, in a high magnetic field regime, the modulation of the Zeeman Hamiltonian by the intramolecular components of the acoustic phonons dominates the relaxation mechanism. In low fields, hyperfine coupling takes over, with the role of spin-spin dipolar interaction remaining the less important for the spin relaxation.

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.

Here we report the investigation of the magnetization dynamics of a vanadyl complex with diethyldithiocarbamate (Etdtc) ligands, namely [VO(Etdtc)] (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.

Vanadium(iv) complexes have recently shown record quantum spin coherence times that in several circumstances are limited by spin-lattice relaxation. The role of the environment and vibronic properties in the low temperature dynamics is here investigated by a comparative study of the magnetization dynamics as a function of crystallite size and the steric hindrance of the β-diketonate ligands in VO(acac) (1), VO(dpm) (2) and VO(dbm) (3) evaporable complexes (acac = acetylacetonate, dpm = dipivaloylmethanate, and dbm = dibenzoylmethanate). A pronounced crystallite size dependence of the relaxation time is observed at unusually high temperatures (up to 40 K), which is associated with a giant spin-phonon bottleneck effect. We model this behaviour by an ad hoc force field approach derived from density functional theory calculations, which evidences a correlation of the intensity of the phenomenon with ligand dimensions and the unit cell size.

Being Φ ij (lm) the force constant, coupling the i-th atomic degrees of freedom in the lattice cell at the position R l and the j-the atomic degrees of freedom in the lattice cell of position R m , the dynamical matrix, K(q), at the q-point, is built aswhere the sum runs over all the infinite periodic cells of the crystal. The eigenvalues of K(q)are ω 2 (q), while the eigenvectors L(q) defines the normal modes of vibration. Magnetic Properties CalculationsThe ORCA software 2 has been employed for the calculation of the g e and A tensors for both equilibrium and distorted geometries. We have used the basis sets def2-TZVP for V and O, def2-SVP for C and H and a def2-TZVP/C auxiliary basis set for all the elements. For the calculation of the A tensors the entire basis set have been de-contracted. The calculations of the g e tensors have been carried out at both the DFT level, with the PBE functional, 3 and at the CASSCF+NEVPT2 level of theory, with a (1,5) active space and spin-orbit contributions included through quasi-degenerate perturbation theory. The calculations of the A tensors have been performed at the DFT level with the PBE functional. Machine Learning Training and Test Sets GenerationsThe training sets for the machine learning (ML) models have been generated by calculating both g e and A for 2600 distorted structures. The distorted structures were obtained by displacing all the Cartesian coordinates of all the atoms of the DFT optimized geometry S2

We present a first-principles investigation of spin-phonon relaxation in a molecular crystal of Co 2+ single-ion magnets. Our study combines electronic structure calculations with machine-learning force fields and unravels the nature of both the Orbach and the Raman relaxation channels in terms of atomistic processes. We find that although both mechanisms are mediated by the excited spin states, the low temperature spin dynamics is dominated by phonons in the THz energy range, which partially suppress the benefit of having a large magnetic anisotropy. This study also determines the importance of intra-molecular motions for both the relaxation mechanisms and paves the way to the rational design of a new generation of single-ion magnets with tailored spin-phonon coupling.