Abstract
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.
Highlights
Lanthanide elements find widespread use in numerous technological[1] and biomedical applications.[2]
The geometry around the lanthanide ion can be approximated to a structure with point-group symmetry D2d, the actual symmetry is too low to provide hints about the orientation and the values of the components of the magnetic anisotropy tensor
In order to accurately simulate the chemical environment of the Dy ion, our model includes (i) the molecular unit made of [Dy(acac)3(H2O)2] and two cocrystallized ethanol and water molecules and (ii) a surrounding 7 × 5 × 7 supercell of point charges placed at the atomic crystallographic positions to reproduce the Madelung potential inside the crystal
Summary
Lanthanide elements find widespread use in numerous technological[1] and biomedical applications.[2]. For both vib[1] and vib[2], we compute an atomically resolved expansion of the electrostatic potential for different vibrational amplitudes and compute the crystal field parameters by replacing one acac ligand (acac[1] in Figure S1) with the corresponding atomic point charges, dipoles, and quadrupoles within the LOPROP scheme.[71] Such an electrostatic analysis allows us to extrapolate atomic-centered multipolar expansion from the computed all-electron CASSCF wave function.[72,73] The spin-phonon coupling coefficients obtained with an electrostatic model that includes only the contribution of the acac’s oxygen donor atoms are in excellent agreement with the original ones obtained with the explicit model This demonstrates that, the static crystal field is generally determined by both electrostatic[21] and covalent interactions,[74] its modulation by small atomic displacements, i.e., the spinphonon coupling, is largely driven by the electrostatic effects of Dyacac’s first coordination sphere. This has been observed for molecular qubits presenting acac ligands[37,41] suggesting a critical role of this low-energy motion in promoting admixture of intra- and intermolecular motions
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