The unique electronic and magnetic properties of Lanthanides molecular complexes place them at the forefront of the race towards high-temperature single-ion magnets and magnetic quantum bits. The design of compounds of this class has so far been almost exclusively driven by static crystal field considerations, with emphasis on increasing the magnetic anisotropy barrier. This guideline has now reached its maximum potential and new progress can only come from a deeper understanding of spin-phonon relaxation mechanisms. 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-ion 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 ions 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
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