Ab Initio Prediction of High-Temperature Magnetic Relaxation Rates in Single-Molecule Magnets

Organometallic molecules based on [Dy(Cp^R)₂]⁺ cations (where Cp^R is a substituted cyclopentadienyl anion) have emerged as clear front-runners in the search for high-temperature single-molecule magnets. Within this family of structurally similar molecules, significant variations in their magnetic properties are seen, demonstrating the importance of understanding magneto-structural relationships to develop more efficient design strategies. Here we develop an ab initio spin dynamics methodology and show that it is capable of quantitative prediction of relative relaxation rates in the Orbach region. Applying it to all reported [Dy(Cp^R)₂]⁺ cations allows us understand differences in their relaxation dynamics, highlighting that the main discriminant is the magnitude of the crystal field splitting, rather than differences in spin-vibrational coupling. We subsequently employ the method to predict relaxation rates for a series of hypothetical organometallic sandwich compounds, revealing an upper limit to the effective barrier to magnetic relaxation of around 2100-2200 K, which has been reached by existing compounds. Our conclusion is that further improvements to monometallic single-molecule magnets require moving vibrational modes off-resonance with electronic excitations.