The lanthanide-based single-molecule magnets (SMMs) are characterized by magnetic bistability and hysteresis at elevated temperatures as high as that of liquid nitrogen, making SMMs promising candidates for applications in memory storage devices. The rate of relaxation of magnetization in SMMs determines the lifetime of stored information and thus the usefulness of such memory storage devices. This relaxation rate depends on the strength of magnetic anisotropy, which can be predicted from the high-level ab initio electronic structure calculations. The spin-orbit coupling (SOC) plays a critical role in predicting the electronic structure and magnetic properties of the lanthanide-based SMMs. Traditionally, the relativistic SOC effect has been calculated using the perturbation theory, which is a questionable approach for such heavy elements as lanthanides.  In this work, we address this potential problem by utilizing the variational fully-relativistic electronic structure calculations to accurately predict the magnetic properties of lanthanide-based SMMs. We focus on the electronic structure of [DyO]<sup>+</sup> molecule with the perfect axial symmetry that maximizes the magnetic anisotropy. The results obtained with the four- and two-component high-level relativistic electronic structure methods are compared with the predictions from the traditional perturbative SOC calculations. We find significant differences between the magnetic properties predicted by the variational relativistic methods and the perturbational SOC calculations. These results have direct implication for the design of lanthanide-based SMMs with long spin relaxation time.

Predicting electronic structure of the lanthanide-based molecular magnets with non-perturbative relativistic methods

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