Unraveling the Contributions to Spin–Lattice Relaxation in Kramers Single-Molecule Magnets

Abstract

The study of how spin interacts with lattice vibrations and relaxes to equilibrium provides unique insights into its chemical environment and the relation between electronic structure and molecular composition. Despite its importance for several disciplines, ranging from magnetic resonance to quantum technologies, a convincing interpretation of spin dynamics in crystals of magnetic molecules is still lacking due to the challenging experimental determination of the correct spin relaxation mechanism. We apply ab initio spin dynamics to a series of 12 coordination complexes of Co 2+ and Dy 3+ ions selected among ∼240 compounds that largely cover the literature on single-molecule magnets and well represent different regimes of spin relaxation. Simulations reveal that the Orbach spin relaxation rate of known compounds mostly depends on the ions' zero-field splitting and little on the details of molecular vibrations. Raman relaxation is instead found to be also significantly affected by the features of low-energy phonons. These results provide a complete understanding of the factors limiting spin lifetime in single-molecule magnets and revisit years of experimental investigations by making it possible to transparently distinguish Orbach and Raman relaxation mechanisms.

Trityl‐Based Lanthanide‐Supramolecular Assemblies Exhibiting Slow Magnetic Relaxation

“…This indicates the dominance of the under‐barrier Raman relaxation which is not directly related to the calculated magnetic anisotropy being more sensitive to the phonon modes of the crystal lattice. The related calculations are beyond the scope of this work [27] . As both 1 and 2 contain two crystallographically distinguishable Dy(III) complexes closely attached by hydrogen bonds, it is expected that the dipolar interactions will play a non‐negligible role in their magnetism.…”

Multifunctionality of luminescent molecular nanomagnets based on lanthanide complexes

“…A difficult issue is to control the Raman relaxation, which is related to the presence of lattice vibrations that can disturb the SMM properties, even for a large magnetic anisotropy. [181][182][183] In addition, if the magnetic Ln(II/III) system shows non-negligible transverse anisotropy, quantum tunneling of the magnetization (QTM) is observed. The occurrence of QTM in the majority of Ln-based SMM systems implies the presence of a swift relaxation pathway and drastically limits the relaxation times.…”

QBithm: towards the coherent control of robust spin qubits in quantum algorithms

“…This issue has been addressed over the last years with fruitful results and we refer the reader interested in using the purely ab initio mode to SI, the adapted version of SIMPRE, and the relevant contributions. [56][57][58][59][60][61][62][70][71][72][73] In case of operating under the said mode, QBithm connects in a natural way with them as their output is part of the input required to determine Γ ab , Γ em . Interestingly, whenever Eq.1 provides an accurate enough description of the given physical process, the values of Γ ab,add , Γ em,add , Γ mag,add that result from fitting relevant experimental data under either the semi-empirical or the combined mode can be used as a benchmark to guide which additional mechanisms should be included in Γ ab , Γ em , Γ mag until the values of these rates resemble those of Γ ab,add , Γ em,add , Γ mag,add .…”

“…The relaxation rates are rather an input of our master equation and hence this work connects in a natural way with all the the-oretical efforts made over the past years devoted to compute them from ab initio methods. [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] In the race for the highly-prized scalable architectures, the realization of many-qubit systems will certainly depend on a proper understanding of the singlequbit dynamics under relaxation, external control, and imperfections as a key building block. Hence, we expect that our contribution will help to lay the foundations in the modeling of, firstly, qubit pairs for logical gates and, then, quantum algorithms involving larger numbers of qubits.…”