Spin–phonon coupling and magnetic relaxation in single-molecule magnets

Abstract

Electron–phonon coupling underlies many physical phenomena, but its microscopic origins are nuanced. This Review derives the spin–phonon interactions in molecules from first principles, and describes an implementation for molecular spin dynamics calculations.

Theoretical Magnetic Relaxation and Spin–Phonon Coupling Study in a Series of Molecular Engineering Designed Bridged Dysprosocenium Analogues

“…In the context of SMMs, they function as transmitters of energy to/from the magnetic centers that are in contact with the thermal bath (heat transfer) under the condition of thermal equilibrium. Recently, the need to include the effects of phonons to compute magnetic relaxation times has risen, and several methods to quantify their effect have been developed . In a nutshell, these methods rely on a study of the dependence of g -factors, zero-field splitting parameters D and E , crystal field operators, or energy separations between KDs.…”

Accurate and Efficient Spin–Phonon Coupling and Spin Dynamics Calculations for Molecular Solids

“…The Hessian is then “mass-weighted” using the atomic masses to give the dynamical matrix, which is diagonalized to give the normal modes of vibration and squared frequencies. The process is slightly more involved than this, as the calculations are periodic, and we refer the interested reader to our recent Tutorial Review, which covers this in detail . The Phono3py code is similarly used to generate a sequence of distorted structures in which pairs of atoms are displaced to obtain the third-order force constants, which are combined with the harmonic frequencies and eigenvectors to determine the phonon lifetimes and line widths.…”

“…Magnetic relaxation rates are then determined using our Tau code (commit e058b24959), considering Orbach and Raman rates, ,, given by eqs 40, 41, and 46–49 in reference . There are two forms of the Raman mechanism, which arise from their derivation using different orders of perturbation theory: ,, the Raman-I mechanism (first-order in spin–phonon coupling, second-order in time) does not depend on the magnitude of an external magnetic field, while the Raman-II mechanism (second-order in spin–phonon coupling, first-order in time) has a quadratic dependence on the field and vanishes in zero field . Since our experiments are performed in zero field, we do not consider the Raman-II mechanism, and we therefore refer to the Raman-I mechanism simply as “the Raman mechanism” throughout.…”

T1 Anisotropy Elucidates Spin Relaxation Mechanisms in an S = 1 Cr(IV) Optically Addressable Molecular Qubit

“…The decrease in the sin 2 (2θ) contribution to the T 1 anisotropy with increasing temperature also suggests that the rotational motion arises from low-energy acoustic or pseudoacoustic phonons. The latter may carry significant rotational character when there are multiple molecules per unit cell, as is the case here ( Z = 10) . Further exploration of structurally diverse S = 1 complexes will be required to ascertain the generality of the rotational sin 2 (2θ) contributions.…”

“…Over the temperature range of 7–60 K, the amount of T 1 anisotropy for Cr­( o -tolyl) 4 steadily decreases, with the dominant sin 2 (2θ) anisotropic contribution decreasing from 23% to 10% of the total T 1 (Figure ). This decrease with increasing temperature indicates that sin 2 (2θ) anisotropy arises from very low energy degrees of freedom, likely acoustic or pseudoacoustic phonons ( vide infra ). Indeed, the isotropic field-dependent contribution to 1/ T 1 decreases at the same pace over this temperature range, and this contribution is commonly ascribed to the direct process of spin relaxation .…”