Fig. 1: Quantum tunnelling in Dy(III) single-molecule magnets.
From: Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets
a Typical energy level diagram of the lowest-energy J multiplet with angular momentum J = 15/2 in a Dy(III) single-molecule magnet (SMM), with degenerate doublets at energies E1, E2, etc. States are organised according to the expectation value of the total angular momentum along the magnetic anisotropy axis \(\left\langle {\hat{J}}_{z}\right\rangle\). Dipolar and hyperfine magnetic fields (Bint) can lift the degeneracy of the ground doublet and cause quantum tunnelling of the magnetisation (QTM), which results in avoided crossings when sweeping an external magnetic field Bext. Molecular vibrations can influence the magnitude of the energy splitting Δ1. b Top: Molecular structure of \({[{{{{{{{\rm{Dy}}}}}}}}{({{{{{{{{\rm{Cp}}}}}}}}}^{{{{{{{{\rm{ttt}}}}}}}}})}_{2}]}^{+}\) surrounded by a dichloromethane (DCM) bath. Bottom: Structure of a [Dy(bbpen)Br] molecular crystal. Only the two SMMs in the primitive unit cell are shown; violet spheres represent Dy atoms at other lattice positions. Atoms are colour-coded as follows: Dy (violet), Br (brown), Cl (green), O (red), N (cyan), C (grey), H (white). In both cases, z indicates the direction of the easy axis. c Idea behind the polaron transformation \(\hat{S}\) of Eq. (6). Each spin state \(\left|{1}_{\pm }^{{\prime} }\right\rangle\) is accompanied by a vibrational distortion (greatly exaggerated for visualisation), thus forming a magnetic polaron. Vibrational states \(\left|\nu \right\rangle\) are now described in terms of harmonic displacements around the deformed structure, which depends on the state of the spin. Polarons provide an accurate physical picture when the spin–phonon coupling is strong and mostly modulates the energy of different spin states but not the coupling between them.
