Inter-Kramers Transitions and Spin-Phonon Couplings in a Lanthanide-Based Single-Molecule Magnet

Spin-phonon coupling plays a critical role in magnetic relaxation in single-molecule magnets (SMMs) and molecular qubits. Yet, few studies of its nature have been conducted. Phonons here refer to both intermolecular and intramolecular vibrations. In the current work, we show spin-phonon couplings between IR-active phonons in a lanthanide molecular complex and Kramers doublets (from the crystal field). For the SMM Er[N(SiMe₃)₂]₃ (1, Me = methyl), the couplings are observed in the far-IR magnetospectroscopy (FIRMS) of crystals with coupling constants ≈ 2-3 cm^-1. In particular, one of the magnetic excitations couples to at least two phonon excitations. The FIRMS reveals at least three magnetic excitations (within the ⁴I_15/2 ground state/manifold; hereafter, manifold) at 0 T at 104, ∼180, and 245 cm^-1, corresponding to transitions from the ground state, M_J = ±15/2, to the first three excited states, M_J = ±13/2, ±11/2, and ±9/2, respectively. The transition between the ground and first excited Kramers doublet in 1 is also observed in inelastic neutron scattering (INS) spectroscopy, moving to a higher energy with an increasing magnetic field. INS also gives complete phonon spectra of 1. Periodic DFT computations provide the energies of all phonon excitations, which compare well with the spectra from INS, supporting the assignment of the inter-Kramers doublet (magnetic) transitions in the spectra. The current studies unveil and measure the spin-phonon couplings in a typical lanthanide complex and throw light on the origin of the spin-phonon entanglement.