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 4
I
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.