Spin–phonon coupling plays an important role in single-molecule magnets and molecular qubits. However, there have been few detailed studies of its nature. Here, we show for the first time distinct couplings of g phonons of CoII(acac)2(H2O)2 (acac = acetylacetonate) and its deuterated analogs with zero-field-split, excited magnetic/spin levels (Kramers doublet (KD)) of the S = 3/2 electronic ground state. The couplings are observed as avoided crossings in magnetic-field-dependent Raman spectra with coupling constants of 1–2 cm−1. Far-IR spectra reveal the magnetic-dipole-allowed, inter-KD transition, shifting to higher energy with increasing field. Density functional theory calculations are used to rationalize energies and symmetries of the phonons. A vibronic coupling model, supported by electronic structure calculations, is proposed to rationalize the behavior of the coupled Raman peaks. This work spectroscopically reveals and quantitates the spin–phonon couplings in typical transition metal complexes and sheds light on the origin of the spin–phonon entanglement.

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.

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh 3 ) 2 X 2 (Co-X; X = Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S = 3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X, showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spinphonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

Co(acac)2(H2O)2 (1, acac = acetylacetonate), a transition metal complex (S = 3/2), displays field‐induced slow magnetic relaxation as a single‐molecule magnet. For 1 and its isotopologues Co(acac)2(D2O)2 (1‐d4) and Co(acac‐d7)2(D2O)2 (1‐d18) in approximately D4h symmetry, zero‐field splitting of the ground electronic state leads to two Kramers doublets (KDs): lower energy MS = ±1/2 (ϕ1,2) and higher energy MS = ±3/2 (ϕ3,4) states. This work employs inelastic neutron scattering (INS), a unique method to probe magnetic transitions, to probe different magnetic excitations in 1‐d4 and 1‐d18. Direct‐geometry, time‐of‐flight Disk‐Chopper Spectrometer (DCS), with applied magnetic fields up to 10 T, has been used to study the intra‐KD transition as a result of Zeeman splitting, MS = –1/2 (ϕ1) → MS = +1/2 (ϕ2), in 1‐d18. This is a rare study of the MS = –1/2 → MS = +1/2 excitation in transition metal complexes by INS. Indirect‐geometry INS spectrometer VISION has been used to probe the inter‐KD, ZFS transition, MS = ±1/2 (ϕ1,2) → MS = ±3/2 (ϕ3,4) in both 1‐d4 and 1‐d18, by variable‐temperature (VT) properties of this excitation. The INS spectra measured on VISION also give phonon features of the complexes that are well described by periodic DFT phonon calculations.

Large separations between ground and excited magnetic states in single‐molecule magnets (SMMs) are desirable to reduce the likelihood of spin reversal in the molecules. Spin‐phonon coupling is a process leading to magnetic relaxation. Both the reversal and coupling, making SMMs lose magnetic moments, are undesirable. However, direct determination of large magnetic states separations (>45 cm−1) is challenging, and few detailed investigations of the spin‐phonon coupling have been conducted. The magnetic separation in [Co(12‐crown‐4)2](I3)2(12‐crown‐4) (1) is determined and its spin‐phonon coupling is probed by inelastic neutron scattering (INS) and far‐IR spectroscopy. INS, using oriented single crystals, shows a magnetic transition at 49.4(1.0) cm−1. Far‐IR reveals that the magnetic transition and nearby phonons are coupled, a rarely observed phenomenon, with spin‐phonon coupling constants of 1.7–2.5 cm−1. The current work spectroscopically determines the ground–excited magnetic states separation in an SMM and quantifies its spin‐phonon coupling, shedding light on the process causing magnetic relaxation.

α-Sb 2 O 3 (senarmontite), β-Sb 2 O 3 (valentinite), and α-TeO 2 (paratellurite) are compounds with pronounced stereochemically active Sb and Te lone pairs. The vibrational and lattice properties of each have been previously studied but often lead to incomplete or unreliable results due to modes being inactive in infrared or Raman spectroscopy. Here, we present a study of the relationship between bonding and lattice dynamics of these compounds. Mossbauer spectroscopy is used to study the structure of Sb in α-Sb 2 O 3 and β-Sb 2 O 3 , whereas the vibrational modes of Sb and Te for each oxide are investigated using nuclear inelastic scattering, and further information on O vibrational modes is obtained using inelastic neutron scattering. Additionally, vibrational frequencies obtained by density functional theory (DFT) calculations are compared with experimental results in order to assess the validity of the utilized functional. Good agreement was found between DFT-calculated and experimental density of phonon states with a 7% scaling factor. The Sb−O−Sb wagging mode of α-Sb 2 O 3 whose frequency was not clear in most previous studies is experimentally observed for the first time at ∼340 cm −1 . Softer lattice vibrational modes occur in orthorhombic β-Sb 2 O 3 compared to cubic α-Sb 2 O 3 , indicating that the antimony bonds are weakened upon transforming from the molecular α phase to the layer-chained β structure. The resulting vibrational entropy increase of 0.45 ± 0.1 k B /Sb 2 O 3 at 880 K accounts for about half of the α−β transition entropy. The comparison of experimental and theoretical approaches presented here provides a detailed picture of the lattice dynamics in these oxides beyond the zone center and shows that the accuracy of DFT is sufficient for future calculations of similar material structures.

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A combination of inelastic neutron scattering (INS), far-IR magnetospectroscopy (FIRMS), and Raman magneto-spectroscopy (RaMS) has been used to comprehensively probe magnetic excitations in Co(AsPh 3 ) 2 I 2 (1), a reported singlemolecule magnet (SMM). With applied field, the magnetic zero-field splitting (ZFS) peak (2D′) shifts to higher energies in each spectroscopy. INS placed the ZFS peak at 54 cm −1 , as revealed by both variable-temperature (VT) and variable-magnetic-field data, giving results that agree well with those from both far-IR and Raman studies. Both FIRMS and RaMS also reveal the presence of multiple spin−phonon couplings as avoided crossings with neighboring phonons. Here, phonons refer to both intramolecular and lattice vibrations. The results constitute a rare case in which the spin− phonon couplings are observed with both Raman-active (g modes) and far-IR-active phonons (u modes; space group P2 1 /c, no. 14, Z = 4 for 1). These couplings are fit using a simple avoided crossing model with coupling constants of ca. 1−2 cm −1 . The combined spectroscopies accurately determine the magnetic excited level and the interaction of the magnetic excitation with phonon modes. Density functional theory (DFT) phonon calculations compare well with INS, allowing for the assignment of the modes and their symmetries. Electronic calculations elucidate the nature of ZFS in the complex. Features of different techniques to determine ZFS and other spin-Hamiltonian parameters in transition-metal complexes are summarized.