Comprehensive Studies of Magnetic Transitions and Spin-Phonon Couplings in the Tetrahedral Cobalt Complex Co(AsPh3)2I2.

A combination of inelastic neutron scattering (INS), far-IR magneto-spectroscopy (FIRMS), and Raman magneto-spectroscopy (RaMS) has been used to comprehensively probe magnetic excitations in Co(AsPh3)2I2 (1), a reported single-molecule 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 P21/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.

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 4I15/2 ground state/manifold; hereafter, manifold) at 0 T at 104, ∼180, and 245 cm-1, corresponding to transitions from the ground state, MJ = ±15/2, to the first three excited states, MJ = ±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.

Spectroscopic Studies of the Magnetic Excitation and Spin-Phonon Couplings in a Single-Molecule Magnet.

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.

Effect of magnetic fields on the methyl rotation in a paramagnetic cobalt(ii) complex. Quasielastic neutron scattering studies.

Molecular dynamics is a fundamental property of metal complexes. These dynamic processes, especially for paramagnetic complexes under external magnetic fields, are in general not well understood. Quasielastic neutron scattering (QENS) in 0-4 T magnetic fields has been used to study the dynamics of Co(acac)2(D2O)2 (1-d4, acac = acetylacetonate). At 80-100 K, rotation of the methyl groups on the acac ligands is the dominant dynamical process. This rotation is slowed down by the magnetic field increase. Rotation times at 80 K are 5.6(3) × 10-10 s at 0 T and 2.04(10) × 10-9 s at 4 T. The QENS studies suggest that methyl groups in these paramagnetic Co(ii) molecules do not behave as isolated units, which is consistent with results from earlier magnetic susceptibility studies indicating the presence of intermolecular interactions. DFT calculations show that unpaired electron spin density in 1 is dispersed to the atoms of both acac and H2O ligands. Methyl torsions in 1-d4 have also been observed at 5-100 K in inelastic neutron spectroscopy (INS). The QENS and INS results here help understand the dynamics of the compound in the solid state.

Spin-phonon couplings in transition metal complexes with slow magnetic relaxation.

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.

Slow Magnetic Relaxations in Cobalt(II) Tetranitrate Complexes. Studies of Magnetic Anisotropy by Inelastic Neutron Scattering and High-Frequency and High-Field EPR Spectroscopy.

Three mononuclear cobalt(II) tetranitrate complexes (A)2[Co(NO3)4] with different countercations, Ph4P+ (1), MePh3P+ (2), and Ph4As+ (3), have been synthesized and studied by X-ray single-crystal diffraction, magnetic measurements, inelastic neutron scattering (INS), high-frequency and high-field EPR (HF-EPR) spectroscopy, and theoretical calculations. The X-ray diffraction studies reveal that the structure of the tetranitrate cobalt anion varies with the countercation. 1 and 2 exhibit highly irregular seven-coordinate geometries, while the central Co(II) ion of 3 is in a distorted-dodecahedral configuration. The sole magnetic transition observed in the INS spectroscopy of 1-3 corresponds to the zero-field splitting (2(D2 + 3E2)1/2) from 22.5(2) cm-1 in 1 to 26.6(3) cm-1 in 2 and 11.1(5) cm-1 in 3. The positive sign of the D value, and hence the easy-plane magnetic anisotropy, was demonstrated for 1 by INS studies under magnetic fields and HF-EPR spectroscopy. The combined analyses of INS and HF-EPR data yield the D values as +10.90(3), +12.74(3), and +4.50(3) cm-1 for 1-3, respectively. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal the slow magnetization relaxation in 1 and 2 at an applied dc field of 600 Oe, which is a characteristic of field-induced single-molecule magnets (SMMs). The electronic structures and the origin of magnetic anisotropy of 1-3 were revealed by calculations at the CASPT2/NEVPT2 level.

Magnetic Transitions in Iron Porphyrin Halides by Inelastic Neutron Scattering and Ab Initio Studies of Zero-Field Splittings.

Zero-field splitting (ZFS) parameters of nondeuterated metalloporphyrins [Fe(TPP)X] (X = F, Br, I; H2TPP = tetraphenylporphyrin) have been directly determined by inelastic neutron scattering (INS). The ZFS values are D = 4.49(9) cm⁻¹ for tetragonal polycrystalline [Fe(TPP)F], and D = 8.8(2) cm⁻¹, E = 0.1(2) cm⁻¹ and D = 13.4(6) cm⁻¹, E = 0.3(6) cm⁻¹ for monoclinic polycrystalline [Fe(TPP)Br] and [Fe(TPP)I], respectively. Along with our recent report of the ZFS value of D = 6.33(8) cm⁻¹ for tetragonal polycrystalline [Fe(TPP)Cl], these data provide a rare, complete determination of ZFS parameters in a metalloporphyrin halide series. The electronic structure of [Fe(TPP)X] (X = F, Cl, Br, I) has been studied by multireference ab initio methods: the complete active space self-consistent field (CASSCF) and the N-electron valence perturbation theory (NEVPT2) with the aim of exploring the origin of the large and positive zero-field splitting D of the 6A1 ground state. D was calculated from wave functions of the electronic multiplets spanned by the d5 configuration of Fe(III) along with spin­orbit coupling accounted for by quasi degenerate perturbation theory. Results reproduce trends of D from inelastic neutron scattering data increasing in the order from F, Cl, Br, to I. A mapping of energy eigenvalues and eigenfunctions of the S = 3/2 excited states on ligand field theory was used to characterize the σ- and π-antibonding effects decreasing from F to I. This is in agreement with similar results deduced from ab initio calculations on CrX6³â» complexes and also with the spectrochemical series showing a decrease of the ligand field in the same directions. A correlation is found between the increase of D and decrease of the π- and σ-antibonding energies e(λ)(X) (λ = σ, π) in the series from X = F to I. Analysis of this correlation using second-order perturbation theory expressions in terms of angular overlap parameters rationalizes the experimentally deduced trend. D parameters from CASSCF and NEVPT2 results have been calibrated against those from the INS data, yielding a predictive power of these approaches. Methods to improve the quantitative agreement between ab initio calculated and experimental D and spectroscopic transitions for high-spin Fe(III) complexes are proposed.