Applying Unconventional Spectroscopies to the Single-Molecule Magnets, Co(PPh3 )2 X2 (X=Cl, Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling

Spectroscopic techniques to probe magnetic anisotropy and spin-phonon coupling in metal complexes

Magnetism of molecular quantum materials such as single-molecule magnets (SMMs) has been actively studied for potential applications in the new generation of high-density data storage using SMMs and quantum information science. Magnetic anisotropy and spin-phonon coupling are two key properties of d- and f-metal complexes. Here, phonons refer to both intermolecular and intramolecular vibrations. Direct determination of magnetic anisotropy and experimental studies of spin-phonon coupling are critical to the understanding of molecular magnetism. This article discusses our recent approach in using three complementary techniques, far-IR and Raman magneto-spectroscopies (FIRMS and RaMS, respectively) and inelastic neutron scatterings (INS), to determine magnetic excited states. Spin-phonon couplings are observed in FIRMS and RaMS. DFT phonon calculations give energies and symmetries of phonons as well as calculated INS spectra which help identify magnetic peaks in experimental INS spectra.

Increasing the Magnetic Blocking Temperature of Single-Molecule Magnets

The synthesis of single-molecule magnets (SMMs), magnetic complexes capable of retaining magnetization blocking for a long time at elevated temperatures, has been a major concern for magnetochemists over the last three decades. In this review, we describe basic SMMs and the different approaches that allow high magnetization-blocking temperatures to be reached. We focus on the basic factors affecting magnetization blocking, magnetic axiality and the height of the blocking barrier, which can be used to group different families of complexes in terms of their SMM efficiency. Finally, we discuss several practical routes for the design of mono- and polynuclear complexes that could be applied in memory devices.

Slow magnetic relaxation in 8-coordinate Mn(II) compounds

The design and synthesis of high-spin Mn(II)-based single-molecule magnets (SMMs) have not been well developed to a great extent, as compared with a large number of SMMs based on the other first row transition metal complexes. In light of our success in designing Fe(II), Co(II) and Fe(III)-based SMMs with a high coordination number of 8, it is of great interest to design Mn(II) analogues with such a strategy. In this contribution, four Mn(II) compounds, [MnII(Ln)2](ClO4)2 (1-4) were obtained from reactions of neutral tetradentate ligands, L1-L4, with hydrated MnII(ClO4)2 (L1 = 2,9-bis(carbomethoxy)-1,10-phenanthroline, L2 = 2,9-bis(carbomethoxy)-2,2'-dipyridine, L3 = N2,N9-dibutyl-1,10-phenanthroline-2,9-dicarboxamide, L4 = 6,6'-bis(2-(tert-butyl)-2H-tetrazol-5-yl)-2,2'-bipyridine). Their crystal structures have been determined by X-ray crystallography and it clearly shows that the Mn(II) centers in these compounds have an oversaturated coordination number of 8. Their magnetic properties have been investigated in detail; to our surprise, all of these Mn(II) compounds show interesting slow magnetic relaxation behaviors under an applied direct current field, although they have very small negative D values.

Direct observation of magnetoelastic coupling in a molecular spin qubit: new insights from crystal field neutron scattering data

Single-molecule magnets are promising candidates for data storage and quantum computing applications. A major barrier to their use is rapid magnetic relaxation and quantum decoherence due to thermal vibrations. Here we report a reanalysis of inelastic neutron scattering (INS) data of the candidate qubit Na9[Ho(W5O18)2]·35D2O, wherein we demonstrate for the first time that magnetic relaxation times and mechanisms can be directly observed as crystal field (CF) peak broadening in INS spectra of a lanthanoid molecular system. The magnetoelastic coupling between the lower energy CF states and phonons (lattice vibrations) is determined by the simultaneous measurement of CF excitations and the phonon density of states, encoded within the same INS experiment. This directly results in the determination of relaxation coupling pathways that occur in this molecule. Such information is invaluable for the further advancement of SMMs and to date has only been obtained from techniques performed in external magnetic fields. Additionally, we determine a relaxation rate of quantum-tunnelling of magnetisation that is consistent with previously measured EPR spectroscopy data.

Spectroscopic and Magnetic Studies of Co(II) Scorpionate Complexes: Is There a Halide Effect on Magnetic Anisotropy?

The observation of single-molecule magnetism in transition-metal complexes relies on the phenomenon of zero-field splitting (ZFS), which arises from the interplay of spin-orbit coupling (SOC) with ligand-field-induced symmetry lowering. Previous studies have demonstrated that the magnitude of ZFS in complexes with 3d metal ions is sometimes enhanced through coordination with heavy halide ligands (Br and I) that possess large free-atom SOC constants. In this study, we systematically probe this "heavy-atom effect" in high-spin cobalt(II)-halide complexes supported by substituted hydrotris(pyrazol-1-yl)borate ligands (Tp^tBu,Me and Tp^Ph,Me). Two series of complexes were prepared: [Co^IIX(Tp^tBu,Me)] (1-X; X = F, Cl, Br, and I) and [Co^IIX(Tp^Ph,Me)(Hpz^Ph,Me)] (2-X; X = Cl, Br, and I), where Hpz^Ph,Me is a monodentate pyrazole ligand. Examination with dc magnetometry, high-frequency and -field electron paramagnetic resonance, and far-infrared magnetic spectroscopy yielded axial (D) and rhombic (E) ZFS parameters for each complex. With the exception of 1-F, complexes in the four-coordinate 1-X series exhibit positive D-values between 10 and 13 cm^-1, with no dependence on halide size. The five-coordinate 2-X series exhibit large and negative D-values between -60 and -90 cm^-1. Interpretation of the magnetic parameters with the aid of ligand-field theory and ab initio calculations elucidated the roles of molecular geometry, ligand-field effects, and metal-ligand covalency in controlling the magnitude of ZFS in cobalt-halide complexes.

Possible Violation of the Spin-Hamiltonian Concept in Interpreting the Zero-Field Splitting

The majority of experimental data in electron spin resonance and molecular magnetism are interpreted in terms of the spin-Hamiltonian (SH) formalism. However, this is an approximate theory that requires a proper testing. In the older variant, the multielectron terms are used as a basis in which the D-tensor components are evaluated by employing the second-order perturbation theory (PT) for nondegenerate states; here, the spin-orbit interaction expressed via the spin-orbit splitting parameter λ serves for the perturbation. The model space is restricted only to the fictitious spin functions |S, M⟩. In the case of the orbital (quasi) degeneracy of the ground term, the PT tends to diverge and the subtracted D, E, and g parameters are false. In the second variant working in the "complete active space" (CAS), the spin-orbit coupling operator is involved by the variation method resulting in the spin-orbit multiplets (energies and eigenvectors) The multiplets can be evaluated either by applying ab initio CASSCF + NEVPT2 + SOC calculations or by using semiempirical generalized crystal-field theory (with the one-electron SOC operator depending upon ξ). The resulting states can be projected onto the subspace of the spin-only kets in the way that the eigenvalues stay invariant. Such an effective Hamiltonian matrix can be reconstructed using six independent components of the symmetric D-tensor from which the D and E values are obtained by solving linear equations. The eigenvectors of the spin-orbit multiplets in the CAS allow determining the dominating composition of the spin projection─cumulative weights of |±M⟩. These are conceptually different from those generated by the SH alone. It is shown that in some cases, the SH theory works satisfactorily for a series of transition-metal complexes; however, sometimes it fails. The ab initio calculations on the SH parameters are compared with the approximate generalized crystal-field theory conducted at the experimental geometry of the chromophore. In total, 12 metal complexes have been analyzed. One of the criteria that assesses the validity of SH is the projection norm N for spin multiplets (this has not to be far from 1). Another criterion is the gap in the spectrum of the spin-orbit multiplets that separates the hypothetical (fictitious) spin-only manifold from the rest of the states.

Multi-Technique Experimental Benchmarking of the Local Magnetic Anisotropy of a Cobalt(II) Single-Ion Magnet

A comprehensive understanding of the ligand field and its influence on the degeneracy and population of d-orbitals in a specific coordination environment are crucial for the rational design and enhancement of magnetic anisotropy of single-ion magnets (SIMs). Herein, we report the synthesis and comprehensive magnetic characterization of a highly anisotropic Co^II SIM, [L₂Co](TBA)₂ (L is an N,N'-chelating oxanilido ligand), that is stable under ambient conditions. Dynamic magnetization measurements show that this SIM exhibits a large energy barrier to spin reversal U _eff > 300 K and magnetic blocking up to 3.5 K, and the property is retained in a frozen solution. Low-temperature single-crystal synchrotron X-ray diffraction used to determine the experimental electron density gave access to Co d-orbital populations and a derived U _eff, 261 cm^-1, when the coupling between the d _{x ² - y ²} and d_xy orbitals is taken into account, in very good agreement with ab initio calculations and superconducting quantum interference device results. Powder and single-crystal polarized neutron diffraction (PNPD, PND) have been used to quantify the magnetic anisotropy via the atomic susceptibility tensor, revealing that the easy axis of magnetization is pointing along the N-Co-N' bisectors of the N,N'-chelating ligands (3.4° offset), close to the molecular axis, in good agreement with complete active space self-consistent field/N-electron valence perturbation theory to second order ab initio calculations. This study provides benchmarking for two methods, PNPD and single-crystal PND, on the same 3d SIM, and key benchmarking for current theoretical methods to determine local magnetic anisotropy parameters.

Magnetic anisotropy and structural flexibility in the field-induced single ion magnets [Co{(OPPh2)(EPPh2)N}2], E = S, Se, explored by experimental and computational methods

During the last few years, a large number of mononuclear Co(II) complexes of various coordination geometries have been explored as potential single ion magnets (SIMs). In the work presented herein, the Co(II) S = 3/2 tetrahedral [Co{(OPPh2)(EPPh2)N}2], E = S, Se, complexes (abbreviated as CoO2E2), bearing chalcogenated mixed donor-atom imidodiphosphinato ligands, were studied by both experimental and computational techniques. Specifically, direct current (DC) magnetometry provided estimations of their zero-field splitting (zfs) axial (D) and rhombic (E) parameter values, which were more accurately determined by a combination of far-infrared magnetic spectroscopy and high-frequency and -field EPR spectroscopy studies. The latter combination of techniques was also implemented for the S = 3/2 tetrahedral [Co{(EPiPr2)2N}2], E = S, Se, complexes, confirming the previously determined magnitude of their zfs parameters. For both pairs of complexes (E = S, Se), it is concluded that the identity of the E donor atom does not significantly affect their zfs parameters. High-resolution multifrequency EPR studies of CoO2E2 provided evidence of multiple conformations, which are more clearly observed for CoO2Se2, in agreement with the structural disorder previously established for this complex by X-ray crystallography. The CoO2E2 complexes were shown to be field-induced SIMs, i.e., they exhibit slow relaxation of magnetization in the presence of an external DC magnetic field. Advanced quantum-chemical calculations on CoO2E2 provided additional insight into their electronic and structural properties.

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.

Evidence for zero-field slow magnetic relaxation in a Co(II) complex with a pseudo-tetrahedral N2I2 environment

Herein, we report on the synthesis, structure and magnetic properties of a four-coordinate mononuclear Co(II) diiodide complex with the 3,5-dimethylpyrazole ligand. A distorted tetrahedral local coordination environment around the central cobalt ion is formed by the two nitrogen atoms of two monodentate pyrazole ligands and by iodide ions. Direct current (dc) magnetic measurements in combination with ab initio SA-CASSCF/NEVPT2 quantum-chemical calculations revealed a strong easy-axis-type magnetic anisotropy with a record value D_exp = -30.58(3) cm^-1 of the axial zero field splitting parameter for pseudo-tetrahedral Co(II)-based CoL₂Hal₂ complexes. Moreover, it is the only complex in this series demonstrating the slow relaxation of magnetization at zero dc field. The Orbach process is shown to be the dominant mechanism of magnetic relaxations in the high temperature range, while the quantum tunneling of magnetization produces the leading contribution to the overall relaxation at temperatures below 4 K.

Magnetic anisotropy of two tetrahedral Co(II)-halide complexes with triphenylphosphine ligands

Recently, the choice of ligand and geometric control of mononuclear complexes, which can affect the relaxation pathways and blocking temperature, have received wide attention in the field of single-ion magnets (SIMs). To find out the influence of the coordination environment on SIMs, two four-coordinate mononuclear Co(II) complexes [NEt₄][Co(PPh₃)X₃] (X = Cl^-, 1; Br^-, 2) have been synthesized and studied by X-ray single crystallography, magnetic measurements, high-frequency and -field EPR (HF-EPR) spectroscopy and theoretical calculations. Both complexes are in a cubic space group Pa3̄ (No. 205), containing a slightly distorted tetrahedral moiety with crystallographically imposed C_3v symmetry through the [Co(PPh₃)X₃]^- anion. The direct-current (dc) magnetic data and HF-EPR spectroscopy indicated the anisotropic S = 3/2 spin ground states of the Co(II) ions with the easy-plane anisotropy for 1 and 2. Ab initio calculations were performed to confirm the positive magnetic anisotropies of 1 and 2. Frequency- and temperature-dependent alternating-current (ac) magnetic susceptibility measurements revealed slow magnetic relaxation for 1 and 2 at an applied dc field. Finally, the magnetic properties of 1 and 2 were compared to those of other Co(II) complexes with a [CoAB₃] moiety.

Synthesis and Magnetic Properties of Antimony-Ligated Co(II) Complexes: Stibines versus Phosphines

Herein, we test the hypothesis that neutral, heavy-atom stibine donors can increase the extent of spin-orbit coupling on light, 3d transition metal. To this end, we developed a novel synthetic route toward coordinating a paramagnetic 3d metal ion─cobalt(II)─with neutral stibine ligands. Such complexes have not been reported in the literature due to the weak σ donor strength of stibines and the hard-soft mismatch between a 3d metal and a 5p ligand─which herein has been overcome using alkylated Sb donors. Magnetometry of [(SbⁱPr₂Ph)₂Co(I)₂] (1) reveals that the stibine complex 1 exhibits a higher magnitude D value (D = |24.96| cm^-1) than the spectroscopically derived value for the corresponding phosphine complex 3 (D = -13.13 cm^-1), indicative of large zero-field splitting. CASSCF/NEVPT2 calculations corroborate the experimental D values for 1 and 3, predicting D = -31.9 and -8.9 cm^-1, respectively. A re-examination of magnetic parameters across the entire series [(ER₃)₂Co(X)₂] (E = P → Sb; X = Cl → I) reveals that (i) increasingly heavy pnictogens lead to an increased X-Co-X bond angle, which is correlated with larger magnitude D values, and (ii) for a given X-Co-X bond angle, the D value is always higher in the presence of a heavy pnictogen as compared with a heavy halide. Ab initio ligand field theory calculations for 1 (stibine complex) and 3 (phosphine complex) reveal no substantial differences in spin-orbit coupling (ζ = 479.2, 480.2 cm^-1) or Racah parameter (B = 947.5, 943.9 cm^-1), an indicator of covalency. Thus, some "heavy atom effect" on the D value beyond geometric perturbation is operative, but its precise mechanism(s) of action remains obscure.

Extreme -Tensor Anisotropy and Its Insensitivity to Structural Distortions in a Family of Linear Two-Coordinate Ni(I) Bis-N-heterocyclic Carbene Complexes

We report a new series of homoleptic Ni(I) bis-N-heterocyclic carbene complexes with a range of torsion angles between the two ligands from 68° to 90°. Electron paramagnetic resonance measurements revealed a strongly anisotropic g-tensor in all complexes with a small variation in g_∥ ∼ 5.7-5.9 and g_⊥ ∼ 0.6. The energy of the first excited state identified by variable-field far-infrared magnetic spectroscopy and SOC-CASSCF/NEVPT2 calculations is in the range 270-650 cm^-1. Magnetic relaxation measured by alternating current susceptibility up to 10 K is dominated by Raman and direct processes. Ab initio ligand-field analysis reveals that a torsion angle of <90° causes the splitting between doubly occupied d_xz and d_yz orbitals, which has little effect on the magnetic properties, while the temperature dependence of the magnetic relaxation appears to have no correlation with the torsion angle.

Effect of Spin-Orbit Coupling on Phonon-Mediated Magnetic Relaxation in a Series of Zero-Valent Vanadium, Niobium, and Tantalum Isocyanide Complexes

Spin-vibronic coupling leads to spin relaxation in paramagnetic molecules, and an understanding of factors that contribute to this phenomenon is essential for designing next-generation spintronics technology, including single-molecule magnets and spin-based qubits, wherein long-lifetime magnetic ground states are desired. We report spectroscopic and magnetic characterization of the isoelectronic and isostructural series of homoleptic zerovalent transition metal triad M(CNDipp)₆ (M = V, Nb, Ta; CNDipp = 2,6-diisopropylphenyl isocyanide) and show experimentally the significant increase in spin relaxation rate upon going from V to Nb to Ta. Correlated electronic calculations and first principle spin-phonon computations support the role of spin-orbit coupling in modulating spin-phonon relaxation. Our results provide experimental evidence that increasing magnetic anisotropy through spin-orbit coupling interactions leads to increased spin-vibronic relaxation, which is detrimental to long spin lifetime in paramagnetic molecules.

Electronic Structure and Magnetic Properties of a Low-Spin CrII Complex: trans-[CrCl2(dmpe)2] (dmpe = 1,2-Bis(dimethylphosphino)ethane)

Octahedral coordination complexes of the general formula trans-[MX₂(R₂ECH₂CH₂ER₂)₂] (M^II = Ti, V, Cr, Mn; E = N, P; R = alkyl, aryl) are a cornerstone of both coordination and organometallic chemistry, and many of these complexes are known to have unique electronic structures that have been incompletely examined. The trans-[CrCl₂(dmpe)₂] complex (dmpe = Me₂PCH₂CH₂PMe₂), originally reported by Girolami and co-workers in 1985, is a rare example of a six-coordinate d⁴ system with an S = 1 (spin triplet) ground state, as opposed to the high-spin (S = 2, spin quintet) state. The ground-state properties of S = 1 systems are challenging to study using conventional spectroscopic methods, and consequently, the electronic structure of trans-[CrCl₂(dmpe)₂] has remained largely unexplored. In this present work, we have employed high-frequency and -field electron paramagnetic resonance (HFEPR) spectroscopy to characterize the ground-state electronic structure of trans-[CrCl₂(dmpe)₂]. This analysis yielded a complete set of spin Hamiltonian parameters for this S = 1 complex: D = +7.39(1) cm^-1, E = +0.093(1) (E/D = 0.012), and g = [1.999(5), 2.00(1), 2.00(1)]. To develop a detailed electronic structure description for trans-[CrCl₂(dmpe)₂], we employed both classical ligand-field theory and quantum chemical theory (QCT) calculations, which considered all quintet, triplet, and singlet ligand-field states. While the high density of states suggests an unexpectedly complex electronic structure for this "simple" coordination complex, both the ligand-field and QCT methods were able to reproduce the experimental spin Hamiltonian parameters quite nicely. The QCT computations were also used as a basis for assigning the electronic absorption spectrum of trans-[CrCl₂(dmpe)₂] in toluene.