A four-coordinate cobalt(II) single-ion magnet with coercivity and a very high energy barrier

Slowing magnetic relaxation with open-shell diluents

Strategies for slowing magnetic relaxation via local environmental design are vital for developing next-generation spin-based technologies (e.g., quantum information processing). Herein, we demonstrate a technique to do so via chemical design of a local magnetic environment. We show that embedding the open-shell complex (Ph₄P)₂[Co(SPh)₄] in solid-state matrices of the isostructural, open-shell species (Ph₄P)₂[M(SPh)₄] (M = Ni²⁺, S = 1; M = Fe²⁺, S = 2; M = Mn²⁺, S = 5 2 ) will slow magnetic relaxation for the embedded [Co(SPh)₄]^2- ion by three orders of magnitude. Magnetometry, electron paramagnetic resonance (EPR), and computational analyses reveal that integer spin and large, positive zero-field splitting (D) values for the diluent produce a quiet, local magnetic field that slows relaxation rates for the embedded Co molecules. These results will enable the investigation of magnetic systems for which strictly diamagnetic congeners are either synthetically inaccessible or are not isostructural.

Hydrogen-Bonded Framework of a Cobalt(II) Complex Showing Superior Stability and Field-Induced Slow Magnetic Relaxation

A unique hydrogen-bonded organic-inorganic framework (HOIF) constructed from a mononuclear cobalt(II) complex, [Co(MCA)₂·(H₂O)₂] (HMCA = 4-imidazolecarboxylic acid), via multiple hydrogen-bonding interactions was synthesized and structurally characterized. The Co(II) center in the HOIF features a highly distorted octahedral coordination environment. Remarkably, the Co^II HOIF showed permanent porosity with superior stability as established by combined thermogravimetric analysis (TGA), variable-temperature infrared spectra (IR), variable-temperature powder X-ray diffraction data (PXRD), and a CO₂ isotherm. Structural studies reveal that short multiple hydrogen bonds should be responsible for the superior thermal and chemical stability of a HIOF. Magnetic investigations reveal the large easy-plane magnetic anisotropy of the Co²⁺ ions with the fitted D values being 22.1 (magnetic susceptibility and magnetization data) and 29.1 cm^-1 (reduced magnetization data). In addition, the HOIF exhibits field-induced slow magnetic relaxation at low temperature with an effective energy barrier of U_eff = 45.2 cm^-1, indicative of a hydrogen-bonded framework single-ion magnet of the compound. The origin of the significant magnetic anisotropy of the complex was also understood from computational studies. In addition, BS-DFT calculations indicate that the superexchange interactions between the neighboring Co^II ions are non-negligible antiferromagnetism with J_Co-Co = -0.5 cm^-1. The foregoing results provide not only a carboxylate-imidazole ligand approach toward a stable HOIF but also a promising way to build a robust single-ion magnet via hydrogen-bond interactions.

Revisiting the Fundamental Nature of Metal‐Ligand Bonding: An Impartial and Automated Fitting Procedure for Angular Overlap Model Parameters

The properties and reactivities of transition metal complexes are often discussed in terms of Ligand Field Theory (LFT), and with ab initio LFT a direct connection to quantum chemical wavefunctions was recently established. The Angular Overlap Model (AOM) is a widely used, ligand‐specific parameterization scheme of the ligand field splitting that has, however, been restricted by the availability and resolution of experimental data. Using ab initio LFT, we present here a generalised, symmetry‐independent and automated fitting procedure for AOM parameters that is even applicable to formally underdetermined or experimentally inaccessible systems. This method allows quantitative evaluations of assumptions commonly made in AOM applications, for example, transferability or the relative magnitudes of AOM parameters, and the response of the ligand field to structural or electronic changes. A two‐dimensional spectrochemical series of tetrahedral halido metalates ([M^IIX₄]²⁻, M=Mn−Cu) served as a case study. A previously unknown linear relationship between the halide ligands’ chemical hardness and their AOM parameters was found. The impartial and automated procedure for identifying AOM parameters introduced here can be used to systematically improve our understanding of ligand–metal interactions in coordination complexes.

Chlorocobalt complexes with pyridylethyl-derived diazacycloalkanes

With cobalt(II) chloride, some piperazine- and homo-piperazine-derived ligands yield tetra- or penta­coordinate complexes. Observed variations in coordination number are ascribed as being related to chloride solvophobicity. Optical spectra are presented, while magnetism measurements indicate governance of the magnetism by zero-field splitting of the cobalt ion.

Syntheses are described for the blue/purple complexes of cobalt(II) chloride with the tetra­dentate ligands 1,4-bis­[2-(pyridin-2-yl)eth­yl]piperazine (Ppz), 1,4-bis­[2-(pyridin-2-yl)eth­yl]homopiperazine (Phpz), trans-2,5-dimethyl-1,4-bis­[2-(pyridin-2-yl)eth­yl]piperazine (Pdmpz) and tridentate 4-methyl-1-[2-(pyridin-2-yl)eth­yl]homopiperazine (Pmhpz). The CoCl₂ complexes with Ppz, namely, {μ-1,4-bis­[2-(pyridin-2-yl)eth­yl]piperazine}bis­[di­chlorido­cobalt(II)], [Co₂Cl₄(C₁₈H₂₄N₄)] or Co₂(Ppz)Cl₄, and Pdmpz (structure not reported as X-ray quality crystals were not obtained), are shown to be dinuclear, with the ligands bridging the two tetra­hedrally coordinated CoCl₂ units. Co₂(Ppz)Cl₄ and {di­chlorido­{4-methyl-1-[2-(pyridin-2-yl)eth­yl]-1,4-di­aza­cyclo­hepta­ne}cobalt(II) [CoCl₂(C₁₃H₂₁N₃)] or Co(Pmhpz)Cl₂, crystallize in the monoclinic space group P2₁/n, while crystals of the penta­coordinate mono­chloro chelate 1,4-bis­[2-(pyr­id­in-2-yl)eth­yl]piperazine}chlorido­cobalt(II) perchlorate, [CoCl(C₁₈H₂₄N₄)]ClO₄ or [Co(Ppz)Cl]ClO₄, are also monoclinic (P2₁). The complex {1,4-bis­[2-(pyridin-2-yl)eth­yl]-1,4-di­aza­cyclo­hepta­ne}di­chlorido­cobalt(II) [CoCl₂(C₁₉H₂₆N₄)] or Co(Phpz)Cl₂ (P) is mononuclear, with a penta­coordinated Co^II ion, and entails a Phpz ligand acting in a tridentate fashion, with one of the pyridyl moieties dangling and non-coordinated; its displacement by Cl⁻ is attributed to the solvophobicity of Cl⁻ toward MeOH. The penta­coordinate Co atoms in Co(Phpz)Cl₂, [Co(Ppz)Cl]⁺ and Co(Pmhpz)Cl₂ have substantial trigonal–bipyramidal character in their stereochemistry. Visible- and near-infrared-region electronic spectra are used to differentiate the two types of coordination spheres. TDDFT calculations suggest that the visible/NIR region transitions contain contributions from MLCT and LMCT character, as well as their expected d–d nature. For Co(Pmhpz)Cl₂ and Co(Phpz)Cl₂, variable-temperature magnetic susceptibility data were obtained, and the observed decreases in moment with decreasing temperature were modelled with a zero-field-splitting approach, the D values being +28 and +39 cm⁻¹, respectively, with the S = 1/2 state at lower energy.

Analysis of vibronic coupling in a 4f molecular magnet with FIRMS

Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H₃trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an "envelope effect" in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C₃ symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.

Mononuclear Transition Metal Cymantrenecarboxylates as Precursors for Spinel-Type Manganites

Novel mononuclear cymantrenecarboxylate complexes of transition metals, [Co(H₂O)₆](CymCO₂)₂·4H₂O (Cym = (η⁵-C₅H₄)Mn(CO)₃) (1), [Ni(H₂O)₆](CymCO₂)₂·4H₂O (2), [Zn(H₂O)₆](CymCO₂)₂·4H₂O (3), [Co(CymCO₂)₂(imz)₂] (imz = imidazole, 4), [Co(CymCO₂)₂(bpy)₂]·2PhMe (bpy = 2,2′-bipyridyl, 5), [Ni(CymCO₂)(bpy)₂(H₂O)][CymCO₂]·0.5MePh·2H₂O (6), [Cu(CymCO₂)₂(imz)₂] (7), and [Cu(CymCO₂)₂(bpy)(H₂O)] (8), were obtained and characterized by single-crystal X-ray analysis. Complexes 1–3 are isostructural. Magnetism of the Co complexes 1, 4, and 5 was studied; it was shown that they exhibit the properties of field-induced single-molecule magnets with magnetization reversal barriers (ΔE/k_B) of 44, 13, and 10 K, respectively. Thermal decomposition of complexes 1–8 was studied by means of DSC and TGA methods. The final products of thermolysis of 1–6 in air, according to powder XRD data, are the pure spinel phases MMn₂O₄; for the cases of copper complexes, the mixtures of CuMn₂O₄ and CuO were found in the products.

Trigonally Distorted Hexacoordinate Co(II) Single-Ion Magnets

By simple reactions involving various cobalt(II) carboxylates (acetate and in situ prepared pivalate and 4-hydroxybenzoate salts) and neocuproine (neo), we were able to prepare three different carboxylate complexes with the general formula [Co(neo)(RCOO)₂] (R = –CH₃ for 1, (CH₃)₃C– for 2, and 4OH-C₄H₆– for 3). The [Co(neo)(RCOO)₂] molecules in the crystal structures of 1–3 adopt a rather distorted coordination environment, with the largest trigonal distortion observed for 1, whereas 2 and 3 are similarly distorted from ideal octahedral geometry. The combined theoretical and experimental investigations of magnetic properties revealed that the spin Hamiltonian formalism was not a valid approach and the L-S Hamiltonian had to be used to reveal very large magnetic anisotropies for 1–3. The measurements of AC susceptibility showed that all three compounds exhibited slow-relaxation of magnetization in a weak external static magnetic field, and thus can be classified as field-induced single-ion magnets. It is noteworthy that 1 also exhibits a weak AC signal in a zero-external magnetic field.

Effect of an axial coordination environment on quantum tunnelling of magnetization for dysprosium single-ion magnets with theoretical insight

Herein, we report two mononuclear dysprosium complexes [Dy(H₄L){B(OMe)₂(Ph)₂}₂](Cl)·MeOH (1) and [Dy(H₄L){MeOH)₂(NCS)₂}](Cl) (2) [where H₄L = 2,2'-(pyridine-2,6-diylbis(ethan-1-yl-1-ylidene))bis(N-phenylhydrazinecarboxamide)] with different axial coordination environments. The structural analysis revealed that the pentadentate H₄L ligand binds through the equatorial position in both complexes. In complex 1, the axial positions are occupied by bidentate dimethoxydiphenyleborate [B(OMe)₂(Ph)₂]^-. On the other hand, in complex 2, one axial position is occupied by two NCS^- and one MeOH molecule while another MeOH molecule is coordinated to the other axial position. Magnetic measurements disclose the presence of field-induced slow relaxation of magnetization with an energy barrier of U_eff = 30 K for 1 whereas no such effective barrier was observed in complex 2. Detailed analysis of field and temperature dependence of the relaxation time confirms the major role of Raman, QTM, and direct processes rather than the Orbach process in complex 1. It was observed that [B(OMe)₂(Ph)₂]^- provides higher axial anisotropy which slows down the QTM process (relaxation time for the QTM process is 2.70 × 10^-5 s) in 1 as compared to NCS anions and MeOH molecules in 2 (1.03 × 10^-8 s), and is responsible for the absence of an effective energy barrier in the latter complex as confirmed by ab initio calculations. The calculations also show that the presence of a large bidentate dimethoxydiphenyleborate ligand in axial positions may result in high-performance Dy-based single-ion magnets.

Rhodium Diamidobenzene Complexes: A Tale of Different Substituents on the Diamidobenzene Ligand

Diamidobenzene ligands are a prominent class of redox-active ligands owing to their electron reservoir behaviour, as well as the possibility of tuning the steric and the electronic properties of such ligands through the substituents on the N-atoms of the ligands. In this contribution, we present Rh(iii) complexes with four differently substituted diamidobenzene ligands. By using a combination of crystallography, NMR spectroscopy, electrochemistry, UV-vis-NIR/EPR spectroelectrochemistry, and quantum chemical calculations we show that the substituents on the ligands have a profound influence on the bonding, donor, electrochemical and spectroscopic properties of the Rh complexes. We present, for the first time, design strategies for the isolation of mononuclear Rh(ii) metallates whose redox potentials span across more than 850 mV. These Rh(ii) metallates undergo typical metalloradical reactivity such as activation of O₂ and C–Cl bond activations. Additionally, we also show that the substituents on the ligands dictate the one versus two electron nature of the oxidation steps of the Rh complexes. Furthermore, the oxidative reactivity of the metal complexes with a [CH₃]⁺ source leads to the isolation of a unprecedented, homobimetallic, heterovalent complex featuring a novel π-bonded rhodio-o-diiminoquionone. Our results thus reveal several new potentials of the diamidobenzene ligand class in organometallic reactivity and small molecule activation with potential relevance for catalysis.

Diamidobenzene ligands are versatile platforms in organometallic Rh-chemistry. They allow the isolation of tunable mononuclear ate-complexes, and the formation of a unprecedented homobimetallic, heterovalent complex.

Pentacoordinate Cobalt(II) Single Ion Magnets with Pendant Alkyl Chains: Shall We Go for Chloride or Bromide?

Four pentacoordinate complexes 1-4 of the type [Co(L1)X2] and [Co(L2)X2] (where L1=2,6-bis(1-octyl-1H-benzimidazol-2-yl)pyridine for 1 and 2, L2=2,6-bis(1-dodecyl-1H-benzimidazol -2-yl)-pyridine for 3 and 4; X = Cl- for 1 and 3, X...

Field-induced slow magnetic relaxation behaviours in binuclear cobalt(II) metallocycle and exchange-coupled cluster

Precise control of structures and magnetic properties of a molecular material constitutes an important challenge to realize the tailor-made magnetic function. Herein, we reported that the ligand-directed coordination self-assembly of...

Single-ion magnet behaviour in homoleptic Co(ii) complexes bearing 2-iminopyrrolyl ligands

Four-coordinate distorted tetrahedral bis(2-iminopyrrolyl)cobalt(ii) complexes behave as Single-Ion Magnets (SIMs) in the absence of an external magnetic field.

Slow magnetic relaxation in a trigonal-planar mononuclear Fe(II) complex

Based on a β-diketiminate ligand, an iron(III) tetrahedral high-spin complex, [LFeIII(Cl)2] (1), and an iron(II) high-spin triangular planar complex, [LFeIICl] (2), have been synthesized and structurally characterized. Also, complex 1...

The rationalized pathway from field-induced slow magnetic relaxation in CoII–WIV chains to single-chain magnetism in isotopological CoII–WV analogues

The change of the oxidation state from WIV to WV in isotopological CoII–[W(CN)8]n− chains leads to the appearence of pronounced single-chain magnet behaviour.

Symmetry-Breaking Phase Transitions, Dielectric and Magnetic properties of Pyrrolidinium-Tetrahalidocobaltates

We report the physicochemical characteristics of novel Co-based pyrrolidinium analogs: (C4H10N)2CoCl4 (PCC) and (C4H10N)2CoBr4 (PCB). Both compounds consist of the zero-dimensional (OD) anionic network and disordered pyrolidinium cations. The structural...

A C,S Bonded Quasi-Two-Coordinate Chromium(II) Complex Showing Field-induced Slow Magnetic Relaxation Behaviour

A C,S bonded quasi-two-coordinate Cr(II) complex, Cr(SAr*)2 (HSAr* = HSC6H3-2,6(C6H2-2,4,6-Pri3)2), has been successfully synthesized. Magnetic, high-frequency / field electron paramagnetic resonance (HF-EPR) experiments and ab initio calculation studies show that...

Modulation of the architectures and magnetic dynamics in pseudotetrahedral cobalt(II) complexes

Two β-Diketiminate cobalt(II) compounds of formula [LCo(μ-Cl)]2∙2C6H14 (1) and [LCoClPy]∙0.5C7H8∙0.5C6H14 (2) (L = [PhC-(PhCN-Dip)2]−, Dip = 2,6-iPr2C6H3) have been synthesized and structurally characterized by single crystal X-ray diffraction. Compound 1...

A Dicobalt(II) Single-Molecule Magnet via a Well-Designed Dual-Capping Tetrazine Radical Ligand

The recent years have witnessed the glory development for the construction of high-performance mononuclear single molecule magnets (SMMs) within a specific coordination geometry, which, however, is not well applied in cluster-based SMMs due to the synthetic challenges. Given that the monocobalt(II) complexes within a trigonal-prismatic (TPR) coordination geometry have been classified as excellent SMMs with huge axial anisotropy (D ≈ -100 cm^-1), here we designed and synthesized a new dual-capping tetrazine ligand, 3,6-bis(6-(di(1H-pyrazol-1-yl)methyl)pyridin-2-yl)-1,2,4,5-tetrazine (bpptz), and prepared a novel dicobalt(II) complex, [Cp₂Co^III][{(hfac)Co^II}₂(bpptz^•-)][hfac]₂·2Et₂O (1, hfac = hexafluoroacetylacetonate). In the structure of 1, the bpptz^•- radical ligand enwraps two Co(II) centers within quasi-TPR geometries, which are further bridged by the tetrazine radical in the trans mode. The magnetic study revealed that the interaction between the Co centers and the tetrazine radical is strongly antiferromagnetic with a coupling constant (J) of -65.8 cm^-1 (in the -2J formalism). Remarkably, 1 exhibited the typical SMM behavior with an effective energy barrier of 69 cm^-1 under a 1.5 kOe dc field, among the largest for polynuclear transition metal SMMs. In addition, DFT and ab initio calculations suggested that the presence of a strong Co(II)-radical magnetic interaction effectively quenches the QTM effect and enhances the barrier height for the magnetization reversal.

Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments

We propose a machine learning method to model molecular tensorial quantities, namely, the magnetic anisotropy tensor, based on the Gaussian moment neural network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3-0.4 cm^-1 and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin-phonon relaxation.

A cyanide-bridged Fe-Co pearl-chain-like single-chain magnet containing 4-coordinate cobalt(II) ions

Treatment of CoCl₂·6H₂O and tris(pyrazolyl-1-yl)borate tricyanoiron(III) anions at an elevated temperature (55 °C) afforded two less-common pearl-chain-like compounds, {[(Tp^R)Fe(CN)₃CoCl₂]₂Co(DMF)₄}·nDMF (1, Tp^R = Tp^4-Me = hydridotris(4-methylpyrazol-1-yl)borate, n = 1 and 2, Tp^R = Tp*^Me = hydridotris(3,4,5-trimethylpyrazol-1-yl)borate, n = 4.5), in which the 4-coordinate Co(II) ions and [(Tp^R)Fe^III(CN)₃]^- units are alternately bridged by cyanide groups into squares, which are further linked with the 6-coordinate Co(II) ions into an infinite chain. Interestingly, the magnetic study revealed that 1 exhibits a typical single-chain magnet behaviour with an effective energy barrier of 28.0 K, while surprisingly no Glauber dynamics was observed for 2 despite their very similar structures. The variations of the local coordination environments of the cobalt ions and the cyanide linkages were evidenced, and they may account for the significant difference in their magnetic properties related to the global magnetic anisotropy and magnetic exchange of the chain.

Radical-Bridged Ln4 Metallocene Complexes with Strong Magnetic Coupling and a Large Coercive Field

Inducing magnetic coupling between 4f elements is an ongoing challenge. To overcome this formidable difficulty, we incorporate highly delocalized tetrazinyl radicals, which strongly couple with f-block metallocenes to form discrete tetranuclear complexes. Synthesis, structure, and magnetic properties of two tetranuclear [(Cp*₂ Ln)₄ (tz^. )₄ ]⋅3(C₆ H₆ ) (Cp*=pentamethylcyclopentadienyl; tz=1,2,4,5-tetrazine; Ln=Dy, Gd) complexes are reported. An in-depth examination of their magnetic properties through magnetic susceptibility measurements as well as computational studies support a highly sought-after radical-induced "giant-spin" model. Strong exchange interactions between the Ln^III ions and tz^. radicals lead to a strong magnet-like behaviour in this molecular magnet with a large coercive field of 30 kOe.

Modern physical methods for the molecular design of single-molecule magnets

Many paramagnetic metal complexes have emerged as unique magnetic materials (single-molecule magnets), which behave as conventional magnets at the single-molecule level, thereby making it possible to use them in modern devices for data storage and processing. The rational design of these complexes, however, requires a deep understanding of the physical laws behind a single-molecule magnet behaviour, the mechanisms of magnetic relaxation that determines the magnetic properties and the relationship of these properties with the structure of single-molecule magnets. This review focuses on the physical methods providing such understanding, including different versions and various combinations of magnetometry, electron paramagnetic and nuclear magnetic resonance spectroscopy, optical spectroscopy and X-ray diffraction. Many of these methods are traditionally used to determine the composition and structure of new chemical compounds. However, they are rarely applied to study molecular magnetism.

The bibliography includes 224 references.

Influence of F-position and solvent on coordination geometry and single ion magnet behavior of Co(II) complexes

Three mononuclear Co(II) complexes with the compositions of [Co(L₁)₂] (1), [Co(L₂)₂(CH₃CN)] (2) and [Co(L₃)₂] (3) (HL₁ = 2-((E)-(2-fluorobenzylimino)methyl)-4,6-dibromophenol, HL₂ = 2-((E)-(3-fluorobenzylimino)methyl)-4,6-dibromophenol and HL₃ = 2-((E)-(4-fluorobenzylimino)methyl)-4,6-dibromophenol) were prepared and structurally determined. The changes in the F-positions in the ligands and solvents led to the formation of these products with various coordination geometries. Both complexes 1 and 3 are four-coordinated and their coordination geometries can be described as tetrahedron and seesaw, whereas complex 2 is five coordinated with a coordination configuration in between trigonal bipyramid and square pyramid. Static magnetic studies reveal that all these complexes exhibit considerable easy-axis magnetic anisotropy. The easy-axis magnetic anisotropy of 1 and 3 mainly derives from the first quartet excited state, whereas that of 2 primarily originates from the first, third and fourth quartet excited states established by theoretical calculations. All the resulting complexes display field-induced slow magnetic relaxation. Complex 3 represents the first Co(II) single ion magnet with a seesaw coordination geometry. Ab initio calculations predict that the magnetic anisotropy will enhance when the seesaw coordination geometry varies from distortion to regulation.

Slow Magnetic Relaxation in {[CoCxAPy)] 2.15 H2O}n MOF Built from Ladder-Structured 2D Layers with Dimeric SMM Rungs

We present the magnetic properties of the metal-organic framework {[CoCxAPy]·2.15 H2O}n (Cx = bis(carboxypropyl)tetramethyldisiloxane; APy = 4,4`-azopyridine) (1) that builds up from the stacking of 2D coordination polymers. The 2D-coordination polymer in the bc plane is formed by the adjacent bonding of [CoCxAPy] 1D two-leg ladders with Co dimer rungs, running parallel to the c-axis. The crystal packing of 2D layers shows the presence of infinite channels running along the c crystallographic axis, which accommodate the disordered solvate molecules. The Co(II) is six-coordinated in a distorted octahedral geometry, where the equatorial plane is occupied by four carboxylate oxygen atoms. Two nitrogen atoms from APy ligands are coordinated in apical positions. The single-ion magnetic anisotropy has been determined by low temperature EPR and magnetization measurements on an isostructural compound {[Zn0.8Co0.2CxAPy]·1.5 CH3OH}n (2). The results show that the Co(II) ion has orthorhombic anisotropy with the hard-axis direction in the C2V main axis, lying the easy axis in the distorted octahedron equatorial plane, as predicted by the ab initio calculations of the g-tensor. Magnetic and heat capacity properties at very low temperatures are rationalized within a S* = 1/2 magnetic dimer model with anisotropic antiferromagnetic interaction. The magnetic dimer exhibits slow relaxation of the magnetization (SMM) below 6 K in applied field, with a tlf ≈ 2 s direct process at low frequencies, and an Orbach process at higher frequencies with U/kB = 6.7 ± 0.5 K. This compound represents a singular SMM MOF built-up of Co-dimers with an anisotropic exchange interaction.

Binding Sites, Vibrations and Spin-Lattice Relaxation Times in Europium(II)-Based Metallofullerene Spin Qubits

To design molecular spin qubits with enhanced quantum coherence, a control of the coupling between the local vibrations and the spin states is crucial, which could be realized in principle by engineering molecular structures via coordination chemistry. To this end, understanding the underlying structural factors that govern the spin relaxation is a central topic. Here, we report the investigation of the spin dynamics in a series of chemically designed europium(II)-based endohedral metallofullerenes (EMFs). By introducing a unique structural difference, i. e. metal-cage binding site, while keeping other molecular parameters constant between different complexes, these manifest the key role of the three low-energy metal-displacing vibrations in mediating the spin-lattice relaxation times (T1 ). The temperature dependence of T1 can thus be normalized by the frequencies of these low energy vibrations to show an unprecedentedly universal behavior for EMFs in frozen CS2 solution. Our theoretical analysis indicates that this structural difference determines not only the vibrational rigidity but also spin-vibration coupling in these EMF-based qubit candidates.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion’s first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Quantifying magnetic anisotropy using X-ray and neutron diffraction

In this work, the magnetic anisotropy in two iso-structural distorted tetrahedral Co(II) complexes, CoX 2tmtu2 [X = Cl(1) and Br(2), tmtu = tetra-methyl-thio-urea] is investigated, using a combination of polarized neutron diffraction (PND), very low-temperature high-resolution synchrotron X-ray diffraction and CASSCF/NEVPT2 ab initio calculations. Here, it was found consistently among all methods that the compounds have an easy axis of magnetization pointing nearly along the bis-ector of the compression angle, with minute deviations between PND and theory. Importantly, this work represents the first derivation of the atomic susceptibility tensor based on powder PND for a single-molecule magnet and the comparison thereof with ab initio calculations and high-resolution X-ray diffraction. Theoretical ab initio ligand field theory (AILFT) analysis finds the d xy orbital to be stabilized relative to the d xz and d yz orbitals, thus providing the intuitive explanation for the presence of a negative zero-field splitting parameter, D, from coupling and thus mixing of d xy and . Experimental d-orbital populations support this interpretation, showing in addition that the metal-ligand covalency is larger for Br-ligated 2 than for Cl-ligated 1.

On the Accuracy of Mean-Field Spin-Orbit Operators for 3d Transition-Metal Systems

We present an extensive study of the performance of mean-field approximations to the spin-orbit operators on realistic molecular systems, as widely used in applications like single-molecule magnets, molecular quantum bits, and molecular spintronic devices. The test systems feature a 3d transition-metal center ion (V, Cr, Mn, Fe, Co, and Ni) in various coordinations and a multitude of energetically close-lying open-shell configurations that can couple via the spin-orbit operator. We performed complete active space spin-orbit configuration interaction calculations and compared the full two-electron Breit-Pauli spin-orbit operator to different approximations: the one-center approximation, the spin-orbit mean-field approach with electron densities from different state-averaging procedures, and the atomic mean-field integral approximation. We show that the mean-field approaches can lead to significant errors in the spin-orbital coupling matrix elements, which becomes particularly visible for the computed zero-field splittings. The one-center approximation, keeping all relevant two-electron terms, seems to be a significantly more accurate choice for the examples from our test set.

Modulation of Magnetic Anisotropy and Exchange Interaction in Phenoxide-Bridged Dinuclear Co(II) Complexes

We report a new class of four dimeric Co(II) complexes [Co₂(bbpen)(X)₂] (H₂bbpen = N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethylenediamine) [X^- = SCN (1), Cl (2), Br (3), and I (4)] with different coordination geometry of two Co(II) centers (trigonal-prismatic and pseudo-tetrahedral) and their magnetic study. Interestingly, the two Co(II) centers show two different types of magnetic anisotropy. State of the art ab initio CASSCF analysis reveals that the six-coordinate or the trigonal-prismatic Co(II) center possesses a consistently large negative axial zero-field splitting (negative D) parameter (∼-60 cm^-1), while the four-coordinate or the pseudo-tetrahedral Co(II) center exhibits a range of D values from +13 to -23 cm^-1. Ab initio calculations employing the lines model were used to estimate the magnetic exchange as both the Co(II) centers possess significant magnetic anisotropy. All the complexes display rare ferromagnetic interaction, and the strength of this interaction decreases as the ligand field on the pseudo-tetrahedral Co(II) center decreases from SCN^- > Cl^- > Br^- > I^-.

Janus Pyrrolopyrrole Aza-dipyrrin: Hydrogen-Bonded Assemblies and Slow Magnetic Relaxation of the Cobalt(II) Complex in the Solid State

A novel pyrrolopyrrole azadipyrrin (Janus-PPAD) with Janus duality was synthesized by a Schiff base-forming reaction of diketopyrrolopyrrole. The orthogonal interactions of the hydrogen-bonding ketopyrrole and metal-coordinating azadipyrrin moieties in Janus-PPAD enabled the metal ions to be arranged at regular intervals: zinc(II) and cobalt(II) coordination provided metal-coordinated Janus-PPAD dimers, which can subsequently form hydrogen-bonded one-dimensional arrays both in solution and in the solid state. The supramolecular assembly of the zinc(II) complex in solution was investigated by ¹ H NMR spectroscopy based on the isodesmic model, in which a binding constant for the elongation of assemblies is constant. Owing to the tetrahedral coordination, in the solid state, the cobalt(II) complex exhibited a slow magnetic relaxation due to the negative D value of -27.1 cm^-1 with an effective relaxation energy barrier U_eff of 38.0 cm^-1 . The effect of magnetic dilution on the relaxation behavior is discussed. The relaxation mechanism at low temperature was analyzed by considering spin lattice interactions and quantum tunneling effects. The easy-axis magnetic anisotropy was confirmed, and the relevant wave functions were obtained by ab initio CASSCF calculations.

Rotaxane CoII Complexes as Field-Induced Single-Ion Magnets

Mechanically chelating ligands have untapped potential for the engineering of metal ion properties. Here we demonstrate this principle in the context of CoII -based single-ion magnets. Using multi-frequency EPR, susceptibility and magnetization measurements we found that these complexes show some of the highest zero field splittings reported for five-coordinate CoII complexes to date. The predictable coordination behaviour of the interlocked ligands allowed the magnetic properties of their CoII complexes to be evaluated computationally a priori and our combined experimental and theoretical approach enabled us to rationalize the observed trends. The predictable magnetic behaviour of the rotaxane CoII complexes demonstrates that interlocked ligands offer a new strategy to design metal complexes with interesting functionality.

Trigonal Planar Iron(II) and Cobalt(II) Complexes Containing [RS(NtBu)3]n- (R = NtBu, n = 2; CH2PPh2, n = 1) as Acute Bite-Angle Chelating Ligands: Soft P Donor Proves Beneficial to Magnetic Co Species

We prepared four new complexes, 4a,b and 5a,b, from polyimido sulfur-centered ligands with Fe^II and Co^II amides. Their molecular structures were elucidated by single-crystal X-ray diffraction. Cobalt magnetic investigations and multiconfigurational calculations provided insight into magneto-structural correlations between the acute N,N' chelating bite angle and P-side arm donation. The deviation from an ideal trigonal planar geometry and the magnetic performance correlated in an unprecedented manor. Mononuclear cobalt species 4b and 5b showed slow magnetic relaxation under a small applied dc field with energy barriers of up to 33.0 and 21.9 cm^-1, respectively. Although they possess some of the largest zero-field splitting parameters among three-coordinate cobalt single-ion magnets, both theory and experiment suggest that the high rhombicity (E/D) hampers large effective energy barriers to spin reversal at zero field from being obtained.

Record High Magnetic Anisotropy in Three-Coordinate MnIII and CrII Complexes: A Theoretical Perspective

Ab initio calculations performed in two three-coordinate complexes [Mn{N(SiMe₃)₂}₃] (1) and [K(18-crown-6) (Et₂O)₂][Cr{N(SiMe₃)₂}₃] (2) reveal record-high magnetic anisotropy with the D values -64 and -15 cm^-1, respectively, enlisting d⁴ ions back in the race for single-ion magnets. A detailed spin-vibrational analysis performed of 1 and 2 suggests dominance under barrier relaxation due to the flexible coordination spheres around the metal ion. Furthermore, several in silico models were constructed by varying the nature of donor atoms based on the X-ray structure of 1 and 2, unveiling much larger anisotropy and robust single-ion magnet (SIM) characteristics for some of the models offering design clues for low-coordinate transition-metal SIMs.

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

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(PPh₃ )₂ X₂ (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 spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

A trapped hexaaqua CoII complex between the polyanionic sheets of decavanadate reveals high axial anisotropy and field induced SIM behaviour

In this work, we report an inorganic compound [{Co(H₂O)₆}²⁺{Na₄V₁₀O₂₈}^2-] (1) in which the polyanionic sheets of decavanadate play the role of a diamagnetic matrix that reduces the dipolar-dipolar and spin-spin interactions between [Co(H₂O)₆]⁺² units to suppress the fast tunnelling of magnetization. Structural analysis reveals that each [Co(H₂O)₆]⁺² complex is surrounded by four decavanadates and separated by a large internuclear distance (9 Å). It was also found that the adjacent decavanadates are connected via sodium ions and form a 2D sheet of the inorganic layer in which the [Co(H₂O)₆]²⁺ ions are present in between two layers. Detailed dc (direct current) and ac (alternating current) magnetic measurements disclose the presence of large easy-axis anisotropy (D = -102 cm^-1) and field induced slow magnetic relaxation behaviour with a spin reversal barrier of U_eff = 50 K. Additionally, the temperature dependence of the relaxation time reveals that the Raman and QTM processes mainly play an important role rather than the thermally activated Orbach process in the overall relaxation dynamics of the studied compound. To analyse the electronic structure and magnetic properties of compound 1, ab initio calculations were performed which further support the experimental observations. Notably, the U_eff value of 1 represents the highest energy barrier reported for POM based SMMs with transition metal ions to date.

Positive zero-field splitting and unexpected slow magnetic relaxation in the magneto-chemical calibrant HgCo(NCS)4

DC magnetization data for HgCo(NCS)4 confirm positive value of the zero-field splitting D-parameter. High-frequency and -field EPR gave gz = 2.05, gx = 2.16 and D/hc = 5.39 cm-1. The complex exhibits a field-induced slow magnetic relaxation with two relaxation modes and unusual temperature evolution of the relaxation time.

Theoretical modeling of the singlet-triplet spin transition in different Ni(II)-diketo-pyrphyrin-based metal-ligand octahedral complexes

The structural stability, charge transfer effects and strength of the spin-orbit couplings in different Ni(ii)-ligand complexes have been studied at the DFT (B3LYP and CAM-B3LYP) and coupled cluster (DLPNO-CCSD(T)) levels of theory. Accordingly, two different, porphyrin- and diketo-pyrphyrin-based four-coordination macrocycles as planar ligands as well as pyridine (or pyrrole) and mesylate anion molecular groups as vertical ligands were considered in order to build metal-organic complexes with octahedral coordination configurations. For each molecular system, the identification of equilibrium geometries and the intersystem crossing (the minimum energy crossing) points between the potential energy surfaces of the singlet and triplet spin states is followed by computing the spin-orbit couplings between the two spin states. Structures, based on the diketo-pyrphyrin macrocycle as the planar ligand, show stronger six-coordination metal-organic complexes due to the extra electrostatic interaction between the positively charged central metal cation and the negatively charged vertical ligands. The results also show that the magnitude of the spin-orbit coupling is influenced by the atomic positions of deprotonations of the ligands, and implicitly the direction of the charge transfer between the ligand and the central metal ion.