Slow magnetic relaxation in a family of trigonal pyramidal iron(II) pyrrolide complexes

Field-Induced Slow Magnetization Relaxation of a Tetrahedral S=2 FeIIS4-Containing Complex

In the work described herein, the spin relaxation properties of the mononuclear tetrahedral S=2 [Fe{(SPiPr2)2N}2] complex (1) were studied by employing static and dynamic magnetic measurements at liquid helium temperatures. In the absence of an external direct current (DC) magnetic field, 1 exhibits fast magnetization relaxation. However, in the presence of external magnetic fields of a few kOe, slow relaxation is induced as monitored by alternating current (AC) magnetic susceptibility measurements up to 10 kHz, in the temperature range 2-5 K. Analysis of the temperature dependence of the corresponding relaxation time reveals contributions by Quantum Tunnelling of Magnetization, and the Direct and Orbach processes in the magnetization relaxation mechanism of 1. The energy barrier, Ueff, of the Orbach process, as determined by this analysis, is compared with that related to the zero-field splitting parameters of 1 which were previously determined by high- frequency and -field electron paramagnetic resonance and Mössbauer spectroscopies.

Structural, optical and magnetic properties of a new metal-organic CoII-based complex

A mononuclear cobalt(ii) complex [C5H8N3]2[CoCl4(C5H7N3)2] (I) was synthesized and structurally characterized. Single crystal X-ray diffraction analysis indicates that monometallic Co(ii) ions acted as coordination nodes in a distorted octahedral geometry, giving rise to a supramolecular architecture. The latter is made up of a ½ unit form composed of an anionic element [Co0.5Cl2(C5H7N3)]- and one 2-amino-4-methylpyrimidinium cation [C5H8N3]+. The crystalline arrangement of this compound adopts the sandwich form where inorganic parts are sandwiched between the organic sheets following the [100] direction. More information regarding the structure hierarchy has been supplied based on Hirshfeld surface analysis; the X⋯H (X = N, Cl) interactions play a crucial role in stabilizing the self-assembly process of I, complemented by the intervention of π⋯π electrostatic interaction created between organic entities. Thermal analyses were carried out to study the thermal behavior process. Static magnetic measurements and ab initio calculations of compound I revealed the easy-axis anisotropy character of the central Co(ii) ion. Two-channel field-induced slow-magnetic relaxation was observed; the high-frequency channel is characterized by underbarrier relaxation with U eff = 16.5 cm-1, and the low-frequency channel involves a direct relaxation process affected by the phonon-bottleneck effect.

Toward Ultimate Memory with Single-Molecule Multiferroics

The demand for high-density storage is urgent in the current era of data explosion. Recently, several single-molecule (-atom) magnets and ferroelectrics have been reported to be promising candidates for high-density storage. As another promising candidate, single-molecule multiferroics are not only small in size but also possess ferroelectric and magnetic orderings, which can sometimes be strongly coupled and used as data storage to realize the combination of electric writing and magnetic reading. However, they have been rarely proposed and have never been experimentally reported. Here, by building Hamiltonian models, we propose a new model of single-molecule multiferroics in which electric dipoles and magnetic moments are parallel and can rotate with the rotation of the single molecule. Furthermore, by performing spin-lattice dynamics simulations, we reveal the conditions (e.g., large enough single-ion anisotropy and an appropriate electric field) under which the new single-molecule multiferroic can arise. Based on this model, as well as first-principles calculations, a realistic example of Co(NH3)4N@SWCNT is constructed and numerically confirmed to demonstrate the feasibility of the new single-molecule multiferroic model. Our work not only sheds light on the discovery of single-molecule multiferroics but also provides a new guideline to design multifunctional materials for ultimate memory devices.

Field induced single ion magnet behavior in CoII complexes in a distorted square pyramidal geometry

We report three CoII-based complexes with the general formula [CoII(L)(X)2] by changing the halide/pseudo-halide ions [X = NCSe (1SeCN); Cl (2Cl) and Br (3Br)]. The obtained τ5 and CShM values confirm a distorted square pyramidal geometry around the CoII ion in all these complexes. In these three complexes, the central CoII ion is situated above the basal plane of the square pyramidal geometry. The extent of distortion from the ideal SPY-5 geometry differs upon changing the coordinating halide/pseudo-halide ion in these complexes. This essentially results in the alteration of the anisotropic parameter D and hence impacts the magnetic properties in these complexes. This phenomenon has been corroborated with the aid of theoretical investigations. All these complexes display field-induced SIM behaviour with magnetic relaxation occurring through a combination of processes depending on the applied dc magnetic field values and dilution.

Ultrafast Jahn-Teller Photoswitching in Cobalt Single-Ion Magnets

Single-ion magnets (SIMs) constitute the ultimate size limit in the quest for miniaturizing magnetic materials. Several bottlenecks currently hindering breakthroughs in quantum information and communication technologies could be alleviated by new generations of SIMs displaying multifunctionality. Here, ultrafast optical absorption spectroscopy and X-ray emission spectroscopy are employed to track the photoinduced spin-state switching of the prototypical complex [Co(terpy)2 ]2+ (terpy = 2,2':6',2″-terpyridine) in solution phase. The combined measurements and their analysis supported by density functional theory (DFT), time-dependent-DFT (TD-DFT) and multireference quantum chemistry calculations reveal that the complex undergoes a spin-state transition from a tetragonally elongated doublet state to a tetragonally compressed quartet state on the femtosecond timescale, i.e., it sustains ultrafast Jahn-Teller (JT) photoswitching between two different spin multiplicities. Adding new Co-based complexes as possible contenders in the search for JT photoswitching SIMs will greatly widen the possibilities for implementing magnetic multifunctionality and eventually controlling ultrafast magnetization with optical photons.

Spin-state energetics and magnetic anisotropy in penta-coordinated Fe(III) complexes with different axial and equatorial ligand environments

The penta-coordinated trigonal-bi-pyramidal (TBP) Fe(III) complex (PMe₂Ph)₂FeCl₃ shows a reduced magnetic anisotropy in its intermediate-spin (IS) state as compared to its methyl-analog (PMe₃)₂Fe(III)Cl₃. In this work, the ligand environment in (PMe₂Ph)₂FeCl₃ is systematically altered by replacing the axial -P with -N and -As, the equatorial -Cl with other halides, and the axial methyl group with an acetyl group. This has resulted in a series of Fe(III) TBP complexes modelled in their IS and high-spin (HS) states. Lighter ligands -N and -F stabilize the complex in the HS state, while the magnetically anisotropic IS state is stabilized by -P and -As at the axial site, and -Cl, -Br, and -I at the equatorial site. Larger magnetic anisotropies appear for complexes with nearly degenerate ground electronic states that are well separated from the higher excited states. This requirement, largely controlled by the d-orbital splitting pattern due to the changing ligand field, is achieved with a certain combination of axial and equatorial ligands, such as -P and -Br, -As and -Br, and -As and -I. In most cases, the acetyl group at the axial site enhances the magnetic anisotropy compared to its methyl counterpart. In contrast, the presence of -I at the equatorial site compromises the uniaxial type of anisotropy of the Fe(III) complex leading to an enhanced rate of quantum tunneling of magnetization.

Slow magnetic relaxation in two mononuclear Mn(II) complexes not governed by the over-barrier Orbach process

Two hexacoordinate Mn(II) complexes containing a chelating residue of hexafluoroacetylacetone and (Cl-substituted) 4-benzylpyridine show DC magnetic functions typical for S = 5/2 spin systems: g ∼ 2, D - small. The AC susceptibility confirms a field supported slow magnetic relaxation in which the over-barrier Orbach relaxation process does not play a role. Both systems possess two or three slow relaxation channels.

Pentagonal-bipyramidal 4d and 5d complexes with unquenched orbital angular momentum as a unique platform for advanced single-molecule magnets: current state and perspectives

This article overviews the current state and prospects of the concept of advanced single-molecule magnets (SMMs) based on low-spin (S = 1/2) pentagonal-bipyramidal (PBP) 4d³ and 5d³ complexes with unquenched orbital angular momentum. This approach is based on the unique property of PBP 4d³ and 5d³ complexes to cause highly anisotropic spin coupling of perfect uniaxial symmetry, -J_zSziSzj - J_xy(SxiSxj + SyiSyj), regardless of the local geometric symmetry. The M(4d/5d)-M(3d) exchange-coupled pairs in the apical positions of the PBP complexes produce Ising-type exchange interactions (|J_z| > |J_xy|), which serve as a powerful source of uniaxial magnetic anisotropy of a SMM cluster. In polynuclear heterometallic 4d/5d-3d complexes embodying PBP 4d/5d units and high-spin 3d ions, anisotropic Ising-type exchange interactions produce a double-well potential with high energy barriers U_eff, which is controlled by the anisotropic exchange parameters J_z, J_xy. Theoretical analysis shows that the barrier is proportional to the difference |J_z - J_xy| and to the number n of the apical 4d/5d-3d pairs in a SMM cluster, U_eff ∝ |J_z - J_xy|n, which provides an opportunity to scale up the barrier U_eff and blocking temperature T_B up to the record values. A novel family of 4d/5d complexes with forced PBP coordination provided by structurally rigid planar pentadentate Schiff-base ligands in the equatorial plane is discussed as a better alternative to the cyanometallates. The possibility of a significant increase in the anisotropic exchange parameters J_z, J_xy in PBP complexes with monoatomic apical μ-bridging ligands is examined. The basic principles of molecular engineering the highest barrier through anisotropic exchange interactions of PBP 4d/5d complexes are formulated. The theoretical and experimental results taken together indicate that the concept of high-performance SMMs based on 4d/5d PBP complexes with unquenched orbital angular momentum is an attractive alternative to the currently dominant lanthanide-based SMM strategy.

Unraveling the Contributions to Spin-Lattice Relaxation in Kramers Single-Molecule Magnets

The study of how spin interacts with lattice vibrations and relaxes to equilibrium provides unique insights into its chemical environment and the relation between electronic structure and molecular composition. Despite its importance for several disciplines, ranging from magnetic resonance to quantum technologies, a convincing interpretation of spin dynamics in crystals of magnetic molecules is still lacking due to the challenging experimental determination of the correct spin relaxation mechanism. We apply ab initio spin dynamics to a series of 12 coordination complexes of Co2+ and Dy3+ ions selected among ∼240 compounds that largely cover the literature on single-molecule magnets and well represent different regimes of spin relaxation. Simulations reveal that the Orbach spin relaxation rate of known compounds mostly depends on the ions' zero-field splitting and little on the details of molecular vibrations. Raman relaxation is instead found to be also significantly affected by the features of low-energy phonons. These results provide a complete understanding of the factors limiting spin lifetime in single-molecule magnets and revisit years of experimental investigations by making it possible to transparently distinguish Orbach and Raman relaxation mechanisms.

Single-Ion Magnets with Giant Magnetic Anisotropy and Zero-Field Splitting

The design of mononuclear molecular nanomagnets exhibiting a huge energy barrier to the reversal of magnetization have seen a surge of interest during the last few decades due to their potential technological applications. More specifically, single-ion magnets are peculiarly attractive by virtue of their rich quantum behavior and distinct fine structure. These are viable candidates for implementation as single-molecule high-density information storage devices and other applications in future quantum technologies. The present review presents the comprehensive state of the art in the topic of single-ion magnets possessing an eminent magnetization-reversal barrier, very slow magnetic relaxation and high blocking temperature. We turn our attention to the achievements in the synthesis of 3d and 4f single-ion magnets during the last two decades and discuss the observed magnetostructural properties underlying the anisotropy behavior and the ensuing remanence. Furthermore, we highlight the fundamental theoretical aspects to shed light on the complex behavior of these nanosized magnetic entities. In particular, we focus on key notions, such as zero-field splitting, anisotropy energy and quantum tunneling of the magnetization and their interdependence.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Iron Insertion at the Assembly Site of the ISCU Scaffold Protein Is a Conserved Process Initiating Fe-S Cluster Biosynthesis

Iron-sulfur (Fe-S) clusters are prosthetic groups of proteins biosynthesized on scaffold proteins by highly conserved multi-protein machineries. Biosynthesis of Fe-S clusters into the ISCU scaffold protein is initiated by ferrous iron insertion, followed by sulfur acquisition, via a still elusive mechanism. Notably, whether iron initially binds to the ISCU cysteine-rich assembly site or to a cysteine-less auxiliary site via N/O ligands remains unclear. We show here by SEC, circular dichroism (CD), and Mössbauer spectroscopies that iron binds to the assembly site of the monomeric form of prokaryotic and eukaryotic ISCU proteins via either one or two cysteines, referred to the 1-Cys and 2-Cys forms, respectively. The latter predominated at pH 8.0 and correlated with the Fe-S cluster assembly activity, whereas the former increased at a more acidic pH, together with free iron, suggesting that it constitutes an intermediate of the iron insertion process. Iron not binding to the assembly site was non-specifically bound to the aggregated ISCU, ruling out the existence of a structurally defined auxiliary site in ISCU. Characterization of the 2-Cys form by site-directed mutagenesis, CD, NMR, X-ray absorption, Mössbauer, and electron paramagnetic resonance spectroscopies showed that the iron center is coordinated by four strictly conserved amino acids of the assembly site, Cys35, Asp37, Cys61, and His103, in a tetrahedral geometry. The sulfur receptor Cys104 was at a very close distance and apparently bound to the iron center when His103 was missing, which may enable iron-dependent sulfur acquisition. Altogether, these data provide the structural basis to elucidate the Fe-S cluster assembly process and establish that the initiation of Fe-S cluster biosynthesis by insertion of a ferrous iron in the assembly site of ISCU is a conserved mechanism.

Combined experimental and theoretical investigation on the magnetic properties derived from the coordination of 6-methyl-2-oxonicotinate to 3d-metal ions

Five new compounds are reported herein starting from 2-hydroxy-6-methylnicotinic acid (H2h6mnic) and first-row transition metal ions, although H2h6mnic shows a prototropy in solution to lead to the 6-methyl-2-oxonicotinate (6m2onic) ligand that is the molecule eventually present in the compounds. The structural and chemical characterization reveals the following chemical formulae: {[MnNa(μ₃-6m2onic)₂(μ-6m2onic)(MeOH)]·H₂O·MeOH}_n (1Mn), {[M₂Na₂(μ₃-6m2onic)₂(μ-6m2onic)₂(μ-H₂O)(H₂O)₆](NO₃)₂}_n [M^II = Co (2Co) and Ni (3Ni)], 2[Cu₂(6m2onic)₃(μ-6m2onic)(MeOH)]·[Cu₂(6m2onic)₂(μ-6m2onic)₂]·2[Cu(6m2onic)₂(MeOH)]·32H₂O (4Cu) and {[Cu(μ-6m2onic)₂]·6H₂O}_n (5Cu) (where 6m2onic = 6-methyl-2-oxonicotinate). An unusual structural diversity is observed for the compounds, ranging from isolated complexes (in 4Cu), 1D arrays (in 1Mn and 5Cu) and 3D frameworks (in 2Co and 3Ni). Magnetic properties have been studied for all compounds. Analysis of the magnetic dc susceptibility and magnetization data for 4Cu and 5Cu suggests the occurrence of ferromagnetic exchange, which is well explained by broken-symmetry and CASSCF calculations. The sizeable easy-plane magnetic anisotropy present in compound 2Co allows for a field-induced magnet behaviour with an experimental effective energy barrier of 16.2 cm^-1, although the slow relaxation seems to be best described through Raman and direct processes in agreement with the results of ab initio calculations.

Recent developments in supramolecular complexes of azabenzenes containing one to four N atoms: synthetic strategies, structures, and magnetic properties

For the last couple of decades, azabenzene-based ligands have drawn much attention from inorganic chemists due to their ability to coordinate with different metal ions to form supramolecular clusters. These azabenzenes are weak σ donors and strong π acceptors and electron-deficient. Metallogrid complexes and non-grid oligomers are well-defined supramolecular clusters, formed by appropriate chelating ligands, and can show interesting optical, magnetic, and electronic properties. Self-assembly of [n × n] metallogrid complexes is dominated by the entropic factor while the formation of oligonuclear metal ion complexes is dominated by other effects like CFSE, electrostatic factors, ligand conformational characters, etc. Herein, the present article gives an overview of six-membered heterocyclic azine-based ligands and their potential for different metal ions to form polynuclear complexes. Moreover, their temperature-dependent magnetic properties and SCO phenomena are well described and tabulated.

Slow magnetic relaxation in mononuclear octa-coordinate Fe(II) and Co(II) complexes from a Bpybox ligand

Two 3d transition metal mononuclear complexes, [(FeL₂)(ClO₄)₂]₂·CH₃CN (1) and (CoL₂)(ClO₄)₂·2CH₃CN (2), have been prepared from a rigid tetradentate bpybox (L = 6,6'-bis(2,5-dihydrooxazol-4-yl)-2,2'-bipyridine) ligand. Single crystal X-ray diffraction analyses together with the help of calculations show that both compounds are octa-coordinate. Direct current magnetic studies reveal their significant magnetic anisotropy. Impressively, field-induced relaxation of magnetism is observed in the two complexes and the apparent anisotropy barriers are 14.1 K for 1 and 21.6 K for 2, respectively. Theoretical calculations reveal that two Fe(II) centers in 1 have small negative D values of -4.897 and -4.825 cm^-1 and relatively small E values of 0.646 and 0.830 cm^-1, indicating a uniaxial magnetic anisotropy. In contrast, the D and E values in the Co(II) center of 2 are 46.42 cm^-1 and 11.51 cm^-1, featuring a rhombic anisotropy. This work demonstrates that field-induced slow magnetic relaxation in 3d transition metal complexes with high coordination numbers can be manipulated through rigid ligand design.

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.

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...

Single-Molecule Magnets beyond a Single Lanthanide Ion: The Art of Coupling

The promising future of storing and processing quantized information at the molecular level has been attracting the study of Single-Molecule Magnets (SMMs) for almost three decades. Although some recent breakthroughs are mainly about the SMMs containing only one lanthanide ion, we believe SMMs can tell a much deeper story than the single-ion anisotropy. Here in this Perspective, we will try to draw a unified picture of SMMs as a delicately coupled spin system between multiple spin centres. The hierarchical couplings will be presented step-by-step, from the intra-atomic hyperfine coupling, to the direct and indirect intra-molecular couplings with neighbouring spin centres, and all the way to the inter-molecular and spin–phonon couplings. Along with the discussions on their distinctive impacts on the energy level structures and thus magnetic behaviours, a promising big picture for further studies is proposed, encouraging the multifaceted developments of molecular magnetism and beyond.

In this Perspective, we draw a unified picture for single-molecule magnets as delicately coupled spin systems, discuss the hierarchical couplings (from intra-atomic to inter-molecular) and their distinctive impacts on the magnetic behaviours.

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.

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.

Towards understanding the magnetism of Os(IV) complexes: an ab initio insight

The magnetism of a recently synthesized trans-[Os^IVCl₄(κN₁-Hind)₂] complex (5d⁴-system), where Hind = 2H-indazole, was studied experimentally and theoretically. Relativistic CASSCF/CASPT2 calculations for this and model [Os^IVCl₆]^2- complexes were employed to understand the nature of the low-lying multiplets. It is found that despite strong metal-ligand covalency they are basically characterized by the total angular pseudo-momentum J̃ originating from the spin-orbit coupling of the ground-state spin S = 1 with the orbital pseudo-momentum L̃ = 1 of the Os^IV ion. The strong spin-orbit interaction also preserves the dominant J̃ = 0 character of the non-magnetic ground state in the trans-[Os^IVCl₄(κN₁-Hind)₂] complex despite significant deviation of the ligand environment of Os^IV from octahedral symmetry. At the same time the spin-orbit admixture of all multiplets arising from the t_2g⁴ strong-field electronic configuration is indispensable for the correct description of magnetic properties of Os^IV complexes. Moreover, based on ab initio calculations, we argue that the charge-transfer states play an important role in the magnetism of the present and probably other 5d complexes, a situation never encountered for 3d and 4f compounds.

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.

Electronic Structure of Tetrahedral, S = 2, [Fe{(EPiPr2)2N}2], E = S, Se, Complexes: Investigation by High-Frequency and -Field Electron Paramagnetic Resonance, 57Fe Mössbauer Spectroscopy, and Quantum Chemical Studies

In this work, we assessed the electronic structures of two pseudotetrahedral complexes of FeII, [Fe{(SPiPr2)2N}2] (1) and [Fe{(SePiPr2)2N}2] (2), using high-frequency and -field EPR (HFEPR) and field-dependent 57Fe Mössbauer spectroscopies. This investigation revealed S = 2 ground states characterized by moderate, negative zero-field splitting (zfs) parameters D. The crystal-field (CF) theory analysis of the spin Hamiltonian (sH) and hyperfine structure parameters revealed that the orbital ground states of 1 and 2 have a predominant dx2-y2 character, which is admixed with dz2 (∼10%). Although replacing the S-containing ligands of 1 by their Se-containing analogues in 2 leads to a smaller |D| value, our theoretical analysis, which relied on extensive ab initio CASSCF calculations, suggests that the ligand spin-orbit coupling (SOC) plays a marginal role in determining the magnetic anisotropy of these compounds. Instead, the dx2-y2β → dxyβ excitations yield a large negative contribution, which dominates the zfs of both 1 and 2, while the different energies of the dx2-y2β → dxzβ transitions are the predominant factor responsible for the difference in zfs between 1 and 2. The electronic structures of these compounds are contrasted with those of other [FeS4] sites, including reduced rubredoxin by considering a D2-type distortion of the [Fe(E-X)4] cores, where E = S, Se; X = C, P. Our combined CASSCF/DFT calculations indicate that while the character of the orbital ground state and the quintet excited states' contribution to the zfs of 1 and 2 are modulated by the magnitude of the D2 distortion, this structural change does not impact the contribution of the excited triplet states.

Equation-of-Motion Coupled-Cluster Protocol for Calculating Magnetic Properties: Theory and Applications to Single-Molecule Magnets

We present a new computational protocol for computing macroscopic magnetic properties of transition-metal complexes using the equation-of-motion coupled-cluster (EOM-CC) framework. The approach follows a two-step state-interaction scheme: we first compute zero-order states using nonrelativistic EOM-CC and then use these states to evaluate matrix elements of the spin-orbit and Zeeman operators. Diagonalization of the resulting Hamiltonian yields spin-orbit- and field-perturbed eigenstates. Temperature- and field-dependent magnetization and susceptibility are computed by numerical differentiation of the partition function. To compare with powder-sample experiments, these quantities are numerically averaged over field orientations. We applied this protocol to several single-molecule magnets (SMMs) with Fe(II) and Fe(III) in trigonal pyramidal, linear, and trigonal bipyramidal coordination environments. We described the underlying electronic structure by the electron-attachment (EOM-EA) and spin-flip (EOM-SF) variants of EOM-CC. The computed energy barriers for spin inversion, and macroscopic magnetization and susceptibility agree well with experimental data. Trends in magnetic anisotropy and spin-reversal energy barriers are explained in terms of a molecular orbital picture rigorously distilled from spinless transition density matrices between many-body states. The results illustrate excellent performances of EOM-CC in describing magnetic behavior of mononuclear transition-metal SMMs.

A reaction-coordinate perspective of magnetic relaxation

Understanding and utilizing the dynamic quantum properties of metal ions is the frontier of many next generation technologies. One property in particular, magnetic relaxation, is a complicated physical phenomenon that is scarcely treated in undergraduate coursework. Consequently, principles of magnetic relaxation are nearly impenetrable to starting synthetic chemists, who ultimately design the molecules that fuel new discoveries. In this Tutorial Review, we describe a new paradigm for thinking of magnetic relaxation in metal complexes in terms of a simple reaction-coordinate diagram to facilitate access to the field. We cover the main mechanisms of both spin-lattice (T1) and spin-spin (T2) relaxation times within this conceptual framework and how molecular and environmental design affects these times. Ultimately, we show that many of the scientific methods used by inorganic chemists to study and manipulate reactivity are also useful for understanding and controlling magnetic relaxation. We also describe the cutting edge of magnetic relaxation within this paradigm.

Tetrairon(II) extended metal atom chains as single-molecule magnets

Iron-based extended metal atom chains (EMACs) are potentially high-spin molecules with axial magnetic anisotropy and thus candidate single-molecule magnets (SMMs). We herein compare the tetrairon(ii), halide-capped complexes [Fe4(tpda)3Cl2] (1Cl) and [Fe4(tpda)3Br2] (1Br), obtained by reacting iron(ii) dihalides with [Fe2(Mes)4] and N2,N6-di(pyridin-2-yl)pyridine-2,6-diamine (H2tpda) in toluene, under strictly anhydrous and anaerobic conditions (HMes = mesitylene). Detailed structural, electrochemical and Mössbauer data are presented along with direct-current (DC) and alternating-current (AC) magnetic characterizations. DC measurements revealed similar static magnetic properties for the two derivatives, with χMT at room temperature above that for independent spin carriers, but much lower at low temperature. The electronic structure of the iron(ii) ions in each derivative was explored by ab initio (CASSCF-NEVPT2-SO) calculations, which showed that the main magnetic axis of all metals is directed close to the axis of the chain. The outer metals, Fe1 and Fe4, have an easy-axis magnetic anisotropy (D = -11 to -19 cm-1, |E/D| = 0.05-0.18), while the internal metals, Fe2 and Fe3, possess weaker hard-axis anisotropy (D = 8-10 cm-1, |E/D| = 0.06-0.21). These single-ion parameters were held constant in the fitting of DC magnetic data, which revealed ferromagnetic Fe1-Fe2 and Fe3-Fe4 interactions and antiferromagnetic Fe2-Fe3 coupling. The competition between super-exchange interactions and the large, noncollinear anisotropies at metal sites results in a weakly magnetic non-Kramers doublet ground state. This explains the SMM behavior displayed by both derivatives in the AC susceptibility data, with slow magnetic relaxation in 1Br being observable even in zero static field.

Rare-Earth-Silyl ate-Complexes Opening a Door to Selective Manipulations

The reactions of a number of rare-earth (RE) trichlorides and an oligosilanylene diide containing a siloxane unit in the backbone in DME are described. The formed products of the type [(DME)4·K][(DME)·RE(Cl)2{Si(SiMe3)2SiMe2}2O] (RE = Y, La, Ce, Pr, Sm, Tb, Dy, and Er) are disilylated dichloro metalate complexes and include the first examples of Si-La and Si-Pr compounds as well as the first structurally characterized example of a Si-Dy complex. A most intriguing aspect of the synthesis of these complexes is that they offer entry into a systematic study of the still largely unexplored field of silyl RE complexes by the possibility of ligand exchange reactions under preservation of the Si-RE interaction. This was demonstrated by the conversion of [(DME)4·K][(DME)·RE(Cl)2{Si(SiMe3)2SiMe2}2O] to [(DME)4·K][Cp2Y{Si(SiMe3)2SiMe2}2O].

Generation of a Hetero Spin Complex from Iron(II) Iodide with Redox Active Acenaphthene-1,2-Diimine

The reaction of the redox active 1,2-bis[(2,6-diisopropylphenyl)imino]acenaphthene (dpp-BIAN) and iron(II) iodide in acetonitrile led to a new complex [(dpp-BIAN)Fe^III₂] (1). Molecular structure of 1 was determined by the single crystal X-ray diffraction analysis. The spin state of the iron cation in complex 1 at room temperature and the magnetic behavior of 1 in the temperature range of 2–300 K were studied using Mossbauer spectroscopy and magnetic susceptibility measurements, respectively. The neutral character of dpp-BIAN in 1 was confirmed by IR and UV spectroscopy. The electrochemistry of 1 was studied in solution and solid state using cyclic voltammetry. The generation of the radical anion form of the dpp-BIAN ligand upon reduction of 1 in a CH₂Cl₂ solution was monitored by EPR spectroscopy.

Molecular and Electronic Structures and Single-Molecule Magnet Behavior of Tris(thioether)-Iron Complexes Containing Redox-Active α-Diimine Ligands

Incorporating radical ligands into metal complexes is one of the emerging trends in the design of single-molecule magnets (SMMs). While significant effort has been expended to generate multinuclear transition metal-based SMMs with bridging radical ligands, less attention has been paid to mononuclear transition metal-radical SMMs. Herein, we describe the first α-diiminato radical-containing mononuclear transition metal SMM, namely, [κ²-PhTt^tBu]Fe(AdNCHCHNAd) (1), and its analogue [κ²-PhTt^tBu]Fe(CyNCHCHNCy) (2) (PhTt^tBu = phenyltris(tert-butylthiomethyl)borate, Ad = adamantyl, and Cy = cyclohexyl). 1 and 2 feature nearly identical geometric and electronic structures, as shown by X-ray crystallography and electronic absorption spectroscopy. A more detailed description of the electronic structure of 1 was obtained through EPR and Mössbauer spectroscopies, SQUID magnetometry, and DFT, TD-DFT, and CAS calculations. 1 and 2 are best described as high-spin iron(II) complexes with antiferromagnetically coupled α-diiminato radical ligands. A strong magnetic exchange coupling between the iron(II) ion and the ligand radical was confirmed in 1, with an estimated coupling constant J < -250 cm^-1 (J = -657 cm^-1, DFT). Calibrated CAS calculations revealed that the ground-state Fe(II)-α-diiminato radical configuration has significant ionic contributions, which are weighted specifically toward the Fe(I)-neutral α-diimine species. Experimental data and theoretical calculations also suggest that 1 possesses an easy-axis anisotropy, with an axial zero-field splitting parameter D in the range from -4 to-1 cm^-1. Finally, dynamic magnetic studies show that 1 exhibits slow magnetic relaxation behavior with an energy barrier close to the theoretical maximum, 2|D|. These results demonstrate that incorporating strongly coupled α-diiminato radicals into mononuclear transition metal complexes can be an effective strategy to prepare SMMs.

Hepta-coordinated Ni(II) assemblies - structure and magnetic studies

Two mononuclear complexes [Ni(dapsc)(H2O)2]Cl(NO3)·H2O (1) and [Ni(dapsc)(NCS)2] (2), and a bimetallic CN-bridged trinuclear molecule [NiII(dapsc)(H2O)]2[WIV(CN)8]·11H2O (3) (dapsc = 2,6-diacetylpyridine-bis(semicarbazone)) were synthesised and characterised in terms of structure and magnetic properties. All three compounds contain Ni(ii) ions in a pentagonal bipyramid coordination geometry afforded by the equatorial pentadentate ligand (dapsc) and two O- or N-donating axial ligands. The compounds differ in the relative arrangement of the complexes, intermolecular interactions and distortion from the ideal coordination geometry. The high-field EPR and magnetometric studies show large anisotropy of the Ni(ii) centres with the D parameters in the range of -10.5 to -21.2 cm-1 and negligible antiferromagnetic interactions. The easy-axis magnetic anisotropies of 1-3 were reproduced by ab initio CASSCF/NEVPT2 calculations. The ground states consist mainly of the |MS = |±1 states, which is consistent with the fact that no out-of-phase signal can be detected in the AC magnetic susceptibility measurements.

First-Principles Investigations of Magnetic Anisotropy and Spin-Crossover Behavior of Fe(III)-TBP Complexes

With the ongoing effort to obtain mononuclear 3d-transition-metal complexes that manifest slow relaxation of magnetization and, hence, can behave as single-molecule magnets (SMMs), we have modeled 14 Fe(III) complexes based on an experimentally synthesized (PMe₃)₂FeCl₃ complex [J. Am. Chem. Soc. 2017, 139 (46), 16474-16477], by varying the axial ligands with group XV elements (N, P, and As) and equatorial halide ligands from F, Cl, Br, and I. Out of these, nine complexes possess large zero field splitting (ZFS) parameter D in the range of -40 to -60 cm^-1. The first-principles investigation of the ground-spin state applying density functional theory (DFT) and wave function-based multiconfigurations methods, e.g., SA-CASSCF/NEVPT2, are found to be quite consistent except for few delicate cases with near-degenerate spin states. In such cases, the hybrid B3LYP functional is found to be biased toward high-spin (HS) state. Altering the percentage of exact exchange admixed in the B3LYP functional leads to intermediate-spin (IS) ground state consistent with the multireference calculations. The origin of large zero field splitting (ZFS) in the Fe(III)-based trigonal bipyramidal (TBP) complexes is investigated. Furthermore, a number of complexes are identified with very small ΔG_HS-IS^adia. values indicating the possible spin-crossover phenomenon between the bistable spin states.

Magnetic Anisotropy: Structural Correlation of a Series of Chromium(II)-Amidinate Complexes

Systematic substituent variations on amidinate ligands bring delicate changes of CrN₄ coordination in a family of chromium(II) complexes with the common formula of Cr(RNC(CH₃)NR)₂, where R = iPr (1), Cy (2), Dipp (Dipp = 2, 6-diisopropylphenyl) (3), and tBu (4). With the largest substituent group, 4 shows the largest distortion of the N₄ coordination geometry from square-planar to seesaw shape, which leads to its field-induced single-molecule magnet (SMM) behavior. This is an indication that 4 has the strongest axial magnetic anisotropy and/or optimized magnetic relaxation process. Combined with high-frequency/field electron paramagnetic resonance (HF-EPR) experiments and ab initio calculations, we deduce that the smallest energy gap between ground ⁴Ψ₀ and the first excited ⁴Ψ₁ orbitals in 4 contributes the most to its strongest magnetic anisotropy. Moreover, the lower E value of 4 ensures its being a field-induced SMM. Specifically, the D and E values were found to be correlated to the dihedral angle between the ΔN₁CrN₂ and ΔN₃CrN₄ triangles, indicating that distortion from ideal square-planar geometry to the seesaw help increase axial magnetic anisotropy and suppress the transversal part. Thus, the study on this system not only expands the family of Cr(II)-based SMMs but also contributes to a deeper understanding of magneto-structural correlation in four-coordinate Cr(II) SMMs.

A cobalt complex with 2,4,6-tris(di-2-pyridylamine)-1,3,5-triazine: antiferromagnetic couple governed single-molecule-magnet behaviour

One cobalt complex with distorted trigonal antiprismatic geometry was obtained using 2,4,6-tris(di-2-pyridylamine)-1,3,5-triazine (dipyatriz) as the ligand. X-ray crystallography showed the complex possessing a pair of metal centers, had an antiferromagnetic coupling between two Co(ii) ions. Further studied showed a field-induced slow relaxation under H_dc = 0.8 kOe. The peak of out-of-phase was observed after 1000 Hz, which exhibited a moderate slow-relaxation behaviour comparing to the magnetic couple for single Co(ii) complex. This study may provide some strategies on designing new functional molecular magnetic materials with distinct magnetic properties and diverse the structures.

One cobalt complex with distorted trigonal antiprismatic geometry was obtained using 2,4,6-tris(di-2-pyridylamine)-1,3,5-triazine (dipyatriz) as the ligand.

Single-molecule magnet achieved through topological tuning with sodium ions

A triangular MnIII3-based 2D framework exhibiting SMM properties was achieved by tuning the topological arrangement of cluster units and the intra-unit parameters through the linkage of diamagnetic Na(i) ions.

Spin crossover phenomena in long chain alkylated complexes

This review presents a discussion of soft metal complexes with a focus on spin crossover behaviours that are associated with structural phase transition, including liquid crystal LC transition.

Field-induced single molecule magnet behavior of a dinuclear cobalt(II) complex: a combined experimental and theoretical study

Two dinuclear cobalt(ii) complexes, [(dmso)CoIIL1(μ-(m-NO2)C6H4COO)CoII(NCS)] (1) and [(dmso)CoIIL2(μ-(m-NO2)C6H4COO)CoII(NCS)] (2) [dmso = dimethylsulfoxide, H2L1 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-methoxyphenol) and H2L2 = (2,2-dimethyl-1,3-propanediyl)bis(iminomethylene)bis(6-ethoxyphenol)] have been synthesized and structurally characterized by single-crystal X-ray diffraction, magnetic-susceptibility measurements and various spectroscopic techniques. Each complex contains a cobalt(ii) center with a slightly distorted octahedral geometry and a second cobalt(ii) center with a distorted trigonal prismatic one. To obtain insight into the physical nature of weak non-covalent interactions, we have extensively used the Bader's quantum theory of atoms-in-molecules (QTAIM). In addition, the non-covalent interaction reduced density gradient (NCI-RDG) methods established the presence of such non-covalent intermolecular interactions. Variable temperature magnetic susceptibility measurements show that both cobalt centers in each complex are in the high spin state (S = 3/2) and both complexes show weak ferromagnetic couplings through the double phenoxido bridges (J = 3.36(3) cm-1 in 1 and 4.56(2) cm-1 in 2). The magnetic properties of both complexes can be fitted to a Co(ii) dimer model including similar orbital reduction factors (α = -0.94(1) for 1 and -0.85(1) for 2) although different zero field splitting parameters D(1) = 11.0(4) cm-1 and D(2) = 19.5(4) cm-1 in 1 and D(1) = 8.2(4) cm-1 and D(2) = -1.3(4) cm-1 in 2. AC magnetic measurements reveal that the CoII2 unit in complex 2 exhibits field-induced slow relaxation of the magnetization at low temperatures and high frequencies.

Zero-field slow relaxation of magnetization in cobalt(ii) single-ion magnets: suppression of quantum tunneling of magnetization by tailoring the intermolecular magnetic coupling

The correlation between magnetic relaxation dynamics and the alignment of single-ion magnets (SIMs) in a crystal was investigated using four analogous cobalt(ii) complexes with unique hydrogen-bond networks. The hydrogen-bonding interactions in the crystals resulted in a relatively short intermolecular Co⋯Co distance, which led to non-zero intermolecular magnetic coupling. All the complexes with a Co⋯Co distance shorter than 6.5 Å exhibited zero-field slow magnetic relaxation as weak magnetic interactions split the ground ±Ms levels and suppressed quantum tunneling of magnetization (QTM). In particular, antiferromagnetically coupled one-dimensional chain SIM networks effectively suppressed QTM when the two intrachain Co⋯Co distances were non-equivalent. However, when the two distances in a chain were equivalent and each molecular symmetry axis aligned parallell within the chain, QTM suppression was insufficient because magnetic coupling from the adjacent molecules was virtually cancelled. Partial substitution of the CoII ion with the diamagnetic ZnII ion up to 33% for this complex resulted in complete QTM suppression in the absence of an external field. These results show that the manipulation of intermolecular distances and alignments is effective for suppressing undesired QTM events in SIMs.

Role of Coordination Number and Geometry in Controlling the Magnetic Anisotropy in FeII , CoII , and NiII Single-Ion Magnets

Since the last decade, the focus in the area of single-molecule magnets (SMMs) has been shifting constructively towards the development of single-ion magnets (SIMs) based on transition metals and lanthanides. Although ground-breaking results have been witnessed for Dy^III -based SIMs, significant results have also been obtained for some mononuclear transition metal SIMs. Among others, studies based on Co^II ion are very prominent as they often exhibit high magnetic anisotropy or zero-field splitting parameters and offer a large barrier height for magnetisation reversal. Although Co^II possibly holds the record for having the largest number of zero-field SIMs known for any transition metal ion, controlling the magnetic anisotropy in these systems are is still a challenge. In addition to the modern spectroscopic techniques, theoretical studies, especially ab initio CASSCF/NEVPT2 approaches, have been used to uncover the electronic structure of various Co^II SIMs. In this article, with some selected examples, the aim is to showcase how varying the coordination number from two to eight, and the geometry around the Co^II centre alters the magnetic anisotropy. This offers some design principles for the experimentalists to target new generation SIMs based on the Co^II ion. Additionally, some important Fe^II /Fe^III and Ni^II complexes exhibiting large magnetic anisotropy and SIM properties are also discussed.

Origins of Slow Magnetic Relaxation in Single-Molecule Magnets

Exponential and power law temperature dependences are widely used to fit experimental data of magnetic relaxation time in single molecular magnets. We derived a theory to show how these rules arise from the underling relaxation mechanisms and to clarify the conditions for their occurrence. The theory solves the puzzle of lower-than-expected Orbach barriers found in recent experiments, and elucidates it as a result of the Raman process in disguise. Our results highlight the importance of reducing the rate of direct tunneling between the ground state doublet so as to achieve longtime coherence in magnetic molecules. To this end, large spin and small transverse magnetic anisotropy can reduce magnitude of the transition operator, and rigid ligands may weaken the spin-phonon coupling in that they raise the energy of vibrational modes and better screen the acoustic phonons.

Orbital energy mismatch engenders high-spin ground states in heterobimetallic complexes

The spin state in heterobimetallic complexes heavily influences both reactivity and magnetism. Exerting control over spin states in main group-based heterobimetallics requires a different approach as the orbital interactions can differ substantially from that of classic coordination complexes. By deliberately engendering an energetic mismatch within the two metals in a bimetallic complex we can mimic the electronic structure of lanthanides. Towards this end, we report a new family of complexes, [^Ph,MeTpMSnPh₃] where M = Mn (3), Fe (4), Co (5), Ni (6), Zn (7), featuring unsupported bonding between a transition metal and Sn which represent an unusual high spin electronic structure. Analysis of the frontier orbitals reveal the desired orbital mismatch with Sn 5s/5p primarily interacting with 4s/4p M orbitals yielding localized, non-bonding d orbitals. This approach offers a mechanism to design and control spin states in bimetallic complexes.

We report a series of high spin bimetallic transition metal–tin complexes. The unusual high spin configuration in a bimetallic complex is enabled by an energetic mismatch in the orbital energies, leading to lanthanide-like nonbonding interactions.

Synthesis, Crystal Structures and Magnetic Properties of Mononuclear High-Spin Cobalt(II) Complex

A new four-coordinated high-spin Co(II) complex was synthesized through the reactions of Co(NSC)2 with bathocuproine, by the diffusion method, resulting in an infinite one-dimension chain. Both static and dynamic magnetic properties were measured. The magnetic properties investigation shows that the single CoII ion properties dominate the magnetic behavior in the complex. Despite the presence of a four-coordinated single CoII ion, no SMM properties were exhibited by the complex.

A large axial magnetic anisotropy in trigonal bipyramidal Fe(ii)

Minimising geometric distortion in the first coordination sphere generates a large axial magnetic anisotropy in trigonal bipyramidal Fe(ii) and rare slow magnetic relaxation.

Coligand effects on the architectures and magnetic properties of octahedral cobalt(ii) complexes with easy-axis magnetic anisotropy

Coligand effects lead to two mononuclear octahedral Co(ii) complexes exhibiting easy-axis magnetic anisotropies and distinct magnetic properties.