Interplay between Local Anisotropies in Binuclear Complexes

Impact of the electric field on isotropic and anisotropic spin Hamiltonian parameters

One may obviously think that the best way to control magnetic properties relies on using a magnetic field. However, it is not convenient to focus a magnetic field on a small object, whereas it is much easier to do so with an electric field. Magnetoelectric coupling allows one to control the magnetization with the electric field and the polarization with the magnetic field and could therefore provide a solution to this problem. This paper aims at quantifying the impact of the electric field on both the isotropic magnetic exchange and the Dzyaloshinskii–Moriya interaction in the case of a binuclear system of S = 1/2 spins. This study follows previous studies that showed that very high Dzyaloshinskii–Moriya interaction, i.e., the antisymmetric exchange, can be generated when close to first order spin orbit coupling. We will, therefore, explore this regime in a model Cu(II) complex that exhibits a quasi-degeneracy of the [Formula: see text] and d xy orbitals. This situation is indeed the one that allows us to obtain the largest spin orbit couplings in transition metal complexes. We will show that both the magnetic exchange and the Dzyaloshinskii–Moriya interaction are very sensitive to the electric field and that it would therefore be possible to modulate and control magnetic properties by the electric field. Finally, rationalizations of the obtained results will be proposed.

Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: First-order spin-orbit coupling model and methodological study

The Dzyaloshinskii-Moriya interaction is expected to be at the origin of interesting magnetic properties, such as multiferroicity, skyrmionic states, and exotic spin orders. Despite this, its theoretical determination is far from being established, neither from the point of view of ab initio methodologies nor from that of the extraction technique to be used afterward. Recently, a very efficient way to increase its amplitude has been demonstrated near the first-order spin-orbit coupling regime. Within the first-order regime, the anisotropic spin Hamiltonian involving the Dzyaloshinskii-Moriya operator becomes inappropriate. Nevertheless, in order to approach this regime and identify the spin Hamiltonian limitations, it is necessary to characterize the underlying physics. To this end, we have developed a simple electronic and spin-orbit model describing the first-order regime and used ab initio calculations to conduct a thorough methodological study.

Magnetic Anisotropy in a Cubane-like Ni4 Complex: An Ab Initio Perspective

Magnetic anisotropy, in the absence of an external magnetic field, relates to the degeneracy lift of energy levels. In the standard case of transition metal complexes, this property is usually modeled by an anisotropic spin Hamiltonian and one speaks of "zero-field splitting" (ZFS) of spin states. While the case of mononuclear complexes has been extensively described by means of ab initio quantum mechanical calculations, the literature on polynuclear complexes studied with these methodologies is rather scarce. In this work, advanced multiconfigurational wave function theory methods are applied to compute the ZFS of the ground S = 4 state of an actual tetranickel(II) complex, displaying a magnet behavior below 0.5 K. First, the isotropic couplings are computed in the absence of the spin-orbit coupling operator, in the full complex and also in clusters with only two active nickel(II) centers, confirming the occurrence of weak ferromagnetic couplings in this system. Second, the single-site magnetic anisotropies are computed on a cluster bearing only one active nickel(II) site, showing that the single-site anisotropy axes are not oriented in an optimal fashion for generating a large uniaxial molecular anisotropy. Furthermore, the possibility for involving only a few local orbital excited states in the calculation is assessed, actually opening the way for a consistent and manageable treatment of the ZFS of the ground S = 4 state. Third, multiconfigurational calculations are performed on the full complex, confirming the weak uniaxial anisotropy occurring for this state and also, interestingly, revealing a significant contribution of the lowest-lying orbitally excited S = 3 states. Overall, by comparison with the experiment, the reported results question the common habit of using only one structure, in particular derived from a crystallography experiment, to compute magnetic anisotropy parameters.

How to create giant Dzyaloshinskii-Moriya interactions? Analytical derivation and ab initio calculations on model dicopper(II) complexes

This paper is a theoretical "proof of concept" on how the on-site first-order spin-orbit coupling (SOC) can generate giant Dzyaloshinskii-Moriya interactions in binuclear transition metal complexes. This effective interaction plays a key role in strongly correlated materials, skyrmions, multiferroics, and molecular magnets of promising use in quantum information science and computing. Despite this, its determination from both theory and experiment is still in its infancy and existing systems usually exhibit very tiny magnitudes. We derive analytical formulas that perfectly reproduce both the nature and the magnitude of the Dzyaloshinskii-Moriya interaction calculated using state-of-the-art ab initio calculations performed on model bicopper(II) complexes. We also study which geometrical structures/ligand-field forces would enable one to control the magnitude and the orientation of the Dzyaloshinskii-Moriya vector in order to guide future synthesis of molecules or materials. This article provides an understanding of its microscopic origin and proposes recipes to increase its magnitude. We show that (i) the on-site mixings of 3d orbitals rule the orientation and magnitude of this interaction, (ii) increased values can be obtained by choosing more covalent complexes, and (iii) huge values (∼1000 cm^-1) and controlled orientations could be reached by approaching structures exhibiting on-site first-order SOC, i.e., displaying an "unquenched orbital momentum."

Slow relaxation of magnetization in lanthanide-biradical complexes based on a functionalized nitronyl nitroxide biradical

Three novel lanthanide-biradical complexes {[Ln(hfac)3]2(mbisNITPyPh)(H2O)}{[Ln(hfac)3](mbisNITPyPh)}·CHCl3 (1-Gd; 2-Tb; 3-Dy) were successfully achieved by reacting the biradical mbisNITPyPh (5-(3-pyridyl)-1,3-bis(1-oxyl-3'-oxido-4',4',5',5'-tetramethyl-4,5-hydro-1H-imidazol-2-yl)benzene) with Ln(hfac)3·2H2O (hfac = hexafluoroacetylacetonate). These Ln-biradical complexes consist of two kinds of spin moieties, namely, dinuclear {[Ln(hfac)3]2(mbisNITPyPh)(H2O)} and mononuclear {[Ln(hfac)3](mbisNITPyPh)}, in which two adjacent dinuclear units are linked by intermolecular hydrogen bonds involving the uncoordinated nitroxide units and the coordinated water molecules of Ln ions, forming a cyclic tetranuclear structure unit. The magnetization study reveals that intramolecular Ln(iii)-coordinated NO ferromagnetic interactions are dominant in the present system. Moreover, the clear frequency dependence of ac magnetic susceptibilities of complex 3-Dy is indicative of slow relaxation of magnetization behavior, indicating its single-molecule magnet nature.

Nitronyl Nitroxide Biradical-Based Binuclear Lanthanide Complexes: Structure and Magnetic Properties

Employing a new nitronyl nitroxide biradical NITPhPzbis(NITPhPzbis = 5-(1-pyrazolyl)-1,3-bis(1’-oxyl-3’-oxido-4’,4’,5’,5’-tetramethyl-4,5-hydro-1H-imidazol-2-yl)benzene), a series of 2p-4f complexes [Ln2(hfac)6(H2O)(NITPhPzbis)] (LnIII = Gd1, Tb2, Dy3; hfac = hexafluoroacetylacetonate) were successfully synthesized. In complexes 1–3, the designed biradical NITPhPzbis coordinates with two LnIII ions in chelating and bridging modes to form a four-spin binuclear structure. Direct-current magnetic study of Gd analogue indicates that ferromagnetic exchange exists between the Gd ion and the radical while antiferromagnetic coupling dominates between two mono-radicals. Dynamic magnetic data show that the χ” signals of complex 3 exhibit frequency dependence under zero field, demonstrating slow magnetic relaxation behavior in complex 3. And the estimated values of Ueff and τ0 are about 8.4 K and 9.1 × 10−8 s, respectively.

Designing Multicoordinating Nitronyl Nitroxide Radical Toward Multinuclear Lanthanide Aggregates

Profiting from a multicoordinating nitronyl nitroxide radical, i.e. a functionalized nitronyl nitroxide biradical ligand, a family of novel tetranuclear lanthanide complexes, formulated as [RE₄(hfac)₁₂(NITPhO-3Pybis)₂] (RE = Gd 1, Tb 2, Dy 3, Ho 4, and Y 5; NITPhO-3Pybis = 5-(3-pyridinyloxy)-1,3-bis(1'-oxyl-3'-oxido-4',4',5',5'-tetramethyl-4,5-hydro-1H-imidazol-2-yl)benzene; hfac = hexafluoroacetylacetonate) were successfully constructed and characterized. In these complexes, the designed functionalized nitronyl nitroxide biradical ligand functions as the chelating and/or bridging ligand to bind the lanthanide ions, resulting in tetranuclear octa-spin lanthanide complexes with a circle-shaped arrangement. Direct-current magnetic data show that antiferromagnetic interaction dominates in the Gd derivative, while ferromagnetic coupling plays a leading role in complex Y, in which the relevant magnetic exchange parameters were obtained through applicable magnetic models. Dynamic magnetic studies of Tb and Dy analogues exhibit apparent frequency-dependent out-of-phase signals, which are typical features for slow magnetic relaxation behavior. The values of U_eff and τ₀ were obtained as follows: U_eff = 10.5 K and τ₀ = 6.6 × 10^-7 s for the Tb complex and U_eff = 5.2 K and τ₀ = 2.5 × 10^-6 s for the Dy compound. Intriguingly, the butterfly shaped hysteresis loop is found for the Tb analogue. Guided by fluorescence spectra, the representative peaks are identified for the Tb derivative.

A ferromagnetic Ni(ii)–Cr(iii) single-chain magnet based on pentagonal bipyramidal building units

The first example of a ferromagnetic Ni(ii)–Cr(iii) single-chain magnet fashioned using pentagonal bipyramidal Ni(ii) complexes with Ising-type anisotropy.

Derivation of Lanthanide Series Crystal Field Parameters From First Principles

Two series of lanthanide complexes have been chosen to analyze trends in the magnetic properties and crystal field parameters (CFPs) along the two series: The highly symmetric LnZn₁₆ (picHA)₁₆ series (Ln=Tb, Dy, Ho, Er, Yb; picHA=picolinohydroxamic acid) and the [Ln(dpa)₃ ](C₃ H₅ N₂ )₃ ⋅3H₂ O series (Ln=Ce-Yb; dpa=2,6-dipicolinic acid) with approximate three-fold symmetry. The first series presents a compressed coordination sphere of eight oxygen atoms whereas in the second series, the coordination sphere consists of an elongated coordination sphere formed of six oxygen atoms. The CFPs have been deduced from ab initio calculations using two methods: The AILFT (ab initio ligand field theory) method, in which the parameters are determined at the orbital level, and the ITO (irreducible tensor operator) decomposition, in which the problems are treated at the many-electron level. It has been found that the CFPs are transferable from one derivative to another, within a given series, as a first approximation. The sign of the second-order parameter B 0 2 differs in the two series, reflecting the different environments. It has been found that the use of the strength parameter S allows for an easy comparison between complexes. Furthermore, in both series, the parameters have been found to decrease in magnitude along the series, and this decrease is attributed to covalent effects.

Influence of ancillary ligands and solvents on the nuclearity of Ni-Ln complexes

A Schiff base ligand resulting from the reaction of ovanillin and 2,2-dimethyl-1,3-diaminopropane allows the preparation of hetero-dinuclear [Ni-Ln]³⁺ or -trinuclear [Ni-Ln-Ni]³⁺ complexes. Although empirical parameters for rationalizing the strength of the ferromagnetic Ni-Gd interaction have already been discussed in several papers, no systematic study has been devoted to the control of the nuclearity of such complexes. With the help of structural determinations, we demonstrate the role of solvent and of the nature of ancillary ligands, linked to the Ln ions, in nuclearity. For instance, the presence of one chelating nitrato ligand is already sufficient to impede an increase in the nuclearity, while the replacement of nitrato ligands by chloride anions still yields dinuclear Ni-Ln complexes. This experimental result evidences the role of protic solvents. In contrast, the use of lanthanide salts, soluble in non-protic solvents, allows the isolation of dinuclear [Ni-Ln]³⁺ or trinuclear cationic [LNi-Ln-NiL]³⁺ complexes, depending on the Ni/Ln ratio. A further synthetic step can be overtaken by the reaction of a Ni-Ln complex, soluble in a non-protic solvent, with a LM complex (M = Cu, Zn). By doing so, a heterotrinuclear complex made of three different metal ions, two distinct 3d ions and a 4f one, has been isolated and structurally characterized. Note that the Ni coordination number decreases from 6 to 5 on going from the dinuclear complex to the trinuclear one. Also, the replacement of water molecules by chloride ligands in the hexacoordinate Ni complexes induces a net increase of the positive zero-field splitting parameter D to 20 cm^-1, which is supported by ab initio calculations. Although the Ni-Ln (Ln = Gd, Tb, Dy) magnetic interactions are ferromagnetic, the corresponding trinuclear complexes are devoid of SMM properties in the absence of an applied magnetic field.

Bromine-bridged Dy2 single-molecule magnet: magnetic anisotropy driven by cis/trans stereoisomers

The peculiar cis/trans stereoisomers in a bromine-bridged Dy2 single-molecule magnet drive the orthogonal magnetic moments and tune the magnetic interactions, leading to a large energy barrier of 684 K.

Slow magnetization dynamics in Co(ii)/Co(iii) triethanolamine/pivalate complexes

We report the synthesis, structural characterization and a combined computational and experimental study of the magnetic properties of two pivalate cobalt complexes, a mononuclear Co(ii) one and a tetranuclear Co(ii)₃Co(iii) mixed valence polynuclear one. The latter shows SMM behaviour revealed under an applied DC field with a thermal barrier of ca. 30 cm^-1 competing with direct and Raman relaxation processes. The Orbach thermal barrier can be understood from the doublets energy ladder arising from the anisotropic exchange interaction among ground S_eff = 1/2 of each Co(ii) sites. The strong local zero-field splitting of the S = 3/2 Co(ii) states affords these well isolated ground Kramers doublets. DC and AC magnetic susceptibility measurements as well as HF-EPR spectra support this interpretation. CASSCF quantum chemical computations have been also performed in order to aid the overall comprehension of the magnetic behaviour in the reported complexes.

Cyano-Bridged Fe(II)-Cr(III) Single-Chain Magnet Based on Pentagonal Bipyramid Units: On the Added Value of Aligned Axial Anisotropy

A cyano-bridged Fe(II)-Cr(III) single-chain magnet designed to ensure a parallel orientation of the axial anisotropy of the building units is reported. This ferromagnetic chain compound consists of a pentagonal bipyramid Fe(II) complex with Ising-type anisotropy and a dicyanide Cr(III) complex interlinked through their apical positions. It is characterized by an energy gap for the magnetization reversal of Δ_eff/ k_B = 113 K and exhibits magnetic hysteresis with a coercive field of 1400 Oe at 2 K which positions this compound among the very few examples of SCMs with spin reversal barriers above 100 K. The quite remarkable performances of this single-strand SCM are attributed to the alignment of the local anisotropy axes, which is supported by ab initio modeling. A discrete Cr₂Fe complex based on the same building units and behaving as a SMM in zero field is also reported.

Modelling spin Hamiltonian parameters of molecular nanomagnets

Molecular nanomagnets encompass a wide range of coordination complexes possessing several potential applications. A formidable challenge in realizing these potential applications lies in controlling the magnetic properties of these clusters. Microscopic spin Hamiltonian (SH) parameters describe the magnetic properties of these clusters, and viable ways to control these SH parameters are highly desirable. Computational tools play a proactive role in this area, where SH parameters such as isotropic exchange interaction (J), anisotropic exchange interaction (Jx, Jy, Jz), double exchange interaction (B), zero-field splitting parameters (D, E) and g-tensors can be computed reliably using X-ray structures. In this feature article, we have attempted to provide a holistic view of the modelling of these SH parameters of molecular magnets. The determination of J includes various class of molecules, from di- and polynuclear Mn complexes to the {3d-Gd}, {Gd-Gd} and {Gd-2p} class of complexes. The estimation of anisotropic exchange coupling includes the exchange between an isotropic metal ion and an orbitally degenerate 3d/4d/5d metal ion. The double-exchange section contains some illustrative examples of mixed valance systems, and the section on the estimation of zfs parameters covers some mononuclear transition metal complexes possessing very large axial zfs parameters. The section on the computation of g-anisotropy exclusively covers studies on mononuclear Dy(III) and Er(III) single-ion magnets. The examples depicted in this article clearly illustrate that computational tools not only aid in interpreting and rationalizing the observed magnetic properties but possess the potential to predict new generation MNMs.

Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy and Weak Anti-Ferromagnetic Coupling

The preparation of a binuclear Ni(II) complex with a pentacoordinate environment using a cryptand organic ligand and the imidazolate bridge is reported. The coordination sphere is close to trigonal bipyramidal (tbp) for one Ni(II) and to square pyramidal (spy) for the other. The use of the imidazolate bridge that undergoes π-π stacking with two benzene rings of the chelating ligand induces steric hindrance that stabilizes the pentacoordinate environment. Magnetic measurements together with theoretical studies of the spin states energy levels allow fitting the data and reveal a large Ising-type anisotropy and a weak anti-ferromagnetic exchange coupling between the metal ions. The magnitude and the nature of the magnetic anisotropy and the difference in anisotropy between the two metal ions are rationalized using wave-function-based calculations. We show that a slight distortion of the coordination sphere of Ni(II) from spy to tbp leads to an Ising-type anisotropy. Broken-symmetry density functional calculations rationalize the weak anti-ferromagnetic exchange coupling through the imidazolate bridge.

Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets

Pentagonal bipyramid Fe^II complexes have been investigated to evaluate their potential as Ising-spin building units for the preparation of heteropolynuclear complexes that are likely to behave as single-molecule magnets (SMMs). The considered monometallic complexes were prepared from the association of a divalent metal ion with pentadentate ligands that have a 2,6-diacetylpyridine bis(hydrazone) core (H₂ L^N3O2R ). Their magnetic anisotropy was established by magnetometry to reveal their zero-field splitting (ZFS) parameter D, which ranged between -4 and -13 cm^-1 and was found to be modulated by the apical ligands (ROH versus Cl). The alteration of the D value by N-bound axial CN ligands, upon association with cyanometallates, was also assessed for heptacoordinated Fe^II as well as for related Ni^II and Co^II derivatives. In all cases, N-coordinated cyanide ligands led to large magnetic anisotropy (i.e., -8 to -18 cm^-1 for Fe and Ni, +33 cm^-1 for Co). Ab initio calculations were performed on three Fe^II complexes, which enabled one to rationalize the role of the ligand on the nature and magnitude of the magnetic anisotropy. Starting from the pre-existing heptacoordinated complexes, a series of pentanuclear compounds were obtained by reactions with paramagnetic [W(CN)₈ ]^3- . Magnetic studies revealed the occurrence of ferromagnetic interactions between the spin carriers in all the heterometallic systems. Field-induced slow magnetic relaxation was observed for mononuclear Fe^II complexes (U_eff /k_B up to 53 K (37 cm^-1 ), τ₀ =5×10^-9  s), and SMM behavior was evidenced for a heteronuclear [Fe₃ W₂ ] derivative (U_eff /k_B =35 K and τ₀ =4.6 10^-10  s), which confirmed that the parent complexes were robust Ising-type building units. High-field EPR spectroscopic investigation of the ZFS parameters for a Ni derivative is also reported.

Magnetic properties of a Kramers doublet. An univocal bridge between experimental results and theoretical predictions

The magnetic response of a Kramers doublet is analyzed in a general case taking into account only the formal properties derived from time reversal operation. It leads to a definition of a matrix G (gyromagnetic matrix) whose expression depends on the chosen reference frame and on the Kramers conjugate basis used to describe the physical system. It is shown that there exists a reference frame and a suitable Kramers conjugate basis that gives a diagonal form for the G-matrix with all non-null elements having the same sign. A detailed procedure for obtaining this canonical expression of G is presented when the electronic structure of the KD is known regardless the level of the used theory. This procedure provides a univocal way to compare the theoretical predictions with the experimental results obtained from a complete set of magnetic experiments. In this way the problems arising from ambiguities in the g-tensor definition are overcome. This procedure is extended to find a spin-Hamiltonian suitable for describing the magnetic behavior of a pair of weakly coupled Kramers systems in the multispin scheme when the interaction between the two moieties as well as the individual Zeeman interaction are small enough as compared with ligand field splitting. Explicit relations between the physical interaction and the parameters of such a spin-Hamiltonian are also obtained.

Slow magnetic relaxation in a lanthanide helix chain compound [Dy(HNA)(NA)2(NO3)]n (HNA = nicotinic acid)

A racemic helix chain Dy³⁺ compound 1 bridged by μ_1,3-COO groups was synthesized, which showed slow magnetic relaxation behaviour.