Physical origin of the anisotropic exchange tensor close to the first-order spin-orbit coupling regime and impact of the electric field on its magnitude

This article follows earlier studies on the physical origin of magnetic anisotropy and the means of controlling it in polynuclear transition metal complexes. The difficulties encountered when focusing a magnetic field on a molecular object have led to consider the electric field as a more appropriate control tool. It is therefore fundamental to understand what governs the sensitivity of magnetic properties to the application of an electric field. We have already studied the impact of the electric field on the isotropic exchange coupling and on the Dzyaloshinskii-Moriya interaction (DMI). Here, we focus on the symmetric exchange anisotropy tensor. In order to obtain significant values of anisotropic interactions, we have carried out this study on a model complex that exhibits first-order spin-orbit coupling. We will show that (i) large values of the axial parameter of symmetric exchange can be reached when close to the first-order spin-orbit coupling regime, (ii) both correlated energies and wave functions must be used to achieve accurate values of the symmetric tensor components when the DMI is non-zero, and (iii) finally, an interferential effect between the DMI and the axial parameter of symmetric exchange occurs for a certain orientation of the electric field, i.e., the latter decreases in magnitude as the former increases. While DMI is often invoked as being involved in magneto-electric coupling, isotropic exchange and the symmetrical anisotropic tensor also contribute. Finally, we provide a recipe for generating significant anisotropic interactions and a significant change in magnetic properties under an electric field.

Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory. The energies of these configurations are interpreted in terms of the Heisenberg model, H̃=∑i Collapse

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Shadan Ghassemi Tabrizi Department of Chemistry, University of Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam-Golm, Germany

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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.

Antisymmetric Exchange in a Real Copper Triangular Complex

The antisymmetric exchange, also known as the Dzyaloshinskii-Moriya interaction (DMI), is an effective interaction that may be at play in isolated complexes (with transition metals or lanthanides, for instance), nanoparticles, and highly correlated materials with adequate symmetry properties. While many theoretical works have been devoted to the analysis of single-ion zero-field splitting and to a lesser extent to symmetric exchange, only a few ab initio studies deal with the DMI. Actually, it originates from a subtle interplay between weak electronic interactions and spin-orbit couplings. This article aims to highlight the origin of this interaction from theoretical grounds in a real tri-copper(II) complex, capitalizing on previous methodological studies on bi-copper(II) model complexes. By tackling this three-magnetic-center system, we will first show that the multispin model Hamiltonian is appropriate for trinuclear (and likely for higher nuclearity) complexes, then that the correct application of the permutation relationship is necessary to explain the outcomes of the ab initio calculations, and finally, that the model parameters extracted from a binuclear model transfer well to the trinuclear complex. For a more theory-oriented purpose, we will show that the use of a simplified structural model allows one to perform more demanding electronic structure calculations. On this simpler system, we will first check that the previous transferability is still valid, prior to performing more advanced calculations on the derived two-magnetic-center model system. To this end, we will explain in detail the physics of the DMI in the copper triangle of interest, before advocating further theory/experiment efforts.

Combining Open-Shell Verdazyl Environment and Co(II) Spin-Crossover: Spinmerism in Cobalt Oxoverdazyl Compound

The spin states of a Co(II) oxoverdazyl compound are investigated by means of wavefunction-based calculations. Within a ca. 233 K energy window, the ground state and excited states display a structure-sensitive admixture of low-spin SM = 1/2 in a dominant high-spin SM = 3/2 Co(II) ion as read from localized molecular orbitals. This puzzling spins zoology that results from the coupling between open-shell radical ligands and a spin-crossover metal ion gives rise to this unusual scenario which extends the views in molecular magnetism. In agreement with experimental observation, the low-energy spectroscopy is very sensitive to deformations of the coordination sphere, and a growing admixture of Co(II) low-spin is evidenced from the calculations. In analogy with mesomerism that accounts for charge delocalization, entanglement combines different local spin states to generate a given total spin multiplicity, a spinmerism phenomenon.

The interpretation and prediction of lanthanide single-ion magnet from ab initio electronic structure calculation: The capability and limit

Single-molecule magnet (SMM) is a fascinating system holding the potential of being revolutionary micro-electronic device in information technology. However current SMMs are still far away from real-life application due to...

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.

Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes

Polynuclear transition-metal (PNTM) clusters owe their catalytic activity to numerous energetically low-lying spin states and stable oxidation states. The characterization of their electronic structure represents one of the greatest challenges of modern chemistry. We propose a theoretical framework that enables the resolution of targeted electronic states with ease and apply it to two [Fe(III)₄S₄] cubanes. Through direct access to their many-body wave functions, we identify important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters, which are core properties in understanding their catalytic activity. The simulated magnetic coupling constants predicted by our strategy allow us to make qualitative connections between spin interactions and geometrical distortions, demonstrating its predictive power. Moreover, despite its simplicity, the strategy provides magnetic coupling constants in good agreement with the available experimental ones. The complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures together with the geometrical distortions represent two possible ways to release spin frustration (spin-driven Jahn–Teller distortion). Our paradigm provides a simple, yet rigorous, route to uncover the electronic structure of PNTM clusters and may be applied to a wide variety of such clusters.

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.

A new series of 3D lanthanide phenoxycarboxylates: synthesis, crystal structure, magnetism and photoluminescence studies

A new series of 3D Ln-carboxylates was synthesized, where the Tb one shows antiferromagnetic coupling and the Dy one shows ferromagnetic interaction, and with emission spectra combining the intra-4f emission of the Ln ions and that of the ligand.

A Design Criteria to Achieve Giant Ising-Type Anisotropy in CoII -Encapsulated Metallofullerenes

Discovery of permanent magnetisation in molecules just like in hard magnets decades ago led to the proposal of utilising these molecules for information storage devices and also as Q-bits in quantum computing. A significant breakthrough with a blocking temperature as high as 80 K has been recently reported for lanthanocene complexes. While enhancing the blocking temperature further remains one of the primary challenges, obtaining molecules that are suitable for the fabrication of the devices sets the bar very high in this area. Encouraged by the fact that our earlier predictions of potential single-molecule magnets (SMMs) in lanthanide-containing endohedral fullerenes have been verified, here we set out to undertake a comprehensive study on Co^II -ion-encapsulated fullerene as potential SMMs. To study this class of molecules, we have utilised an array of theoretical methods ranging from density functional to ab initio CASSCF/NEVPT2 methods for obtaining reliable estimate of zero-field splitting parameters D and E. Additionally, we have also employed, for the first time a combination of molecular dynamics based on DFT methods coupled with CASSCF/NEVPT2 methods to seek the role of conformational isomers in the relaxation of magnetisation. Particularly, we have studied, Co@C₂₈ , Co@C₃₈ and Co@C₄₈ cages and their isomers as potential target molecules that could yield substantial magnetic anisotropy. Our calculations categorically reveal a very large Ising anisotropy in this class of molecules, with Co@C₄₈ cages predicted to yield D values as high as -127 cm^-1 . Our calculations on the smaller cages reveal the free movement of Co^II ion inside the cage, leading to the likely scenario of faster relaxation of magnetisation. However, larger fullerene cages were found to solve this issue. Further models with incorporating units such as {CoOZn}, {CoScZnN} inside larger fullerenes yield axial zero-field splitting values as high as -200 cm^-1 with negligible E/D values. As these units represent a strong axiality coupled with a viable way to obtain air-stable low-coordinate Co^II complexes, this opens up a new paradigm in the search of SMMs in this class of molecules.

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.

Effect of Second-Order Spin-Orbit Coupling on the Interaction between Spin States in Spin-Crossover Systems

The second-order spin-orbit coupling is evaluated in two transition-metal complexes to establish the effect on the deactivation mechanism of the excited low-spin state in systems that undergo spin transitions under the influence of light. We compare the standard perturbational approach to calculate the second-order interaction with a variational strategy based on the effective Hamiltonian theory and show that the former one can only be applied in some special cases and even then gives results that largely overestimate the interaction. The combined effect of geometry distortions and second-order spin-orbit coupling leads to sizeable interactions for states that are nearly uncoupled in the symmetric (average) structure of the complex. This opens the possibility of a direct deactivation from the singlet and triplet states of the metal-to-ligand charge-transfer manifold to the final high-spin state as suggested from the interpretation of experimental data but so far not supported by theoretical descriptions of the light-induced spin crossover.

Ab initio modelling of magnetic anisotropy in Sr3NiPtO6

First principles calculations in the framework of Density Functional Theory (DFT) and wavefunction-based correlated methods have been performed to investigate in detail the magnetic anisotropy in Sr3NiPtO6. This material is known for the easy-plane anisotropy with a large anisotropy constant of about 7.5-9.3 meV. We find that by properly choosing the onsite Coulomb repulsion and exchange parameters, DFT can correctly explain the easy-plane magnetocrystalline anisotropy of the material, but the magnitude of the anisotropy constant is underestimated. On the other hand, a quantitative agreement with respect to experiments, both in the magnitude and direction of the magnetic anisotropy, can be recovered by using the wavefunction-based approach which is able to fully describe the multiplet physics. We also show that the presence of structural distortions of the local NiO6 coordination is crucial for stabilizing the magnetic anisotropy in this compound.

Origin of the Zero-Field Splitting in Mononuclear Octahedral Mn(IV) Complexes: A Combined Experimental and Theoretical Investigation

The aim of this work was to determine and understand the origin of the electronic properties of Mn(IV) complexes, especially the zero-field splitting (ZFS), through a combined experimental and theoretical investigation on five well-characterized mononuclear octahedral Mn(IV) compounds, with various coordination spheres (N6, N3O3, N2O4 in both trans (trans-N2O4) and cis configurations (cis-N2O4) and O4S2). High-frequency and -field EPR (HFEPR) spectroscopy has been applied to determine the ZFS parameters of two of these compounds, MnL(trans-N2O4) and MnL(O4S2). While at X-band EPR, the axial-component of the ZFS tensor, D, was estimated to be +0.47 cm(-1) for MnL(O4S2), and a D-value of +2.289(5) cm(-1) was determined by HFEPR, which is the largest D-magnitude ever measured for a Mn(IV) complex. A moderate D value of -0.997(6) cm(-1) has been found for MnL(trans-N2O4). Quantum chemical calculations based on two theoretical frameworks (the Density Functional Theory based on a coupled perturbed approach (CP-DFT) and the hybrid Ligand-Field DFT (LF-DFT)) have been performed to define appropriate methodologies to calculate the ZFS tensor for Mn(IV) centers, to predict the orientation of the magnetic axes with respect to the molecular ones, and to define and quantify the physical origin of the different contributions to the ZFS. Except in the case of MnL(trans-N2O4), the experimental and calculated D values are in good agreement, and the sign of D is well predicted, LF-DFT being more satisfactory than CP-DFT. The calculations performed on MnL(cis-N2O4) are consistent with the orientation of the principal anisotropic axis determined by single-crystal EPR, validating the calculated ZFS tensor orientation. The different contributions to D were analyzed demonstrating that the d-d transitions mainly govern D in Mn(IV) ion. However, a deep analysis evidences that many factors enter into the game, explaining why no obvious magnetostructural correlations can be drawn in this series of Mn(IV) complexes.

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.

Inducing magnetic communication in caged dinuclear Co(ii) systems

Magnetic interactions were probed for a series of mono and tri atomic bridged dinuclear Co(ii) azacryptand complexes. Magneto-structural correlations were established usingab initiocalculations.

Magnetic anisotropy of mononuclear Ni(II) complexes: on the importance of structural diversity and the structural distortions

Mononuclear Ni(II) complexes are particularly attractive in the area of single-molecule magnets as the axial zero-field splitting (D) for the Ni(II) complexes is in the range of -200 to +200 cm(-1) . Despite this advantage, very little is known on the origin of anisotropy across various coordination ligands, coordination numbers, and particularly what factors influence the D parameter in these complexes. To answer some of these questions, herein we have undertaken a detailed study of a series of mononuclear Ni(II) complexes with ab initio calculations. Our results demonstrate that three prominent spin-conserved low-lying d-d transitions contribute significantly to the D value. Variation in the sign and the magnitude of D values are found to correlate to the specific structural distortions. Apart from the metal-ligand bond lengths, two different parameters, namely, Δα and Δβ, which are correlated to the cis angles present in the coordination environment, are found to significantly influence the axial D values. Developed magneto-structural D correlations suggest that the D values can be enhanced significantly by fine tuning the structural distortion in the coordination environment. Calculations performed on a series of Ni(II) models with coordination numbers two to six unfold an interesting observation-the D parameter increases significantly upon a reduction in coordination number compared with a reference octahedral coordination. Besides, if high symmetry is maintained, even larger coordination numbers yield large D values.