Magneto-structural maps and bridged-ligand effect for dichloro-bridged dinuclear copper(ii) complexes: a theoretical perspective

Theoretical understanding of magneto-structural correlations in dichloro-bridged dicopper(ii) complexes can guide the design of magnetic materials having broad-scale applications. However, previous reports suggest these correlations are complicated and unclear. To clarify possible correlations, magnetic coupling constants (J _calc) of variants of a representative {Cu-(μ-Cl)₂-Cu} complex A were calculated through BS-DFT. The variation of the Cu-(μ-Cl)-Cu angle (α), Cu⋯Cu distance (R ₀), and Cu-Cl-Cu-Cl dihedral angle (τ) followed by structural optimization and calculation of the magnetic coupling constant (J _calc) revealed several trends. J _calc increased linearly with R ₀ and τ, and initially increased and then decreased with α. Further, bridging ligand effects on J _calc for dicopper(ii) complexes were evaluated through BS-DFT; the results revealed that J _calc increased with increasing ligand field strength (I^- < Br^- < Cl^- < N₃ ^- < F^-). Furthermore, a linear relationship was found between the spin density of the bridging ligand and J _calc.

Heterometallic Hexanuclear [Cu2 Ln4 ] Complexes Showing Zero-field SMM Behaviour and Magnetocaloric Effect

Three heterometallic hexanuclear 3d-4f complexes bearing the formula [Cu₂ (L)₂ Ln₄ (L)₄ (o-van)₂ ] [L=2-((E)-((2-hydroxyphenyl)imino]methyl)phenol; o-van=ortho-vanillin] (Ln^III =Gd^III (1), Dy^III (2), and Tb^III (3)) have been synthesized and characterized. DC magnetic susceptibility measurements reveal overall antiferromagnetic interactions in 1 and 3, whereas co-existence of ferro- as well as antiferromagnetic interactions were observed in 2. The magnetocaloric effect has been observed for 1 with an entropy change (-ΔS_m ) of 22.3 J kg^-1  K^-1 at 3 K and 7 T. Zero-field single molecule magnet (SMM) behaviour has been observed for 2, where Raman relaxation and quantum tunneling of magnetization (QTM) played a role in magnetization relaxation. The Cu-O-Ln angle well explains the magnetic exchange coupling occurring in the complexes. BS-DFT calculation for the complexes provides an estimate of the exchange interactions between the paramagnetic centres. Ab initio calculations performed for complex 2 established a good correlation to the experimental relaxation dynamics.

Exchange-Driven Slow Relaxation of Magnetization in NiII2LnIII2 (LnIII = Y, Gd, Tb and Dy) Butterfly complexes: Experimental and Theoretical Studies

The tetranuclear NiII2LnIII2 complexes, [{L′2{Ni(MeOH)(μ-OAc)}2(μ3-MeO)2Ln2}; LnIII = YIII (1), GdIII (2), TbIII (3), DyIII (4)] were prepared using a Schiff base ligand, H3L [H3L = 3-((2-hydroxy-3-methoxybenzylidene)amino)-2-(2-hydroxy-3-methoxyphenyl)-2,3-dihydroquinazolin-4(1H)-one, whereas {L′}3- is the...

Are lanthanide-transition metal direct bonds a route to achieving new generation {3d-4f} SMMs?

Lanthanide based single-molecule magnets are gaining wide attention due to their potential applications in emerging technologies. One of the main challenges in this area is quenching quantum tunnelling of magnetisation (QTM), which often undercuts the magnetisation reversal barrier. Among the several strategies employed, enhancing exchange coupling has been studied in detail, with large exchanges resulting in stronger quenching of QTM effects. Lanthanides, however, suffer from weak exchanges offered by the deeply buried 4f orbitals and the numerous attempts to enhance the exchange coupling in the {3d-4f} pairs have not exceeded values larger than 30 cm^-1. In this work, using a combination of DFT and the ab initio CASSCF/RASSI-SO method, we have explored lanthanide-transition metal direct bonds as a tool to quench QTM effects. In this direction, we have modelled [PyCp₂LnMCp(CO)₂] (Ln = Gd(III), Dy(III), and Er(III) and M = V(0), Mn(0), Co(0) and Fe(I) and here PyCp₂ = [2,6-(CH₂C₅H₃)₂C₅H₃N]₂^- using [PyCp₂DyFeCp(CO)₂] as an example as reported by Nippe et al. (C. P. Burns, X. Yang, J. D. Wofford, N. S. Bhuvanesh, M. B. Hall and M. Nippe, Angew. Chem., Int. Ed. 2018, 57, 8144). Bonding analysis reveals a dative Ln-TM bond with a donation of π(V/Mnd_xy-π*CO) to 5d_z² (Gd) in the case of Gd-V and Gd-Mn and 4s(Co) to 5d_xy/5d_yz (Gd) for Gd-Co with the transition metal ion being found in the low-spin S = ½ configurations in all the cases. B3LYP/TZV (Gd;CSDZ) calculations on [PyCp₂GdMCp(CO)₂] yield J_Gd-V = -46.1 cm^-1, J_Gd-Mn = -57.1 cm^-1, J_Gd-Co = +55.3 cm^-1, J_Gd-Fe⁺ = +13.9 cm^-1, J_Gd-Vhs = -162.1 cm^-1 and J_Gd-Mnhs = -343.9 cm^-1 and unveiling record-high J values for {3d-4f} complexes. The mechanism of magnetic coupling is developed, which discloses the dominating presence of strong 3d-4f orbital overlaps in most of the cases studied, leading to antiferromagnetic exchange. When these overlaps are weaker and 3d to Gd(5d_z²), charge transfer dominates, yielding a ferromagnetic coupling for the Gd-Co/Gd-Fe⁺ complexes. Calculations performed on the anisotropic Dy(III) and Er(III) complexes reveal that the ground state g_zz axis lies along the Cp-Ln-Cp axis and the Ln-TM bonds, respectively. Thus the Ln-TM bond hinders the single-ion anisotropy of Dy(III) by offering equatorial ligation and lowering the m_J = ±½ state energy, and at the same time, helping in enhancing the axiality of Er(III). When strong {3d-4f} exchange couplings are introduced, record-high barrier heights as high as 229 cm^-1 were accomplished. Furthermore, the exchange coupling annihilates the QTM effects and suggests the lanthanide-transition metal direct bond as a viable alternative to enhance exchange coupling to bring {3d-4f} complexes back in the race for high-blocking SMMs.

3d-4f magnetic exchange interactions and anisotropy in a series of heterobimetallic vanadium(IV)-lanthanide(III) Schiff base complexes

A series of heterobimetallic Ln^III-V^IV compounds [Ln(VO)L(NO₃)₃(H₂O)] (Ln = Gd(1), Tb(2), Dy(3), and Er(4)) assembled by a Schiff base ligand (H₂L = N,N'-bis(1-hydroxy-2-benzylidene-6-methoxy)-1,7-diamino-4-azaheptane) were prepared and studied with experimental and theoretical methods. The single-crystal X-ray analysis revealed the change of the coordination number from 10 found in 1-3 to 9 confirmed in 4. The DC magnetic data were fit with several Hamiltonians to extract the exchange and anisotropy parameters of complexes 1-4. This investigation of magnetic properties was carried out using both DFT and CASSCF theoretical calculations. It was found out that exchange interactions in 1, 3 and 4 are antiferromagnetic, while 2 has ferromagnetic exchange interactions. Moreover, the AC susceptibility measurements revealed the field-induced slow relaxation of magnetization in complexes 2 and 3 which is complicated by the presence of three relaxation channels. Nevertheless, these compounds belong to the first Tb^III-V^IV and Dy^III-V^IV single-molecule magnets in this class of compounds.

Probing the strong magnetic exchange behaviour of transition metal–radical complexes: a DFT case study

Alteration of the structural parameters of metal–radical complexes may pave the way forward for fine tuning the magnetic exchange coupling value as high as >−500 cm⁻¹ – a much sought-after parameter in the area of SMMs.

Syntheses, Structures, and Magnetic Properties of a Series of Heterotri-, Tetra- and Pentanuclear LnIII⁻CoII Compounds

Three types of Ln(III)⁻Co(II) heterometallic compounds, LnCo₂(L1)₇(bipy)₂ (Ln = Pr-1, Eu-2, Sm-3, Gd-4, Tb-5, Dy-6) (L1 = 4-chlorobenzoate, bipy = 2,2'-bipyridine), Ln₂Co₂(L₂)10(bipy)₂ (Ln = Sm-7, Gd-8, Tb-9, Dy-10, Ho-11, Er-12, Yb-13), (L2 = 2,4-dichlorobenzoate, bipy = 2,2'-bipyridine, phen = 1,10-phenanthroline), and Ln₂Co₃(L1)12(bipy)₂ (Ln = Ho-14, Er-15, Yb-16), were synthesized under hydrothermal conditions and characterized by single crystal X-ray diffraction, IR spectroscopy and magnetic measurements. Structural analyses revealed that 14⁻16 take on a unique linear pentanuclear structural motif. Interestingly, the Ho-containing compound 14 exhibits magnetic relaxation behavior.

Contribution of 155Gd Mössbauer data to the study of the magnetic interaction in heterodinuclear 3d–Gd (3d = Cu, Ni) coordination complexes

The observed ¹⁵⁵Gd Mössbauer isomer shifts of 3d–Gd complexes give an experimental proof for the participation of 5d Gd orbitals to the magnetic interaction in these 3d–Gd complexes.

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.

Quenching the Quantum Tunneling of Magnetization in Heterometallic Octanuclear {TMIII4 DyIII4 } (TM=Co and Cr) Single-Molecule Magnets by Modification of the Bridging Ligands and Enhancing the Magnetic Exchange Coupling

We report the synthesis, structural characterisation, magnetic properties and provide an ab initio analysis of the magnetic behaviour of two new heterometallic octanuclear coordination complexes containing Co^III and Dy^III ions. Single-crystal X-ray diffraction studies revealed molecular formulae of [Co^III₄ Dy^III₄ (μ-OH)₄ (μ₃ -OMe)₄ {O₂ CC(CH₃ )₃ }₄ (tea)₄ (H₂ O)₄ ]⋅4 H₂ O (1) and [Co^III₄ Dy^III₄ (μ-F)₄ (μ₃ -OH)₄ (o-tol)₈ (mdea)₄ ]⋅ 3 H₂ O⋅EtOH⋅MeOH (2; tea^3- =triply deprotonated triethanolamine; mdea^2- =doubly deprotonated N-methyldiethanolamine; o-tol=o-toluate), and both complexes display an identical metallic core topology. Furthermore, the theoretical, magnetic and SMM properties of the isostructural complex, [Cr^III₄ Dy^III₄ (μ-F₄ )(μ₃ -OMe)_1.25 (μ₃ -OH)_2.75 (O₂ CPh)₈ (mdea)₄ ] (3), are discussed and compared with a structurally similar complex, [Cr^III₄ Dy^III₄ (μ₃ -OH)₄ (μ-N₃ )₄ (mdea)₄ (O₂ CC(CH₃ )₃ )₄ ] (4). DC and AC magnetic susceptibility data revealed single-molecule magnet (SMM) behaviour for 1-4. Each complex displays dynamic behaviour, highlighting the effect of ligand and transition metal ion replacement on SMM properties. Complexes 2, 3 and 4 exhibited slow magnetic relaxation with barrier heights (U_eff ) of 39.0, 55.0 and 10.4 cm^-1 respectively. Complex 1, conversely, did not exhibit slow relaxation of magnetisation above 2 K. To probe the variance in the observed U_eff  values, calculations by using CASSCF, RASSI-SO and POLY_ANISO routine were performed on these complexes to estimate the nature of the magnetic coupling and elucidate the mechanism of magnetic relaxation. Calculations gave values of J_Dy-Dy as -1.6, 1.6 and 2.8 cm^-1 for complexes 1, 2 and 3, respectively, whereas the J_Dy-Cr interaction was estimated to be -1.8 cm^-1 for complex 3. The developed mechanism for magnetic relaxation revealed that replacement of the hydroxide ion by fluoride quenched the quantum tunnelling of magnetisation (QTM) significantly, and led to improved SMM properties for complex 2 compared with 1. However, the tunnelling of magnetisation at low-lying excited states was still operational for 2, which led to low-temperature QTM relaxation. Replacement of the diamagnetic Co^III ions with paramagnetic Cr^III led to Cr^III ⋅⋅⋅Dy^III coupling, which resulted in quenching of QTM at low temperatures for complexes 3 and 4. The best example was found if both Cr^III and fluoride were present, as seen for complex 3, for which both factors additively quenched QTM and led to the observation of highly coercive magnetic hysteresis loops above 2 K. Herein, we propose a synthetic strategy to quench the QTM effects in lanthanide-based SMMs. Our strategy differs from existing methods, in which parameters such as magnetic coupling are difficult to control, and it is likely to have implications beyond the Dy^III SMMs studied herein.

Key role of higher order symmetry and electrostatic ligand field design in the magnetic relaxation of low-coordinate Er(iii) complexes

Our theoretical analysis highlights that both symmetry and a suitable ligand field is required to obtain large barrier heights in SIMs. Key role of Lanthanide–halogen covalency in enhancing U_eff is discussed.

Defects-assisted ferromagnetism due to bound magnetic polarons in Ce into Fe, Co:ZnO nanoparticles and first-principle calculations

In the DMS systems of Zn_0.94Fe_0.03Ce_0.03O and Zn_0.94Co_0.03Ce_0.03O, the Ce ions attribute lattice defects as well as enhance antiferromagnetic interactions, which have potential in novel spintronic applications.

The ionothermal synthesis, structure, and magnetism-structure relationship of two biphenyl tetracarboxylic acid-based metal-organic frameworks

Two new metal-organic frameworks (1-2) were ionothermally obtained by the reaction of a biphenyltetracarboxylic sodium (Na4BPTC) ligand and M(OOCCH3)2 (M = Co(1) and Mn(2)). Crystal structure analysis reveals that 1 is a Co3Na6 unit-based three dimensional heterometallic MOF, while 2 exhibits a {Mn(COO)n} chain-based three-dimensional framework. Furthermore, the magnetic measurement shows that both of them have anti-ferromagnetic properties. A combination of Density Functional Theory (DFT) and Quantum Monte Carlo (QMC) simulation uncovers that in 2 the coupling parameters between two adjacent Mn(II) ions are J1 = -2.0 cm(-1) and J2 = -1.6 cm(-1), and the magnetism mainly originates from the propagation of Mn(II) ions by the super-exchange of carboxylates. Interestingly, the superexchange modes of J1 and J2 are different. Two spin nets of -/+/- dominate in the coupling for J1, while for J2 there are two spin nets of -/+/- and one spin net of +/-/+.

Record high magnetic exchange and magnetization blockade in Ln2@C79N (Ln = Gd(iii) and Dy(iii)) molecules: a theoretical perspective

Ln₂@C₇₉N EMFs are found to attain the largest magnetic coupling reported to date between Ln-radical paramagnetic centres. The obtained U_cal values are very large, and strong exchange likely to quench the QTM effects offers a great chance to obtain high blocking temperatures.

Hydroxo-bridged dimers of oxo-centered ruthenium(III) triangle: synthesis and spectroscopic and theoretical investigations

The homometallic hexameric ruthenium cluster of the formula [Ru(III)6(μ3-O)2(μ-OH)2((CH3)3CCO2)12(py)2] (1) (py = pyridine) is solved by single-crystal X-ray diffraction. Magnetic susceptibility measurements performed on 1 suggest that the antiferromagnetic interaction between the Ru(III) centers is dominant, and this is supported by theoretical studies. Theoretical calculations based on density functional methods yield eight different exchange interaction values for 1: J1 = -737.6, J2 = +63.4, J3 = -187.6, J4 = +124.4, J5 = -376.4, J6 = -601.2, J7 = -657.0, and J8 = -800.6 cm(-1). Among all the computed J values, six are found to be antiferromagnetic. Four exchange values (J1, J6, J7 and J8) are computed to be extremely strong, with J8, mediated through one μ-hydroxo and a carboxylate bridge, being by far the largest exchange obtained for any transition-metal cluster. The origin of these strong interactions is the orientation of the magnetic orbitals in the Ru(III) centers, and the computed J values are rationalized by using molecular orbital and natural bond order analysis. Detailed NMR studies ((1)H, (13)C, HSQC, NOESY, and TOCSY) of 1 (in CDCl3) confirm the existence of the solid-state structure in solution. The observation of sharp NMR peaks and spin-lattice time relaxation (T1 relaxation) experiments support the existence of strong intramolecular antiferromagnetic exchange interactions between the metal centers. A broad absorption peak around 600-1000 nm in the visible to near-IR region is a characteristic signature of an intracluster charge-transfer transition. Cyclic voltammetry experiments show that there are three reversible one-electron redox couples at -0.865, +0.186, and +1.159 V with respect to the Ag/AgCl reference electrode, which corresponds to two metal-based one-electron oxidations and one reduction process.

Can anisotropic exchange be reliably calculated using density functional methods? A case study on trinuclear Mn(III)-M(III)-Mn(III) (M=Fe, Ru, and Os) cyanometalate single-molecule magnets

Density functional studies have been performed on a set of trinuclear single-molecule magnets (SMMs) of general formula [{Mn2(5-Br salen)2(MeOH)2}M(CN)6](NEt4) (M=Fe(III) (1), Ru(III) (2) and Os(III) (3); 5-Brsalen=N,N'-ethylenebis(5-bromosalicylidene)iminato anion). We have computed the orbital-dependent exchange interaction for all three complexes for the first time using DFT and complete active space self-consistent field (CASSCF) methods. DFT calculations yield the anisotropic exchange as J(ξξ)=3.5 cm(-1) for 1; J(ξξ)=12.1 cm(-1), J(ζζ)=-6.9 cm(-1) and J(ηη)=-14 cm(-1) for 2; and J(ξξ)=23.7 cm(-1) and J(ζζ) =-11.1 cm(-1) for 3. The computed values are in agreement with the experimental report, and this suggests that the established methodology can be used to compute the anisotropic exchange in larger clusters. Our calculations reiterate the fact that the exchange is described by a three-axis anisotropic exchange for complexes 2 and 3 as evidenced by the experiments. A stronger exchange coupling as we move down the periodic table from 3d to 5d is reproduced by our calculations, and the origin of this enhancement in the exchange interaction has been probed by using molecular orbital analysis. The electronic origin of different types of exchange observed in this series is found to be related to the energy difference between possible degenerate pairs and the nature of orbital interactions. By computing the exchange interaction, the single-ion anisotropy of Mn(III) and zero-field splitting of the S=9/2 ground state of complexes 1-3 using CASSCF and/or DFT methods, we have attempted to shed light on the issue of anisotropic exchange and the barrier height for the magnetisation reversal in SMMs. Comprehensive magneto-structural correlations have been developed to offer clues on how to further enhance the barrier height in this class of SMMs.