Modelling spin Hamiltonian parameters of molecular nanomagnets

Auxiliary Rather Than Dominant. The Role of Direct Dy-S Coordination in Single-Molecule Magnet Unveiled via ab initio Study

The role of Dy-S coordination in a single-molecule magnet (SMM) is investigated via an ab initio study in a group of mononuclear structures. The SMM performance of this group is well interpreted via a concise criterion consisting of long quantum tunneling of magnetization (QTM) time τQTM and high effective barrier for magnetic reversal Ueff. The best SMMs in the selected group, i.e., 1Dy (CCDC refcode: PUKFAF) and 2Dy (CCDC refcode: NIKSEJ), are just those holding the longest τQTM and the highest Ueff simultaneously. Further analysis based on the crystal field model and ab initio magneto-structural exploration indicates that the influence of Dy-S coordination on the SMM performance of 1Dy is weaker than that of axial Dy-O coordination. Thus, Dy-S coordination is more likely to play an auxiliary role rather than a dominant one. However, if placed at the suitable equatorial position, Dy-S coordination could provide important support for good SMM performance. Consequently, starting from 1Dy, we built two new structures where Dy-S coordination only exists at the equatorial position and two axial positions are occupied by strong Dy-O/Dy-F coordination. Compared to 1Dy and 2Dy, these new ones are predicted to have significantly longer τQTM and higher Ueff, as well as a nearly doubled blocking temperature TB. Thus, they are probable candidates of SMM having clearly improved performance.

Insight into ferromagnetic interactions in CuII-LnIII dimers with a compartmental ligand

In the last two decades, efforts have been devoted to obtaining insight into the magnetic interactions between CuII and LnIII utilizing experimental and theoretical means. Experimentally, it has been observed that the exchange coupling (J) in CuII-LnIII systems is often found to be ferromagnetic for ≥4f7 metal ions. However, exchange interactions at sub-Kelvin temperatures between CuII and the anisotropic/isotropic LnIII ions are not often explored. In this report, we have synthesized a series of heterobimetallic [CuLn(HL)(μ-piv)(piv)2] complexes (LnIII = Gd (1), Tb (2), Dy (3) and Er (4)) from a new compartmental Schiff base ligand, N,N'-bis(3-methoxy-5-methylsalicylidene)-1,3-diamino-2-propanol (H3L). X-ray crystallographic analysis reveals that all four complexes are isostructural and isomorphous. Magnetic susceptibility measurements reveal a ferromagnetic coupling between the CuII ion and its respective LnIII ion for all the complexes, as often observed. Moreover, μ-SQUID studies, at sub-Kelvin temperatures, show S-shaped hysteresis loops indicating the presence of antiferromagnetic coupling in complexes 1-3. The antiferromagnetic interaction is explained by considering the shortest Cu⋯Cu distance in the crystal structure. The nearly closed loops for 1-3 highlight their fast relaxation characteristics, while the opened loops for 4 might arise from intermolecular ordering. CASSCF calculations allow the quantitative assessment of the interactions, which are further supported by BS-DFT calculations.

Ab initio prediction of key parameters and magneto-structural correlation of tetracoordinated lanthanide single-ion magnets

Single-molecule magnets (SMMs) have great potential in becoming revolutionary materials for micro-electronic devices. As one type of SMM and holding the performance record, lanthanide single-ion magnets (Ln-SIMs) stand at the forefront of the family. Lowering the coordination number (CN) is an important strategy to improve the performance of Ln-SIMs. Here, we report a theoretical study on a typical group of low-CN Ln-SIMs, i.e., tetracoordinated structures. Our results are consistent with those of experiments and they identify the same three best Ln-SIMs via a concise criterion, i.e., the co-existence of long τ_QTM and high U_eff. Compared to the record-holding dysprosocenium systems, the best SIMs here possess τ_QTM values that are shorter by several orders of magnitude and U_eff values that are lower by ∼1000 Kelvin (K). These are important reasons for the fact that the tetracoordinated Ln-SIMs are clearly inferior to dysprosocenium. A simple but intuitive crystal-field analysis leads to several routes to improve the performance of a given Ln-SIM, including compression of the axial bond length, widening the axial bond angle, elongation of the equatorial bond length and usage of weaker equatorial donor ligands. Although these routes are not brand-new, the most efficient option and the degree of improvement resulting from it are not known in advance. Consequently, a theoretical magneto-structural study, covering various routes, is carried out for the best Ln-SIM here and the most efficient route is shown to be widening the axial ∠O-Dy-O angle. The most optimistic case, having a ∠O-Dy-O of 180°, could have a τ_QTM (up to 10³ s) and U_eff (∼2400 K) close to those of the record-holders. Subsequently, a blocking temperature (T_B) of 64 K is predicted to be possible for it. A more practical case, with ∠O-Dy-O being 160°, could have a τ_QTM of up to 400 s, U_eff of around 2200 K and the possibility of a T_B of 57 K. Although having an inherent precision limit, these predictions provide a guide to performance improvement, starting from an existing system.

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.

Tetranuclear [Cu3Ln] complexes derived from a tetraketone-type ligand

A series of tetranuclear [Cu₃Ln] complexes, [Cu₃Gd(L)₃(NO₃)₂(H₂O)₃](NO₃)·H₂O (1), [Cu₃Tb(L)₃(NO₃)₂(H₂O)₃](NO₃) (2) and [Cu₃Dy(L)₃(NO₃)₃(H₂O)₂]·1.5(H₂O) (3), were synthesized by a one-pot reaction using a simple tetraketone-type ligand (H₂L = (3Z,5Z)-4,5-dihydroxy-3,5-octadiene-2,7-dione). X-ray structural analyses revealed that each complex has a planar tetranuclear core of [Cu₃Ln] (Ln = Gd, Tb, and Dy), in which the Ln ion is accommodated in the centre of a Cu₃O₆ metallocycle. A cryomagnetic study revealed that all complexes show intramolecular ferromagnetic interactions between Cu(II) and Ln(III) ions. The [Cu₃Gd] complex (1) has an S_T = 5 spin ground state and shows a magneto-caloric effect with a maximum magnetic entropy change (-ΔS_m) of 16.4 J kg^-1 K^-1 (5 T, 2.4 K). On the other hand, the [Cu₃Tb] complex (2) shows a slow magnetic relaxation behavior under a zero magnetic field. The analysis of an Arrhenius plot reveals that the effective energy barrier of spin reversal is 13.1 K. The [Cu₃Dy] complex (3) also shows a slow magnetic relaxation under 1300 Oe dc magnetic field with an effective energy barrier of 6.82 K.

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from -6 to -132 cm^-1 , our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm^-1 ). For the tetranuclear SMMs, the computed J constants are within 6 cm^-1 from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

Origin of the Unusual Ground-State Spin S = 9 in a Cr10 Single-Molecule Magnet

The molecular wheel [Cr₁₀(OMe)₂₀(O₂CCMe₃)₁₀], abbreviated {Cr₁₀}, with an unusual intermediate total spin S = 9 and non-negligible cluster anisotropy, D/k_B = -0.045(2) K, is a rare case among wheels based on an even number of 3d-metals, which usually present an antiferromagnetic (AF) ground state (S = 0). Herein, we unveil the origin of such a behavior. Angular magnetometry measurements performed on a single crystal confirmed the axial anisotropic behavior of {Cr₁₀}. For powder samples, the temperature dependence of the susceptibility plotted as χT(T) showed an overall ferromagnetic (FM) behavior down to 1.8 K, whereas the magnetization curve M(H) did not saturate at the expected 30 μ_B/fu for 10 FM coupled 3/2 spin Cr³⁺ ions, but to a much lower value, corresponding to S = 9. In addition, the X-ray magnetic circular dichroism (XMCD) measured at high magnetic field (170 kOe) and 7.5 K showed the polarization of the cluster moment up to 23 μ_B/fu. The magnetic results can be rationalized within a model, including the cluster anisotropy, in which the {Cr₁₀} wheel is formed by two semiwheels, each with four Cr³⁺ spins FM coupled (J_FM/k_B = 2.0 K), separated by two Cr³⁺ ions AF coupled asymmetrically (J₂₃/k_B = J₇₈/k_B = -2.0 K; J₃₄/k_B = J₈₉/k_B = -0.25 K). Inelastic neutron scattering and heat capacity allowed us to confirm this model leading to the S = 9 ground state and first excited S = 8. Single-molecule magnet behavior with an activation energy of U/k_B = 4.0(5) K in the absence of applied field was observed through ac susceptibility measurements down to 0.1 K. The intriguing magnetic behavior of {Cr₁₀} arises from the detailed asymmetry in the molecule interactions produced by small-angle distortions in the angles of the Cr-O-Cr alkoxy bridges coupling the Cr³⁺ ions, as demonstrated by ab initio and density functional theory calculations, while the cluster anisotropy can be correlated to the single-ion anisotropies calculated for each Cr³⁺ ion in the wheel.

The coexistence of long τQTM and high Ueff as a concise criterion for a good single-molecule magnet: a theoretical case study of square antiprism dysprosium single-ion magnets

A systematic theoretical study is performed on a group of 16 square antiprism dysprosium single-ion magnets. Based on ab initio calculations, the quantum tunneling of magnetization (QTM) time, i.e., τ_QTM, and effective barrier of magnetic reversal, U_eff, are theoretically predicted. The theoretical τ_QTM is able to identify the ones with the longest QTM time with small numerical deviations. Similar results occur with respect to U_eff too. The systems possessing the best single-molecule magnet (SMM) properties here are just the ones having both the longest τ_QTM and the highest U_eff, from either experiment or theory. Thus, our results suggest the coexistence of long τ_QTM and high U_eff to be a criterion for high-performance SMMs. Although having its own limits, this criterion is easy to be applied in a large number of systems since both τ_QTM and U_eff could be predicted by theory with satisfactory efficiency and reliability. Therefore, this concise criterion could provide screened candidates for high-performance SMMs quickly and, hence, ease the burden of further exploration aiming for a higher degree of precision. This screening is important since the further exploration could easily demand tens or even hundreds of ab initio calculations for a single SMM. A semi-quantitative crystal field (CF) analysis is performed and shown here to be capable of indicating the general trends in a more chemically intuitive way. This analysis could help to identify the most important coordinating atoms for both diagonal and non-diagonal CF components. Thus, it could give some direct clues for improving the SMM properties: reducing the distance of the axial atom to the central ion, rotating the axial atom closer to the easy axis or increasing the amount of its negative charge. Correspondingly, opposite operations on the equatorial atom could give the same result.

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...

Magnetocaloric effect and slow magnetic relaxation in peroxide-assisted tetranuclear lanthanide assemblies

Investigation of a series of rare peroxide-assisted tetranuclear lanthanide assemblies revealed both significant magnetocaloric effect and slow magnetic relaxation.

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...

Oxidation state variation in bis-calix[4]arene supported decametallic Mn clusters

The reaction of MnCl₂·4H₂O, H₈L (2,2'-bis-p-^tBu-calix[4]arene) and NEt₃ in a dmf/MeOH solvent mixture results in the formation of a mixed valent decametallic cluster of formula [MnII6MnIII4(L)₂(μ₃-OH)₄(μ-OH)₄(MeOH)₄(dmf)₄(MeCN)₂]·MeCN (3). Complex 3 crystallises in the monoclinic space group P2₁/n with the asymmetric unit comprising half of the compound. Structure solution reveals that the bis-calix[4]arene ligands are arranged such that one TBC[4] moiety in each has undergone inversion in order to accommodate a [MnIII4MnII6] metallic skeleton that describes three vertex-sharing [MnIII2MnII2] butterflies. The structure is closely related to the species [MnIII6MnII4(L)₂(μ₃-O)₂(μ₃-OH)₂(μ-OMe)₄(H₂O)₄(dmf)₈]·4dmf (4), the major difference being the oxidation level of the Mn ions in the core of the compound. DFT calculations on the full structures reveal that replacing the Mn^III ions in 4 for Mn^II ions in 3 results in a significant decrease in the magnitude of some antiferromagnetic exchange contributions, a switch from ferromagnetic to antiferromagnetic in others, and the loss of significant spin frustration.

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.

Molecular magnetism in the multi-configurational self-consistent field method

We develop a structured theoretical framework used in our recent articles (2019 Eur. Phys. J. B 92 93 and 2020 Phys. Rev. B 101 094427) to characterize the unusual behavior of the magnetic spectrum, magnetization and magnetic susceptibility of the molecular magnet Ni₄Mo₁₂. The theoretical background is based on the molecular orbital theory in conjunction with the multi-configurational self-consistent field method and results in a post-Hartree-Fock scheme for constructing the corresponding energy spectrum. Furthermore, we construct a bilinear spin-like Hamiltonian involving discrete coupling parameters accounting for the relevant spectroscopic magnetic excitations, magnetization and magnetic susceptibility. The explicit expressions of the eigenenergies of the ensuing Hamiltonian are determined and the physical origin of broadening and splitting of experimentally observed peaks in the magnetic spectra is discussed. To demonstrate the efficiency of our method we compute the spectral properties of a spin-one magnetic dimer. The present approach may be applied to a variety of magnetic units based on transition metals and rare Earth elements.

Magneto-structural studies of an unusual [MnIIIMnIIGdIII(OR)4]4- partial cubane from 2,2'-bis-p-tBu-calix[4]arene

Reaction of 2,2'-bis-p-tBu-calix[4]arene (H8L) with MnCl2·4H2O, GdCl3·6H2O and 2,6-pyridinedimethanol (H2pdm) affords [MnIIIMnIIGdIII(H3L)(pdmH)(pdm)(MeOH)2(dmf)]·3MeCN·dmf (3·3MeCN·dmf) upon vapour diffusion of MeCN into the basic dmf/MeOH mother liquor. 3 crystallises in the tetragonal space group P41212 with the asymmetric unit comprising the entire cluster. The highly unusual core contains a triangular arrangement of MnIIIMnIIGdIII ions housed within a [MnIIIMnIIGdIII(OR)4]4- partial cubane. Magnetic susceptibility and magnetisation data reveal best fit parameters JMn(II)-Mn(III) = +0.415 cm-1, JMn(III)-Gd(III) = +0.221 cm-1, JMn(II)-Gd(III) = -0.258 cm-1 and DMn(III) = -4.139 cm-1. Theoretically derived magnetic exchange interactions, anisotropy parameters, and magneto-structural correlations for 3 are in excellent agreement with the experimental data.

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.

Investigating Complex Magnetic Anisotropy in a Co(II) Molecular Compound: A Charge Density and Correlated Ab Initio Electronic Structure Study

Understanding magnetic anisotropy and specifically how to tailor it is crucial in the search for high-temperature single-ion magnets. Herein, we investigate the magnetic anisotropy in a six-coordinated cobalt(II) compound that has a complex geometry and distinct triaxial magnetic anisotropy from the perspective of the electronic structure, using electronic spectra, ab initio calculations, and an experimental charge density, of which the latter two provides insight into the d-orbital splitting. The analysis showed that the d-orbital splitting satisfactorily predicted the complex triaxial magnetic anisotropy exhibited by the compound. Furthermore, a novel method to directly compare the ab initio results and the d-orbital populations obtained from the experimental charge density was developed, while a topological analysis of the density provided insights into the metal-ligand bonding. This work thus further establishes the validity of using d-orbitals for predicting magnetic anisotropy in transition metal compounds while also pointing out the need for a more frequent usage of the term triaxial anisotropy in the field of single-molecule magnetism.

Novel tetrahedral cobalt(ii) silanethiolates: structures and magnetism

Three heteroleptic complexes of Co(ii) tri-tert-butoxysilanethiolates have been synthesized with piperidine [Co{SSi(OtBu)3}2(ppd)2] 1, piperazine [Co{SSi(OtBu)3}2(NH3)]2(μ-ppz)·2CH3CN 2, and N-ethylimidazole [Co{SSi(OtBu)3}2(etim)2] 3. The complexes have been characterized by a single-crystal X-ray, revealing their tetrahedral geometry on Co(ii) coordinated by two nitrogen and two sulfur atoms. Complexes 1 and 3 are mononuclear, whereas 2 is binuclear. The spectral properties and thermal properties of 1-3 complexes were established by FTIR spectroscopy for solid samples and TGA. The magnetic properties of complexes 1, 2, and 3 have been investigated by static magnetic measurements and X-band EPR spectroscopy. These studies have shown that 1 and 3, regardless of the similarity in structure of CoN2S2 cores, demonstrate different types of local magnetic anisotropy. Magnetic investigations of 2 reveal the presence of weak antiferromagnetic intra-molecular Co(ii)-Co(ii) interactions that are strongly influenced by the local magnetic anisotropy of individual Co(ii) ions.

Ferrocene-Supported Compartmental Ligands for the Assembly of 3d/4f Complexes

Site-specific coordination ligands, also known as compartmental ligands, have been used for the preparation of heterometallic complexes. These ligands, by virtue of possessing specific binding sites, can encapsulate different metal ions in their coordination pockets. Such compartmental ligands have been widely used for the preparation of heterometallic 3d/4f complexes which have applications in molecular magnetism. This Review summarizes our efforts in the use of ferrocene-based compartmental ligands for the preparation of heterometallic 3d/4f complexes, some of which are single-molecule or single-ion magnets.

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.

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.

The effect of the electronic structure and flexibility of the counteranions on magnetization relaxation in [Dy(L)2(H2O)5]3+ (L = phosphine oxide derivative) pentagonal bipyramidal SIMs

The effects of the electronic structure and flexibility of triflate anions in a new high-U_eff TBPY-7 SMM, [Dy(OPCy₃)₂(H₂O)₅](CF₃SO₃)₃·2OPCy₃, have been analyzed.

Investigation of the magnetic anisotropy in a series of trigonal bipyramidal Mn(ii) complexes

Understanding how the magnetic anisotropy in simple coordination complexes can be manipulated is instrumental to the development of single-molecule magnets (SMMs). Clear strategies can then be designed to control both the axial and transverse contributions to the magnetic anisotropy in such compounds, and allow them to reach their full potential. Here we show a strategy for boosting the magnetic anisotropy in a series of trigonal bipyramidal Mn(ii) complexes - [MnCl₃(HDABCO)(DABCO)] (1), [MnCl₃(MDABCO)₂]·[ClO₄] (2), and [MnCl₃(H₂O)(MDABCO)] (3). These have been successfully synthesised using the monodentate [DABCO] and [MDABCO]⁺ ligands. Through static (DC) magnetic measurements and detailed theoretical investigation using ab initio methods, the magnetic anisotropy of each system has been studied. The calculations reveal that the rhombic zero-field splitting (ZFS) term (E) can be tuned as the symmetry around the Mn(ii) ion is changed. Furthermore, an in silico investigation reveals a strategy to increase the axial ZFS parameter (D) of trigonal bipyramidal Mn(ii) by an order of magnitude.

Mechanism of magnetisation relaxation in {MIII2DyIII2} (M = Cr, Mn, Fe, Al) "Butterfly" complexes: how important are the transition metal ions here?

We describe the synthesis, characterisation and magnetic studies of four tetranuclear, isostructural "butterfly" heterometallic complexes: [MIII2LnIII2(μ3-OH)2(p-Me-PhCO2)6(L)2] (H2L = 2,2'-((pyridin-2-ylmethyl)azanediyl)bis(ethan-1-ol), M = Cr, Ln = Dy (1), Y (2), M = Mn, Ln = Dy (3), Y (4)), which extend our previous study on the analogous 5 {Fe2Dy2}, 6 {Fe2Y2} and 7 {Al2Dy2} compounds. We also present data on the yttrium diluted 7 {Al2Dy2}: 8 {Al2Dy0.18Y1.82}. Compounds dc and ac magnetic susceptibility data reveal single-molecule magnet (SMM) behaviour for complex 3 {Mn2Dy2}, in the absence of an external magnetic field, with an anisotropy barrier U eff of 19.2 K, while complex 1 {Cr2Dy2}, shows no ac signals even under applied dc field, indicating absence of SMM behaviour. The diluted sample 8 {Al2Dy0.18Y1.82} shows field induced SMM behaviour with an anisotropy barrier U eff of 69.3 K. Furthermore, the theoretical magnetic properties of [MIII2LnIII2(μ3-OH)2(p-Me-PhCO2)6(L)2] (M = Cr, 1 or Mn, 3) and their isostructural complexes: [MIII2DyIII2(μ3-OH)2(p-Me-PhCO2)6(L)2] (M = Fe, 5 or Al, 7) are discussed and compared. To understand the experimental observations for this family, DFT and ab initio CASSCF + RASSI-SO calculations were performed. The experimental and theoretical calculations suggest that altering the 3dIII ions can affect the single-ion properties and the nature and the magnitude of the 3dIII-3dIII, 3dIII-DyIII and DyIII-DyIII magnetic coupling, thus quenching the quantum tunneling of magnetisation (QTM) significantly, thereby improving the SMM properties within this motif. This is the first systematic study looking at variation and therefore role of trivalent transition metal ions, as well as the diamgnetic AlIII ion, on slow relaxation of magnetisation within a series of isostructural 3d-4f butterfly compounds.

Theoretical Studies on Hexanuclear [M3(μ3-O/OH)]2 (M = Fe(III), Mn(III), and Ni(II)) Clusters: Magnetic Exchange, Magnetic Anisotropy, and Magneto-Structural Correlations

Controlling spin Hamiltonian parameters such as magnetic exchange and magnetic anisotropy of polynuclear clusters is of great interest in the area of single molecule magnets (SMMs). Among large polynuclear clusters, hexanuclear clusters offer the best compromise in terms of size as they are often rigid, solution stable, and chemically amenable. The {M₆O₂} core is one of the common architectures known for many hexanuclear clusters and generally reported to possess a diamagnetic S_T = 0 spin ground state, barring a few exceptions. In these clusters, there are several open questions that are poorly understood: (a) What controls the nature of magnetic exchange, which in turn dictates the ground state spin values? (b) For clusters possessing a nonzero spin ground state, what dictates the magnetic anisotropy? Here, using density functional methods, we have attempted to shed light on these two question by evaluating the exchange coupling constants in [Fe₆^IIIO₂(OH)₂{(C₄N₂H₂SMe)₂C(OH)O}₂( ^tBuCO₂)₁₀] (1), [Fe₆^III(O)₂(O₂CH₂)(O₂CCH₂ ^tBu)₁₂(py)₂] (2), [Fe₆^III(O₂)(O)₂(O₂CCMe₃)₁₂(py)₂] (3), [Fe^III₆O₃(O₂CMe)₉(OEt)₂(bpy)₂]ClO₄ (4), [Mn^III₆O₂(O₂CH₂)(O₂CPe ^t)₁₁(HO₂CPe ^t)₂(O₂CMe)] (5), and [Ni^II₆(OH)₄(O₂C ^tBu)₈( ^tBuCO₂H)₄] (6) complexes. We have estimated all the eight near-neighbor exchange coupling constants in these clusters. Our calculations not only agree with the experimental results but also offer insight on the origin of the spin ground state. Extensive magneto-structural correlations developed by varying M-O-M angles and M-O distances reveal that J values are extremely sensitive to small structural distortions. Correlations developed indicate that both the parameters are important for Fe(III), but for Mn(III) and Ni(II), the angles were found to play a dominant role. Quite interestingly, the computed zero-field splitting parameter D _S=5 of complex 1 reveals that the exchange contribution to the anisotropy controls the sign of the ground state D value-an observation which differs from the general perception that the ground state D is controlled by the single-ion zero-field splitting parameter.

Tetranuclear dysprosium single-molecule magnets: tunable magnetic interactions and magnetization dynamics through modifying coordination number

The study of mononuclear lanthanide-based systems, where the observed Single Molecule Magnets (SMMs) properties originate from the local magnetic anisotropy of the single lanthanide ion, has been extensively investigated in the literature. The case for polynuclear lanthanide SMMs becomes more challenging both experimentally and theoretically due to the complexity of such architectures involving interactions between the magnetic centers. Much interest was devoted to the study of the structural effect on the magnetic interactions and relaxation dynamics. However, the understanding of the structural influence on those two factors remains a difficult task. To address this issue, a system containing two structurally related tetranuclear Dy(iii) SMMs, namely [Dy4(L)4(OH)2(DMF)4(NO3)2]·2(DMF)·(H2O) (1) and [Dy4(L)4(OH)2(DMF)2(NO3)2] (2) (H2L = 2-(2-hydroxy-3-methoxybenzylideneamino)phenol), is introduced and investigated. Through modifying the ligands on the changeable coordination sites, the intramolecular magnetic interactions and relaxation dynamics in these two Dy(iii)4 SMMs can be tuned. Both complexes exhibit slow relaxation of their magnetization with a relaxation barrier of 114 K for complex 2 while a blocking temperature below 2 K is observed for complex 1. Ab initio calculations reveal that changes in coordination numbers and geometries on the Dy(iii) sites can significantly affect the magnetic interactions as well as single-ion anisotropy. The combination of experimental work and ab initio calculations offers insight into the relationship between structures and magnetic properties and sheds light on the rational design of future polynuclear lanthanide SMMs with enhanced magnetic properties.

Field-induced slow magnetic relaxation in pseudooctahedral cobalt(ii) complexes with positive axial and large rhombic anisotropy

The preparation, X-ray crystal structure, spectroscopic and variable-temperature dc and ac magnetic properties of two six-coordinate cobalt(ii) complexes of formula [Co(bim)₄(tcm)₂] (1) and [Co(bmim)₄(tcm)₂] (2) are reported.

A simple methodology for constructing ferromagnetically coupled Cr(iii) compounds

A large family of chromium(iii) dimers has been synthesised and magneto-structurally characterised using a combination of carboxylate and diethanolamine type ligands. The compounds have the general formula [Cr2(R1-deaH)2(O2CR2)Cl2]Cl where R1 = Me and R2 = H (1), Me (2), CMe3 (3), Ph (4), 3,5-(Cl)2Ph (5), (Me)5Ph (6), R1 = Et and R2 = H (7), Ph (8). The compound [Cr2(Me-deaH)2Cl4] (9) was synthesised in order to study the effect of removing/adding the carboxylate bridge on the observed magnetic behaviour. Direct current (DC) magnetic susceptibility measurements showed ferromagnetic (FM) exchange interactions between the Cr(iii) centres in the carboxylate bridged family with coupling constants in the range +0.37 < J < +8.02 cm-1. Removal of the carboxylate to produce the dialkoxide-bridged compound 9 resulted in antiferromagnetic (AFM) exchange between the Cr(iii) ions. DFT calculations reveal the ferromagnetic exchange is the result of an orbital counter-complementarity effect occuring upon introduction of the bridging carboxylate.

Quantitative analysis of zero-field splitting parameter distributions in Gd(iii) complexes

The magnetic properties of paramagnetic species with spin S > 1/2 are parameterized by the familiar g tensor as well as "zero-field splitting" (ZFS) terms that break the degeneracy between spin states even in the absence of a magnetic field. In this work, we determine the mean values and distributions of the ZFS parameters D and E for six Gd(iii) complexes (S = 7/2) and critically discuss the accuracy of such determination. EPR spectra of the Gd(iii) complexes were recorded in glassy frozen solutions at 10 K or below at Q-band (∼34 GHz), W-band (∼94 GHz) and G-band (240 GHz) frequencies, and simulated with two widely used models for the form of the distributions of the ZFS parameters D and E. We find that the form of the distribution of the ZFS parameter D is bimodal, consisting roughly of two Gaussians centered at D and -D with unequal amplitudes. The extracted values of D (σD) for the six complexes are, in MHz: Gd-NO3Pic, 485 ± 20 (155 ± 37); Gd-DOTA/Gd-maleimide-DOTA, -714 ± 43 (328 ± 99); iodo-(Gd-PyMTA)/MOMethynyl-(Gd-PyMTA), 1213 ± 60 (418 ± 141); Gd-TAHA, 1361 ± 69 (457 ± 178); iodo-Gd-PCTA-[12], 1861 ± 135 (467 ± 292); and Gd-PyDTTA, 1830 ± 105 (390 ± 242). The sign of D was adjusted based on the Gaussian component with larger amplitude. We relate the extracted P(D) distributions to the structure of the individual Gd(iii) complexes by fitting them to a model that superposes the contribution to the D tensor from each coordinating atom of the ligand. Using this model, we predict D, σD, and E values for several additional Gd(iii) complexes that were not measured in this work. The results of this paper may be useful as benchmarks for the verification of quantum chemical calculations of ZFS parameters, and point the way to designing Gd(iii) complexes for particular applications and estimating their magnetic properties a priori.

Reconciling the valence state with magnetism in mixed-valent polyoxometalates: the case of a {VO2F2@V22O54} cluster

The electronic structure and magnetism of the recently synthesised mixed-valent {V^VO₂F₂@VO₅₄} (1) host-guest polyoxovanadate envisaged as a potential building block of a molecule-based quantum computer are analysed using density functional theory (DFT) and effective Hamiltonian calculations. The form of the t-J like effective Hamiltonian has been inspired by the acquired DFT data, and the valence state used in DFT calculations has been suggested by the fits to the experimental magnetic data with the effective Hamiltonian. This self-consistent approach breaks through the magnetochemical limitations of vanadium-oxo cluster 1, giving results fully concordant with the experiment and allowing us to determine the valence state of 1, which contrary to other members of this host-guest family appears to feature 9 valence electrons.

Acquiring a record barrier height for magnetization reversal in lanthanide encapsulated fullerene molecules using DFT and ab initio calculations

Ab initio calculations performed on a series of lanthanide encapsulated fullerenes reveal {DyOSc}@C₈₂ to be one of the best host-guest pairs to offer a barrier height exceeding 1400 cm^-1. The high-symmetry environment preserved inside the cage quenches the QTM effects up to third-excited states leading to very larger barrier heights and this opens up a new possibility of obtaining attractive SMMs based on lanthanide based endohedral metallo-fullerenes (EMFs).

New field-induced single ion magnets based on prolate Er(iii) and Yb(iii) ions: tuning the energy barrierUeffby the choice of counterions within an N3-tridentate Schiff-base scaffold

Counterions modulate the structure and magnetic properties of rarely observed high-coordinate SIM species.

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.