Single-Ion versus Dipolar Origin of the Magnetic Anisotropy in Iron(III)-Oxo Clusters: A Case Study

Half-Integer Spin Triangles: Old Dogs, New Tricks

Spin triangles, that is, triangular complexes of half-integer spins, are the oldest molecular nanomagnets (MNMs). Their magnetic properties have been studied long before molecular magnetism was delineated as a research field. This Review presents the history of their study, with references to the parallel development of new experimental investigations and new theoretical ideas used for their interpretation. It then presents an indicative list of spin-triangle families to illustrate their chemical diversity. Finally, it makes reference to recent developments in terms of theoretical ideas and new phenomena, as well as to the relevance of spin triangles to spintronic devices and new physics.

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.

Predetermined Ferromagnetic Coupling via Strict Control of M-O-M Angles

An imidazolidine-phenolate ligand HL yields quadruple-bridged (μ-NCN_{imidazolidine})₂(μ-O_phenolate)₂ ferromagnetic dinuclear nickel and cobalt complexes. Both kinds of bridges contribute to the ferromagnetic coupling, but the ferromagnetism of these samples is mainly ascribed to the double μ-O_phenolate links, on the basis of density functional theory calculations. These studies demonstrate not only that the short M-O-M angles of the M₂O₂ cores favors the parallel alignment of the electrons but also that these angles are the optimal ones for maximizing the ferromagnetic contribution in these complexes. And these acute angles, close to 90°, are predetermined by the geometrical constrictions imposed by the ligand itself. Thus, HL is an uncommon polydentate donor that induces ferromagnetism per se in its metal complexes by strict control of one geometric parameter, the M-O-M angle.

Interweaving spins with their environment: novel inorganic nanohybrids with controllable magnetic properties

We discuss the developments in the synthesis and characterization of magnetic nanohybrids made of molecular magnets and nanostructured materials.

Single crystal EPR study at 95 GHz of a large Fe based molecular nanomagnet: toward the structuring of magnetic nanoparticle properties

A W-band single-crystal EPR study has been performed on a molecular cluster comprising 19 iron(III) ions bridged by oxo- hydroxide ions, Fe(19), in order to investigate magnetic nanosystems with a behavior in between the one of Magnetic NanoParticles (MNP) and that of Single Molecule Magnets (SMM). The Fe(19) has a disk-like shape: a planar Fe(7) core with a brucite (Mg(OH)(2)) structure enclosed in a "shell" of 12 Fe(III) ions. EPR and magnetic measurements revealed an S = 35/2 ground state with an S = 33/2 excited state lying ∼ 8 K above. The presence of other low-lying excited states was also envisaged. Rhombic Zero Field Splitting (ZFS) tensors were determined, the easy axes lying in the Fe(19) plane for both the multiplets. At particular temperatures and orientations, a partially resolved fine structure could be observed which could not be distinguished in powder spectra, due to orientation disorder. The similarities of the EPR behavior of Fe(19) and MNP, together with the accuracy of single crystal analysis, helped to shed light on spectral features observed in MNP spectra, that is a sharp line at g = 2 and a low intensity transition at g = 4. Moreover, a theoretical analysis has been used to estimate the contribution to the total magnetic anisotropy of core and surface; this latter is crucial in determining the easy axis-type anisotropy, alike that of MNP surface.

Spin entanglement in supramolecular structures

Molecular spin clusters are mesoscopic systems whose structural and physical features can be tailored at the synthetic level. Besides, their quantum behavior is directly accessible in the laboratory and their magnetic properties can be rationalized in terms of microscopic spin models. Thus they represent an ideal playground within solid state systems to test concepts in quantum mechanics. One intriguing challenge is to control entanglement between molecular spins. Here we show how this goal can be pursued by discussing specific examples and referring to recent achievements.

Magnetic circular dichroism spectroscopy on the Cr₈ antiferromagnetic ring

A Magnetic Circular Dichroism (MCD) spectroscopic study of the antiferromagnetic ring [Cr₈F₈Piv₁₆] (Piv = pivalate) is reported. From the splitting of the MCD bands, the single ion anisotropy parameters in the cluster spin ground state at different fields were determined to be d(Cr) = -0.33 ± 0.02 cm⁻¹, e(Cr) = 0.11 ± 0.01 cm⁻¹. Analysis of the MCD intensity as a function of field and temperature revealed the influence of spin mixing effects and yielded independent estimates of the single ion anisotropies (d(Cr) = -0.19 cm⁻¹, e(Cr) = 4.3 × 10-4 cm⁻¹), as well as yielding the isotropic exchange interaction strength (J = -6.00 cm⁻¹). Thus it is shown that MCD is a powerful method to unravel the relation between single-ion and cluster anisotropy, furthering the design of molecular magnets with desired properties.

Molecular nanomagnets and magnetic nanoparticles: the EMR contribution to a common approach

The current status and future developments of the use of electron magnetic resonance (EMR) for the investigation of magnetic nano-systems is here reviewed. The aim is to stimulate efforts to provide a unified view of the properties of magnetic nanoparticles (MNP) comprising a few hundred magnetic centres, and molecular nanomagnets which contain up to ca. one hundred magnetic centres (MNM). The size of the systems is becoming the same but the approaches to the interpretation of their properties are still different, being bottom up for the latter and top down for the former. We make the point here of the need for a common viewpoint, highlighting the status of the two fields and giving some hints for the future developments. EMR has been a powerful tool for the investigation of magnetic nano-objects and it can provide a tool of fundamental importance for the development of a unified view.

Al, Ga and In heterometallic wheels and their by-products

Cyclic octanuclear complexes, each containing seven group 13 metals and one d-block metal are reported and preliminary physical characterisation of the compounds discussed.

Methanolysis as a route to gallium(III) clusters: synthesis and structural characterization of a decanuclear molecular wheel

Treatment of a methanolic solution of gallium(III) nitrate with lithium hydroxide in the presence of benzilic acid resulted in the decanuclear cluster [Ga(OMe)2{O2CC(OH)Ph2}]10 (1). The metal and the organic components have assembled to form a cyclic molecule that adopts the structure of a wheel. The 10 Ga(III) ions are approximately coplanar and are coordinated in a distorted octahedral manner by six oxygen atoms. The integrity of the molecular wheel is retained in solution, as evidenced by the 1NMR spectrum of 1 in DMSO-d6, while no signal in the 71Ga NMR could be detected.

Tuning Anisotropy Barriers in a Family of Tetrairon(III) Single-Molecule Magnets with an S = 5 Ground State

Tetrairon(III) Single-Molecule Magnets (SMMs) with a propeller-like structure exhibit tuneable magnetic anisotropy barriers in both height and shape. The clusters [Fe4(L1)2(dpm)6] (1), [Fe4(L2)2(dpm)6] (2), [Fe4(L3)2(dpm)6].Et2O (3.Et2O), and [Fe4(OEt)3(L4)(dpm)6] (4) have been prepared by reaction of [Fe4(OMe)6(dpm)6] (5) with tripodal ligands R-C(CH2OH)3 (H3L1, R = Me; H3L2, R = CH2Br; H3L3, R = Ph; H3L4, R = tBu; Hdpm = dipivaloylmethane). The iron(III) ions exhibit a centered-triangular topology and are linked by six alkoxo bridges, which propagate antiferromagnetic interactions resulting in an S = 5 ground spin state. Single crystals of 4 reproducibly contain at least two geometric isomers. From high-frequency EPR studies, the axial zero-field splitting parameter (D) is invariably negative, as found in 5 (D = -0.21 cm(-1)) and amounts to -0.445 cm(-1) in 1, -0.432 cm(-1) in 2, -0.42 cm(-1) in 3.Et2O, and -0.27 cm(-1) in 4 (dominant isomer). The anisotropy barrier Ueff determined by AC magnetic susceptibility measurements is Ueff/kB = 17.0 K in 1, 16.6 K in 2, 15.6 K in 3.Et2O, 5.95 K in 4, and 3.5 K in 5. Both |D| and U(eff) are found to increase with increasing helical pitch of the Fe(O2Fe)3 core. The fourth-order longitudinal anisotropy parameter B4(0), which affects the shape of the anisotropy barrier, concomitantly changes from positive in 1 ("compressed parabola") to negative in 5 ("stretched parabola"). With the aid of spin Hamiltonian calculations the observed trends have been attributed to fine modulation of single-ion anisotropies induced by a change of helical pitch.

Single-ion and molecular contributions to the zero-field splitting in an iron(III)-oxo dimer studied by single crystal W-band EPR

Detailed knowledge of the type and strength of pair interactions between high-spin metal ions is paramount to the understanding and design of molecular magnetic materials. In this work, the anisotropic magnetic interactions in a beta-diketonate-alkoxide iron(III) dimer compound, [Fe2(OCH3)2(dbm)4, Hdbm=dibenzoylmethane] (Fe2) have been investigated by single crystal electron paramagnetic resonance (EPR) in the W-band (at 95GHz). The diamagnetic substitution method was employed using the isomorphous gallium(III)-based compound doped with iron(III) to produce Ga-Fe dimers (GaFe). The single-ion zero-field splitting (ZFS) tensor could be separately determined in GaFe with the iron ion in a local environment quasi-identical to the one in Fe2. Its principal directions are found to point in arbitrary directions, uncorrelated with the Fe-O bonds. The Fe2 EPR spectra consist of transitions within the lowest multiplet states S=1,2,3, which were analyzed using the full spin Hamiltonian description of an exchange coupled pair of s=5/2 spins. The anisotropic spin-spin interaction tensor of Fe2 possesses a principal axis close to the Fe-Fe direction and was shown to arise both from through-space (dipolar) and through-bond (anisotropic exchange) contributions. The latter involves an rhombic component JE=(JX-JY)/2 approximately 0.093 cm-1 of magnitude comparable to the dipolar interaction, and even to the rhombic part of the single-ion ZFS (E=0.097 cm-1). Our results show that the anisotropic exchange, usually neglected for S-type ions, is significant for the anisotropic interactions in exchange-coupled iron(III) clusters, including the Fe4 and Fe8 families of single-molecule magnets and the antiferromagnetic iron wheels.

Synthesis and Spectroscopic and Magnetic Characterization of Tris(3,5-dimethylpyrazol-1-yl)borate Iron Tricyanide Building Blocks, a Cluster, and a One-Dimensional Chain of Squares

The synthesis and spectroscopic and magnetic characterization of several hydridotris(3,5-dimethylpyrazol-1yl)borate (Tp*) iron(II) and iron(III) tricyanide complexes, a rectangular cluster, and a one-dimensional chain of squares are described. Treatment of [NEt4][(Tp*)Fe(III)(CN)3] (3) with manganese(II) triflate in dimethylformamide (DMF) affords rectangular clusters (6, {[(Tp)Fe(CN)2(mu-CN)Mn(DMF)4]2[OTf]2}.2DMF), while tosylate salts afford one-dimensional networks (5, {Mn(II)(DMF)2(mu-OTs)(mu-NC)2(NC)Fe(III)(Tp*)}n) containing embedded [(Tp*)2Fe(III)2Mn(II)2(CN)6]2+ clusters via in situ trapping; the cluster and network crystallize in the monoclinic (6, P2(1)/n) and triclinic (5, P1) space groups, respectively. The 1-D network (5) appears to be derived from {cis-(mu-O3SC6H4Me)2Mn(II)(DMF)4}n (4, P2(1)/n), which is obtained via crystallization of Mn(OTs)2 from DMF/Et2O mixtures. For 4, magnetic studies indicate that the Mn(II) centers are magnetically isolated, with calculated J, g, and theta constants of 6.7 x 10(-3) cm(-1), 2.03, and -0.52 K. Additional magnetic studies of 5 and 6 indicate that the [(Tp*)Fe(III)(CN)3]- centers are highly anisotropic (g = 2.9) and are antiferromagnetically coupled to adjacent Mn(II) centers. For 5 and 6, fitting of the chiT vs T data via the Curie-Weiss expression affords Curie (6.25 and 10.8 cm(3) K mol(-1)) and Weiss (-14.37 and -8.80 K) constants that are consistent with antiferromagnetically coupled low-spin Fe(III) and high-spin Mn(II) centers; least-squares fitting of the chiT vs T data using molecular field theory affords g(avg.), J1, J2, and J' values of 2.25, -1.72, -0.58, and -0.12 cm(-1) for 5. Overall, bridging tosylates appear to be poor communicators of spin information. For 6, the g, J1, and J2 (2.15, -2.02, and -0.78 cm(-1)) values were obtained via least-squares fitting of the chiT vs T data using an expression derived using the Kambe vector coupling method; simulations of the data via MAGPACK afford g(avg.) and J(iso) values of 2.1 and -2.1 cm(-1).

Molecular routes for spin cluster qubits

We report on real molecular complexes and propose strategies that explore the possibility of implementation of specific quantum computation architectures with molecular spin systems. We focus on Cr3+ carboxylate derivatives and use the Loss-DiVincenzo scheme as reference.

High-field/high-frequency EPR studies of spin clusters with integer spin: the multi-frequency approach

In this paper a rapid overview of the main results obtained from the study with multi-frequency HF-EPR of molecular spin clusters possessing integer spin values is presented. In the first part, two antiferromagnetic rings with zero ground spin state are reported. It is illustrated how the HF-EPR study of the first excited states allows obtaining important information on this kind of spin clusters. In the second part, selected examples of single-molecule magnets (SMM) are treated, starting with complexes involving only a few magnetic ions and going on to more complex systems. Indeed, because of their large zero-field energy gaps, EPR studies of SMM deserve the use of high frequencies and high fields. The approach presented here is twofold. First the interest of studying a series of 'simple' SMM in order to understand the subtle mechanisms underlying their properties is stressed. Then a summary of our HF-EPR studies of the most investigated SMM, Mn12ac and Fe8 is presented.

High-Spin Molecules with Magnetic Anisotropy toward Single-Molecule Magnets

High-spin molecules with easy-axis magnetic anisotropy show slow magnetic relaxation of spin-flipping along the axis of magnetic anisotropy and are called single-molecule magnets (SMMs). SMMs behave as molecular-size permanent magnets at low temperature and magnetic relaxation occurs by quantum tunneling processes; such molecules are promising candidates for use in quantum devices. We first discuss intramolecular ferromagnetic interactions for preparing high-spin molecules. Second, we determine the magnetic anisotropy for single metal ions with d(n) configurations and discuss how molecular anisotropy arises from single-ion anisotropy of the assembled component metal ions.

Magnetic and optical studies on an S = 6 ground-state cluster [Cr12O9(OH)3(O2CCMe3)15]: determination of, and the relationship between, single-ion and cluster spin Hamiltonian parameters

The dodecametallic Cr(III) cluster [Cr(12)O(9)(OH)(3)(O(2)CCMe(3))(15)] has a ground spin state of S = 6 characterized by the spin Hamiltonian parameters g(ZZ)() = 1.965, g(XX)() = g(YY)() = 1.960, D(S=)()(6) = +0.088 cm(-)(1), and E(S=)()(6) = 0 (where D and E are the axial and rhombic zero-field splitting parameters, respectively) as determined by multifrequency EPR spectroscopy and magnetization studies. Micro-SQUID magnetization studies reveal steps due to the fine structure of the ground state, with the spacing between the steps in excellent agreement with the D(S=)()(6) value determined by EPR. Analysis of high-resolution optical data (MCD) allows us to determine the single-ion g values and D value (= -1.035 cm(-)(1)) of the constituent Cr(III) ions directly. A vector coupling analysis demonstrates that the cluster ZFS is almost entirely due to the single-ion component. Thus, the relative orientations of the local and cluster magnetic axes can lead to a cluster ZFS of opposite sign to the single-ion value, even when this is the only significant contribution.

Mechanism of a strongly anisotropic MoIII-CN-MnII spin-spin coupling in molecular magnets based on the [Mo(CN)(7)](4-) heptacyanometalate: a new strategy for single-molecule magnets with high blocking temperatures

Unusual spin coupling between Mo(III) and Mn(II) cyano-bridged ions in bimetallic molecular magnets based on the [Mo(III)(CN)(7)](4-) heptacyanometalate is analyzed in terms of the superexchange theory. Due to the orbital degeneracy and strong spin-orbit coupling on Mo(III), the ground state of the pentagonal-bipyramidal [Mo(III)(CN)(7)](4-) complex corresponds to an anisotropic Kramers doublet. Using a specially adapted kinetic exchange model we have shown that the Mo(III)-CN-Mn(II) superexchange interaction is extremely anisotropic: it is described by an Ising-like spin Hamiltonian JS(z)(Mo) S(z)(Mn) for the apical pairs and by the J(z)S(z)(Mo) S(z)(Mn) + J(xy)(Sx(Mo) Sx(Mn) + Sy(Mo) Sy(Mn)) spin Hamiltonian for the equatorial pairs (in the latter case J(z) and J(xy) can have opposite signs). This anisotropy resulted from an interplay of several Ising-like (Sz(Mo) Sz(Mn)) and isotropic (S(Mo)S(Mn)) ferro- and antiferromagnetic contributions originating from metal-to-metal electron transfers through the pi and sigma orbitals of the cyano bridges. The Mo(III)-CN-Mn(II) exchange anisotropy is distinct from the anisotropy of the g-tensor of [Mo(III)(CN)(7)](4-); moreover, there is no correlation between the exchange anisotropy and g-tensor anisotropy. We indicate that highly anisotropic spin-spin couplings (such as the Ising-like JS(z)(Mo) S(z)(Mn)) combined with large exchange parameters represent a very important source of the global magnetic anisotropy of polyatomic molecular magnetic clusters. Since the total spin of such clusters is no longer a good quantum number, the spin spectrum pattern can differ considerably from the conventional scheme described by the zero-field splitting of the isotropic spin of the ground state. As a result, the spin reorientation barrier of the magnetic cluster may be considerably larger. This finding opens a new way in the strategy of designing single-molecule magnets (SMM) with unusually high blocking temperatures. The use of orbitally degenerate complexes with a strong spin-orbit coupling (such as [Mo(III)(CN)(7)](4-) or its 5d analogues) as building blocks is therefore very promising for these purposes.

Observation of magnetic level repulsion in Fe6:Li molecular antiferromagnetic rings

Heat capacity (C), magnetic torque, and proton NMR relaxation rate (1/T(1)) measurements were performed on Fe6:Li single crystals in order to study the crossings between S = 0 and S = 1 and between S = 1 and S = 2 magnetic states of the molecular rings, at magnetic fields B(c1) = 11.7 T and B(c2) = 22.4 T, respectively. C vs B data at 0.78 K show that the energy gap between two states remains finite at B(c)'s (Delta(1)/k(B) = 0.86 K and Delta(2)/k(B) = 2.36 K) thus proving that levels repel each other. The large Delta(1) value may also explain the anomalously large width of the peak in 1/T(1) vs B, around B(c1). This anticrossing, unexpected in a centrosymmetric system, requires a revision of the Hamiltonian.

Magnetic anisotropy of the antiferromagnetic ring [Cr8F8Piv16]

A new tetragonal (P42(1)2) crystalline form of [Cr8F8Piv16] (HPiv = pivalic acid, trimethyl acetic acid) is reported. The ring-shaped molecules, which are aligned in a parallel fashion in the unit cell, form almost perfectly planar, regular octagons. The interaction between the CrIII ions is antiferromagnetic (J = 12 cm(-1)) which results in a S = 0 spin ground state. The low-lying spin excited states were investigated by cantilever torque magnetometry (CTM) and high-frequency EPR (HFEPR). The compound shows hard-axis anisotropy. The axial zero-field splitting (ZFS) parameters of the first two spin excited states (S = 1 and S = 2, respectively) are D1 = 1.59(3) cm(-1) or 1.63 cm(-1) (from CTM and HFEPR, respectively) and D2 = 0.37 cm(-1) (from HFEPR). The dipolar contributions to the ZFS of the S = 1 and S = 2 spin states were calculated with the point dipolar approximation. These contributions proved to be less than the combined single-ion contributions. Angular overlap model calculations that used parameters obtained from the electronic absorption spectrum, showed that the unique axis of the single-ion ZFS is at an angle of 19.3(1) degrees with respect to the ring axis. The excellent agreement between the experimental and the theoretical results show the validity of the used methods for the analysis of the magnetic anisotropy in antiferromagnetic CrIII rings.