Heisenberg Dirac Van Vleck Research Articles

Evidence of half metal to insulator transition and subsequent photocatalytic action in g-C4N3@Lin =1 to 4: A systematic theoretical analysis

We report herein, emergence of photocatalytic action in Li doped two-dimensional nanosheet of graphitic carbon nitride [g-C4N3@Lin = 0-4]. Doping concentration varied from 3.57 % to 14.28 %. Pristine graphitic carbon nitride is half metallic and at the highest level of doping (14.28 %) it transforms into an insulating system. Observed results have been examined through the estimation of coupling between magnetic centers and the overall magnetic moment of the system. The exchange coupling (JAB) within Heisenberg–Dirac–van Vleck Hamiltonian being negative indicates antiferromagnetic coupling in presence of Li, doping. Related optical spectrum quite clearly illustrates that only at the doping level [14.28 %] the absorption peak is in the optical region. Band structure obtained illustrates a band gap of 1.92 eV and 1.93 eV in both spin channels and both oxidation and reduction potential falls within the band gap. The presence of reduction potential below the conduction band and oxidation potential above the valence band clearly illustrates the possibility of photocatalytic action.

Insight Into The Spin-Vibronic Problem of a Mixed Valence Magnetic Molecular Cell for Quantum Cellular Automata.

The effects of the vibronic coupling in quantum cellular automata (QCA) based on the square planar mixed valence (MV) molecular cells comprising four paramagnetic centers (spin cores) and two excess mobile electrons are analyzed in the important particular case when the Coulomb energy gap between the ground antipodal diagonal-type two-electron configurations and the excited side-type configurations considerably exceeds both the one-electron transfer parameter (strong U-limit) and the vibronic stabilization energy. Under such conditions the developed model involves the second-order double exchange, the Heisenberg-Dirac-Van Vleck (HDVV) exchange and the vibronic coupling of the excess electrons with the molecular B1g -vibration composed of four full-symmetric local vibrations. The latter interaction is shown to significant amplify the ability of the electric field produced by the driver-cell to polarize the excess electrons in the working cell, which can be termed "the effect of the vibronic enhancement of the cell-cell interaction". This effect leads to a redetermination of the conditions for switching between different spin-states, as well as to a significant change in the shapes of the cell-cell response functions. The obtained results demonstrate the importance of the vibronic coupling in all aspects (such as description of a free cell and cell-cell response) of the theory of molecular QCA based on MV clusters.

Toward multifunctional molecular cells for quantum cellular automata: exploitation of interconnected charge and spin degrees of freedom.

We discuss the possibility of using mixed-valence (MV) dimers comprising paramagnetic metal ions as molecular cells for quantum cellular automata (QCA). Thus, we propose to combine the underlying idea behind the functionality of QCA of using the charge distributions to encode binary information with the additional functional options provided by the spin degrees of freedom. The multifunctional ("smart") cell is supposed to consist of multielectron MV dn-dn+1-type (1 ≤ n ≤ 8) dimers of transition metal ions as building blocks for composing bi-dimeric square planar cells for QCA. The theoretical model of such a cell involves the double exchange (DE), Heisenberg-Dirac-Van Vleck (HDVV) exchange, Coulomb repulsion between the two excess electrons belonging to different dimeric half-cells and also the vibronic coupling. Consideration is focused on the topical case in which the difference in Coulomb energies of the two excess electrons occupying nearest neighboring and distant positions significantly exceeds both the electron transfer integral and the vibronic energy. In this case the ground spin-state of the isolated square cell is shown to be the result of competition of the second-order DE producing a ferromagnetic effect and the HDVV exchange that is assumed to be antiferromagnetic. In order to reveal the functionality of the magnetic cells, the cell-cell response function is studied within the developed model. The interaction of the working cell with the polarized driver-cell is shown to produce an antiferromagnetic effect tending to suppress the ferromagnetic second-order DE. As a result, under some conditions the electric field of the driver cell is shown to force the working cell to exhibit spin-switching from the state with maximum dimeric spin values to that having minimal spin values.

Can the Double Exchange Cause Antiferromagnetic Spin Alignment?

The effect of the double exchange in a square-planar mixed-valence dn+1−dn+1−dn−dn–type tetramers comprising two excess electrons delocalized over four spin cores is discussed. The detailed analysis of a relatively simple d2−d2−d1−d1–type tetramer shows that in system with the delocalized electronic pair the double exchange is able to produce antiferromagnetic spin alignment. This is drastically different from the customary ferromagnetic effect of the double exchange which is well established for mixed-valence dimers and tetramers with one excess electron or hole. That is why the question “Can double exchange cause antiferromagnetic spin alignment?” became the title of this article. As an answer to this question the qualitative and quantitative study revealed that due to antiparallel directions of spins of the two mobile electrons which give competitive contributions to the overall polarization of spin cores, the system entirely becomes antiferromagnetic. It has been also shown that depending on the relative strength of the second-order double exchange and Heisenberg–Dirac–Van Vleck exchange the system has either the ground localized spin-triplet or the ground delocalized spin-singlet.

Molecular Identification of a High-Spin Deprotonated Intermediate during the S2 to S3 Transition of Nature's Water-Oxidizing Complex.

The identity of a key intermediate in the S2 to S3 transition of nature's water-oxidizing complex (WOC) in Photosystem 2 is presented. Broken-symmetry density functional theory (BS-DFT) calculations and Heisenberg-Dirac-van Vleck (HDvV) spin ladder calculations show that an S2 state open cubane model of the WOC containing a μ-hydroxo O4 changes from an S = 5/2 form to an S = 7/2, form upon deprotonation of W1. Combined with X-band electron paramagnetic resonance (EPR) spectral analysis, this indicates that the g = 4.1 EPR signal corresponds to an S = 5/2 form of the WOC with W1 present as a water ligand to Mn4, while the g = 4.8/4.9 form observed at high pH values corresponds to an S = 7/2 form, with W1 as a hydroxo ligand. The latter is also likely to represent the form needed to progress to S3 in the functioning enzyme.

Magnetic susceptibility, EPR, NEXAFS and XPS spectra of Fe-doped CaBi2Nb2O9

In order to study the electronic state of Fe atoms and interatomic exchange interactions in solid solutions of Bi2CaNb2−2xFe2xO9−δ with perovskite structure, methods of magnetic dilution, NEXAFS, XPS and EPR spectroscopy were used. Increased values of the magnetic moment of iron atoms in solid solutions compared to pure spin values for Fe(III) are explained by the presence of clusters of Fe(III) atoms predominantly with antiferromagnetic type of exchange. Exchange parameters and cluster distribution in Bi2CaNb2−2xFe2xO9−δ solid solutions depending on the Fe content were calculated according to the Heisenberg–Dirac–van Vleck model. The effect of calcium atoms on the clusterization degree and intensity of Fe interatomic exchange interactions was displayed. XPS spectra of Bi2CaNb2-2xFe2xO9-δ, were identified to enable estimation of the effective charge of the atoms composing it. The analysis of the NEXAFS Fe2p-spectra of iron oxides and the iron-containing solid solutions revealed that Fe atoms were mainly in an oxidation state of +3. EPR spectra of Fe containing solid solution powder show an intense asymmetric line in the low-field part of the spectra at g=4.27 with weakly manifested shoulder g∼8–10 and a broad component in the g∼2 range with a high-field wing.

Influence of Radicals on Magnetization Relaxation Dynamics of Pseudo-Octahedral Lanthanide Iminopyridyl Complexes.

Controlling quantum tunneling of magnetization (QTM) is a persistent challenge in lanthanide-based single-molecule magnets. As the exchange interaction is one of the key factors in controlling the QTM, we targeted lanthanide complexes with an increased number of radicals around the lanthanide ion. On the basis of our targeted approach, a family of pseudo-octahedral lanthanide/transition-metal complexes were isolated with the general molecular formula of [M(L•-)3] (M = Gd (1), Dy (2), Er (3), Y (4)) using the redox-active iminopyridyl (L•-) ligand exclusively, which possess the highest ratio of radicals to lanthanide reported for discrete metal complexes. Direct current magnetic susceptibility studies suggest that dominant antiferromagnetic interactions exist between the radical and lanthanide ions in all of the complexes, which is strongly corroborated by magnetic data fitting using a Heisenberg-Dirac-Van Vleck (HDVV) Hamiltonian (-2 J Hamiltonian). A good agreement between the fit and the experimental magnetic data obtained using g = 2, Jrad-rad = -111.9 cm-1 for 4 and g = 1.99, Jrad-rad = -111.9 cm-1, JGd-rad = -1.85 cm-1 for 1. Complex 2 shows frequency-dependent slow magnetization relaxation dynamics in the absence of an external magnetic field, while 3 shows field-induced frequency-dependent χM'' signals. An ideal octahedral geometry around the lanthanide ion is predicted to be unsuitable for the design of a single-molecule magnet (SMM); nevertheless, complex 2 exhibits slow relaxation of magnetization with a record high anisotropy barrier for a six-coordinate Dy(III) complex. A rationale for this unusual behavior is detailed and reveals the strength of the synthetic methodology developed.

What Are the Physical Contents of Hubbard and Heisenberg Hamiltonian Interactions Extracted from Broken Symmetry DFT Calculations in Magnetic Compounds?

Analytical expressions of the interactions present in the Heisenberg-Dirac van Vleck and Hubbard Hamiltonians have been derived as functions of both the energy of several broken symmetry DFT solutions and their expectation value of the S2 spin operator. Then, following a strategy of decomposition of the magnetic exchange coupling into its main contributions (direct exchange, kinetic exchange, and spin polarization) and using a recently proposed method of spin decontamination, values of these interactions have been extracted. As already observed, they weakly depend on the correlation functional but strongly depend on the exchange one. In order to distinguish between the effect of the delocalization of the magnetic orbitals and that of the amount of Hartree-Fock exchange (HFX) when hybrid exchange-correlation functionals are used, we have disentangled these two contributions by either freezing the magnetic orbitals and varying the amount of HFX or varying the magnetic orbitals while keeping the same amount of HFX. As expected, increasing the amount of HFX induces a slight relocalization of the magnetic orbitals on the magnetic center which results in a weak increase of the repulsion energy U parameter and a weak decrease of both the direct exchange Kab and hopping |t| parameters. Conversely, the amount of HFX has a huge effect on all the parameters, even when some of the parameters should be exchange-independent, like U. Indeed, it is analytically demonstrated that the physical content of the U parameter extracted from several broken-symmetry solutions depends on the amount of HFX and that this pathological behavior has the same origin as the self-interaction error. This result is interesting not only to theoretical chemists working in the field of magnetic systems but also to DFT methodologists interested in using this theory for studying either excited states or strongly correlated systems. Finally, the performance of the range-separated ωB97XD functional for both ferromagnetic and antiferromagnetic transition-metal compounds and organic systems must be noted.

Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches.

In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.

Geometrical structure of meta-xylylene based symmetric polyradicals and their magnetic nature: A density functional study

Quantum chemical investigations on symmetrical polyradicals of meta-xylylene chains are done using unrestricted DFT – broken symmetry formalism, to determine whether the polymers are quasi-linear or helical, and their possible magnetic characteristics. As more radical centers are added, successively placed phenyl rings become twisted in the same direction to form a coiled chain. Each polyradical possesses a high-spin ground state with large adiabatic as well as vertical coupling constants. The adiabatic coupling constant exponentially decays with an increasing number of radical centers. Also, the Heisenberg–Dirac–Van Vleck coupling constants are generally large. The polymers are predicted to be very strong paramagnets.

A Strongly Spin-Frustrated Fe(III) 7 Complex with a Canted Intermediate Spin Ground State of S=7/2 or 9/2.

A disk-shaped [Fe(III) 7 (Cl)(MeOH)6 (μ3 -O)3 (μ-OMe)6 (PhCO2 )6 ]Cl2 complex with C3 symmetry has been synthesised and characterised. The central tetrahedral Fe(III) is 0.733 Å above the almost co-planar Fe(III) 6 wheel, to which it is connected through three μ3 -oxide bridges. For this iron-oxo core, the magnetic susceptibility analysis proposed a Heisenberg-Dirac-van Vleck (HDvV) mechanism that leads to an intermediate spin ground state of S=7/2 or 9/2. Within either of these ground state manifolds it is reasonable to expect spin frustration effects. The (57) Fe Mössbauer (MS) analysis verifies that the central Fe(III) ion easily aligns its magnetic moment antiparallel to the externally applied field direction, whereas the other six peripheral Fe(III) ions keep their moments almost perpendicular to the field at stronger fields. This unusual canted spin structure reflects spin frustration. The small linewidths in the magnetic Mössbauer spectra of polycrystalline samples clearly suggest an isotropic exchange mechanism for realisation of this peculiar spin topology.

Synthesis, crystal structure and magnetic properties of a trinuclear phenolate bridged manganese complex containing Mn(ii)–Mn(iii) ions

A trinuclear manganese complex containing Mn(III)–Mn(II)–Mn(III) cores, [Mn3(bp)4(CH3OH)]·0.875CH3OH·0.125H2O (1), has been prepared and structurally characterized where H2bp is an O3-donor bis(phenolate) ligand {H2bp = 2,2′-sulfinylbis(4-methylphenol)}. The combined structural and magnetic analysis reveals the mixed valence character of the compound with one central Mn(II) ion and two outer Mn(III) ions connected by phenolate bridging groups. The Mn(III)–Mn(II)–Mn(III) angle is close to a linear arrangement (∼160°) and the Mn(II)⋯Mn(III) separations are about 3.21 A. The coordination environment around the two terminal Mn(III) ions is distorted octahedral (O6) and shows Jahn–Teller elongation, while the central Mn(II) has a distorted five coordinated trigonal-bypyramidal (O5) coordination environment. In the central Mn(II) the equatorial Mn–O bond lengths are shorter than the axial Mn–O ones. The crystal packing of 1 involves hydrogen bonding between the complex and the uncoordinated methanol molecule. The analysis of the magnetic susceptibility data is consistent with ferromagnetic intramolecular coupling among the Mn(III) and the Mn(II) ions. The system can be interpreted in terms of a simple Heisenberg–Dirac–Van Vleck model H = −J(S1S2 + S2S3) with a magnetic coupling constant of J = 0.28 cm−1.

Electric field for tuning quantum entanglement in supported clusters

We show that quantum entanglement, nowadays so widely observed and used in a multitude of systems, can be traced in the atomic spins of metal clusters supported on metal surfaces. Most importantly, we show that it can be voluntarily altered with external electric fields. We use a combination of ab initio and model Heisenberg–Dirac–Van Vleck quantum spin Hamiltonian calculations to show, with the example of a prototype system (Mn dimers on Ag(0 0 1) surface), that, in an inherently unentangled system an electric field can ‘switch on’ the entanglement and significantly change its critical temperature parameter. The physical mechanism allowing such rigorous control of entanglement by an electric field is the field-induced change in the internal magnetic coupling of the supported nanostructure.

Polynuclear coordination compounds: a magnetostructural study of ferromagnetically coupled Ni4O4 cubane core motif

A series of tetranuclear nickel(II) complexes [NiII4L14(H2O)4] (1), [NiII4L24(MeOH)3(H2O)] (2), [NiII4L24(H2O)4] (3), [NiII4L34(MeOH)4] (4), [NiII4L44(MeOH)4] (5) have been synthesized by employing alkoxo–phenoxo ligands. All these compounds are characterized structurally and magnetochemically. Single-crystal X-ray diffraction studies suggest all the compounds contain a [Ni4(μ3-OR)4] cubane core motif with the alkoxo oxygen atoms of the ligands and octahedrally coordinated nickel(II) atoms placed alternatively at the corners of the cube. Magnetic susceptibility studies indicate a combination of ferromagnetic and antiferromagnetic exchange interactions between the four metal centers, resulting in an ST = 4 spin ground state in all the NiII4 complexes, which is confirmed by an isothermal magnetization measurement. These data were simulated using the Heisenberg–Dirac–Van Vleck (HDvV) spin Hamiltonian H = −2J1(S1·S2 + S3·S4) − 2J2(S1·S3 + S1·S4 + S2·S3 + S2·S4), affording the parameters J1 = −3.9 cm−1, J2 = +7.55 cm−1,g = 2.06 for 1, J1 = −2.45 cm−1, J2 = +7.3 cm−1,g = 2.055 for 2 and J1 = −3.2 cm−1, J2 = +7.8 cm−1,g = 2.045 for 3 and J1 = −3.9 cm−1, J2 = +8.4 cm−1,g = 2.13 for 4. The differences in the J values result from the differences in the Ni–O–Ni angles in the Ni4O4 cores. It is worth noting that small structural variations were found for the Ni–O–Ni angles of the Ni4O4 cubane cores of compounds 2 and 3 due to the change of terminal MeOH coordination in 2 to terminal H2O coordination in 3. In spite of these slight structural variations, both compounds 2 and 3 posses a ST = 4 spin ground state. Spin ladder calculations based on the magnetostructural data clearly indicate the |J2/J1| ratio is larger than 1.5 and in accord with a nonet spin ground state.

Electronic and Spin Structures of Polyoxometalate V15 from a First‐Principles Non‐Collinear Molecular‐Magnetism Approach

AbstractThe results of first‐principles calculations of the electronic structure of a spin‐frustrated V15 cluster with the use of a generalized density functional scheme that allows non‐collinear spin configurations are presented. By using the results of these calculations, it was possible to determine a Heisenberg–Dirac–Van Vleck (HDVV) Hamiltonian with 21 exchange coupling parameters that link the V ions with predominant spin density and the ligands that carry partially transferred spin density. The numerical procedure is based on a least‐squares fit of the results obtained by deviation of the direction of the magnetic moment on each atom around the energy minimum. The energy pattern was found from the effective HDVV Hamiltonian acting in the restricted spin space of the V ions by the application of the irreducible tensor operators (ITO) technique. Comparisons of the energy pattern with that obtained with the isotropic exchange models conventionally used for the analysis of this system and with the results of non‐collinear spin structure calculations show that our complex investigations provide a good description of the pattern of the spin levels and spin structures of the nanomagnetic V15 cluster. The results are discussed in view of the general problem of spin frustration related to the orbital degeneracy of the antiferromagnetic ground state.

Beyond the spin model: exchange coupling in molecular magnets with unquenched orbital angular momenta

In this critical review we review the problem of exchange interactions in polynuclear metal complexes involving orbitally degenerate metal ions. The key feature of these systems is that, in general, they carry an unquenched orbital angular momentum that manifests itself in all their magnetic properties. Thus, interest in degenerate systems involves fundamental problems related to basic models in magnetism. In particular, the conventional Heisenberg-Dirac-Van Vleck model becomes inapplicable even as an approximation. In the first part we attempt to answer two key questions, namely which theoretical tools are to be used in the case of degeneracy, and how these tools can be employed. We demonstrate that the exchange interaction between orbitally degenerate metal ions can be described by the so-called orbitally-dependent exchange Hamiltonian. This approach has shown to reveal an anomalously strong magnetic anisotropy that can be considered as the main physical manifestation of the unquenched orbital angular momentum in magnetic systems. Along with the exchange coupling, a set of other interactions (such as crystal field effects, spin-orbit and Zeeman coupling), which are specific for the degenerate systems, need to be considered. All these features will be discussed in detail using a pseudo-spin-1/2 Hamiltonian approach. In the second part, the described theoretical background will be used to account for the magnetic properties of several magnetic metal clusters and low-dimensional systems: (i) the dinuclear face-sharing unit [Ti(2)Cl(9)](3-), which exhibits a large magnetic anisotropy; (ii) the rare-earth compounds Cs(3)Yb(2)Cl(9) and Cs(3)Yb(2)Br(9), which, surprisingly, exhibit a full magnetic isotropy; (iii) a zig-zag Co(II) chain exhibiting unusual combination of single-chain magnet behavior and antiferromagnetic exchange coupling; (iv) a trigonal bipyramidal Ni(3)Os(2) complex; (v) various Co(II) clusters encapsulated by polyoxometalate ligands. In the two last examples a pseudospin-1/2 Hamiltonian approach is applied to account for the presence of exchange anisotropy (150 references).

ChemInform Abstract: Magnetic Exchange Between Metal Ions with Unquenched Orbital Angular Momenta: Basic Concepts and Relevance to Molecular Magnetism

AbstractReview: 221 refs.

Exchange Interactions in Systems with Multiple Magnetic Sites

Nonequivalent magnetic interactions in systems with multiple magnetic centers can be explored through a proper description of exchange coupling. The magnetic exchange coupling constant (J) in systems with two magnetic sites is reliably estimated using Heisenberg-Dirac-van Vleck (HDVV) model through broken symmetry approach (BS) within a density functional theory (DFT) framework. However, in case of systems with multiple magnetic centers, exchange coupling constants, evaluated through state-of-the-art techniques, are often found to be inadequate to produce a correct fingerprint of the nature of magnetic interactions therein. This work suggests a new scheme to estimate exchange coupling constants in such systems. In this strategy, distribution of spins on magnetic sites in the ground state of systems with multiple magnetic centers is computed. On the basis of this spin mapping, exchange coupling constants between specific pairs are estimated through BS-DFT approach while keeping all other paramagnetic atoms magnetically inactive. Nonetheless, the effect of magnetically inert paramagnetic sites is already taken into account by the process of spin mapping, which is further justified through expressing the HDVV Hamiltonian in terms of spin density operators. We employ this technique to hypothetical benchmark systems, H(3)He(3) and H(4)He(4) followed by real molecules, cationic manganese trimer, 1,3,5-benzenetriyltris (N-tert-butyl nitroxide), and a pentanuclear manganese complex. Results are found to be concordant with the already established nature of magnetic interaction in these systems. This strategy is different from the most popular scheme to compute J in systems with multiple magnetic centers in the sense that it avoids the formation of a large matrix out of different spin configurations and thus provides a reliable and computationally economic way to address the magnetic interactions in non isotropic systems with multiple magnetic sites.

DFT broken-symmetry exchange couplings calculation in a 1D chain of bridged iron basic carboxylates

DFT broken-symmetry calculations at the B3LYP level were carried out to evaluate the exchange coupling constants defined by the Heisenberg–Dirac–van Vleck spin Hamiltonian (HDvV), Ĥ = −2 JŜ aŜ b, in a 1D chain of iron basic carboxylate cores [Fe 3O(Piv) 6(H 2O)] bridged by dicyanamide, and two related trinuclear Fe 3O moieties. The chain complex was modeled as two Fe 3O units that preserve all features of the repetitive unit in the infinite real system. All geometries were taken from the crystallographic data previously reported. The obtained calculated values for the J constants are in good agreement with experimental results. The weak anti-ferromagnetic inter-Fe 3O core interaction along the chain is also reasonably accounted by the calculations. This methodology appears as a useful tool in the theoretical evaluation of exchange coupling constants in 1D systems.

Magnetic properties of [formula omitted] compounds [formula omitted

In the present work the synthesis and magnetic properties of three compounds with formula KNa M Si 4 O 10 ( M = Mn , Fe , Cu ) are described. These compounds are synthetic analogs to natural occurring minerals: fenaksite— Fe 2 + , litidionite— Cu 2 + and manaksite— Mn 2 + . The crystal structure consists of complex silicate chains interconnected by edge-sharing M O 5 square pyramids dimerized in M 2 O 8 units. This charged metal–silicate framework is compensated by monovalent alkali metals ( K + , Na + ). Despite the isostructural nature of these compounds, and the consequent similarity of the M–O topology, that rules the magnetic properties, these are quite different. While there are antiferromagnetic (AF) interactions within the Mn and Cu dimers (exchange interaction J = - 3.83 ( 1 ) and - 2.86 ( 3 ) K , respectively) with no long range order, a ferromagnetic interaction within Fe dimers ( J =+ 7.6 ( 1 ) K ) is observed with a three-dimensional transition at 9 K to an AF ground state. The magnetic behavior is analyzed using the HDVV (Heisenberg–Dirac–Van Vleck) formalism and discussed in the light of the crystal structure.