Fit Of Magnetic Susceptibility Data Research Articles

Long-Range Ferromagnetic Exchange Interactions Mediated by Mn-CeIV-Mn Superexchange Involving Empty 4f Orbitals.

Reactions involving reductive aggregation of MnO4- in methanol in the presence of CeIV and an excess of carboxylic acid have led to the synthesis of structurally related Ce/Mn clusters, [Ce3Mn5O8(OMe)(O2CBut)13(MeOH)] (1) and [Ce2Mn3O5(O2CPh)9(MeOH)3] (2), containing at least one {Mn2Ce2O4} cubane unit. The cores of both clusters contain Mnx units separated by three (1) or two (2) CeIV ions. Fits of variable-temperature, solid-state dc and ac magnetic susceptibility data reveal dominant ferromagnetic interactions within 1 and 2, resulting in the maximum S = 17/2 and S = 5 ground state spins, respectively, and thus suggesting significant ferromagnetic (F) interactions between the Mnx units that are ≥6 Å apart and separated by four intervening bonds through diamagnetic CeIV. Fits of magnetic susceptibility data also revealed unusual long-range F interactions, and this finding was further supported by high-field EPR measurements and simulations. Density functional theory calculations and a Wannier function analysis confirm long-range interactions and indicate a Mn-Ce-Mn superexchange pathway via Mn-d/Ce-f orbital overlap/hybridization.

Analysis of Exchange Interactions in Dimers of Mn3 Single-Molecule Magnets, and Their Sensitivity to External Pressure

In light of the potential use of single-molecule magnets (SMMs) in emerging quantum information science initiatives, we report first-principles calculations of the magnetic exchange interactions in [$\mathrm{Mn}_{3}$]$_{2}$ dimers of $\mathrm{Mn}_3$ SMMs, connected by covalently-attached organic linkers, that have been synthesized and studied experimentally by magnetochemistry and EPR spectroscopy. Energy evaluations calibrated to experimental results give the sign and order of magnitude of the exchange coupling constant ($J_{12}$) between the two $\mathrm{Mn}_{3}$ units that match with fits of magnetic susceptibility data and EPR spectra. Downfolding into the $\mathrm{Mn}$ $d$-orbital basis, Wannier function analysis has shown that magnetic interactions can be channeled by ligand groups that are bonded by van der Waals interaction and/or by the linkers via covalent bonding of specific systems, and effective tight-binding Hamiltonians are obtained. We call this long-range coupling that involves a group of atoms a collective exchange. Orbital projected spin density of states and alternative Wannier transformations support this observation. To assess the sensitivity of $J_{12}$ to external pressure, stress-strain curves have been investigated for both hydrostatic and uniaxial pressure, which have revealed a switch of $J_{12}$ from ferromagnetic to antiferromagnetic with increasing pressure.

Syntheses, crystal structures, and magnetic properties for two spin-ladder complexes based on bis(2-thioxo-1,3-dithiole-4,5-dithiolato)nickelate monoanion building block

Two isostructural complexes based on bis(2-thioxo-1,3-dithiole-4,5-dithiolato)nickelate monoanion ([Ni(Dmit)2]−) building block, (C19H11NNiF3S10 (I) and C18H10N2F3NiS10 (II)), have been synthesized and characterized structurally and magnetically. Two complexes crystallize in monoclinic space group \(P\bar 1\) with very similar cell parameters and packing structures. The planar [Ni(Dmit)2]− monoanions form face-to-face π-type dimer, and the neighboring dimers are aligned into a ladder-type arrangement via lateral-to-lateral S…S contacts along x axis in the crystals of I and II. Two complexes exhibit similar magnetic behaviors, and their magnetic susceptibility data can be fitted to a Heisenberg antiferromagnetic two-legged spin ladder formula in high-temperature region and reproduced well by the Troyer expression in low-temperature region. The spin-gap values, obtained, respectively, from the fits of magnetic susceptibility data in high- and low-temperature regions, are closed to each other, indicating the chose magnetic exchange model and the results of fits are reasonable.

Magnetic properties of Zn0.9(Mn0.05,Ni0.05)O nanoparticle: Experimental and theoretical investigation

The crystalline and magnetic properties of 5% Mn and 5% Ni co-doped nanocrystalline ZnO particles, obtained by the co-precipitation method, are performed. X-ray diffraction data revealed that Zn0.90Mn0.05Ni0.05O crystallizes in the monophasic wurtzite structure. DC magnetization measurement showed that the samples are paramagnetic at room temperature. However, a large increase in the magnetization is observed below 50K. This behavior, along with the negative value of Weiss constant obtained from the linear fit of magnetic susceptibility data below room temperature, indicates ferrimagnetic behavior. The ferrimagnetic properties observed at low temperature are explained and confirmed from ab-initio calculations using the Korringa–Kohn–Rostoker method combined with the coherent potential approximation.

Comparison of Semiempirical ZILSH and DFT Calculations of Exchange Constants in Fe4 Butterfly Complexes.

Magnetic interactions in a series of tetranuclear Fe(3+) complexes with the butterfly core structure have been studied with semiempirical ZILSH and density functional theory (DFT) calculations (B3LYP functional). A theoretical analysis of a previously used method of estimating exchange constants from a restricted number of spin configurations reveals systematic errors arising from asymmetry in the complexes, which cause large variations in results with different choices of spin configurations. Correction factors are derived that yield the correct results obtained from full configuration space (FCS) calculations. Exchange constants obtained from DFT FCS calculations for the "body-body" interaction were large and ferromagnetic, in disagreement with values obtained from empirical fits of magnetic susceptibility data for the complexes, established magnetostructural correlations in polynuclear Fe(3+) complexes, and ZILSH calculations. DFT calculations also gave unreasonably large antiferromagnetic exchange constants for interaction between "wingtip" ions that are not directly bridged, again in disagreement with ZILSH calculations. Estimates of exchange constants for interaction of body and wingtip ions obtained with ZILSH and DFT were similar, with the ZILSH values in slightly better agreement with empirical fits. Considering all interactions, the ZILSH method provides results in better accord with experiment than DFT for these complexes. Additional comparisons of exchange constants obtained with different spin coupling schemes showed that values appropriate for two-center spin eigenfunctions gave consistently better results than values calculated with the local spin operator. The effect of basis set was found to be very small. A brief analysis of these findings is given.

Carboxylate-Bridged Diiron(II) Complexes: Synthesis, Characterization, and O2-Reactivity of Models for the Reduced Diiron Centers in Methane Monooxygenase and Ribonucleotide Reductase

Diiron(II) complexes with an oxygen-rich coordination environment were assembled with the dinucleating dicarboxylate ligands m-xylylenediamine bis(Kemp's triacid)imide (H2XDK) and the more soluble analogue m-xylylenediamine bis(propyl Kemp's triacid)imide (H2PXDK). X-ray crystallographic analysis revealed that, in most of the complexes, only one monodentate N-donor ligand is bound to each iron(II) ion. In addition to XDK and PXDK, a variety of other ligands bridge the dimetallic core including chloride, fluoride, triflate, or carboxylate. The tris(carboxylate-bridged) complexes [Fe2(μ-XDK)(μ-O2CPh)(ImH)2(O2CPh)(MeOH)] (3) and [Fe2(μ-O2CC(CH3)3)(μ-PXDK)(N-MeIm)2(O2CC(CH3)3)] (4) have the same ligand composition as the diiron(II) cores in the hydroxylase component of methane monooxygenase (MMO) and in the R2 protein of ribonucleotide reductase (RNR). The coordination environments of the two iron centers in 3 and 4 are inequivalent, with one iron being 6-coordinate and the other being 4-coordinate. The bridging benzoate and pivalate ligands have an unusual coordination mode with a Fe−O−C bond angle close to 180°. Fits of magnetic susceptibility data collected for several of the complexes between 300 and 4 K indicated that the two iron(II) centers are weakly antiferromagnetically coupled with a coupling constant which does not depend on the nature of the bridging ligands. Mössbauer spectra of polycrystalline and frozen THF solution samples of 4 exhibited two overlapping doublets of equal intensity, reflecting the different coordination environments of the two iron(II) ions. The nearly identical Mössbauer parameters for the solid and frozen solution samples indicate that the dinuclear core remains intact upon dissolution. Stopped-flow studies of the reaction of 3 and 4 with O2 in THF showed the rapid formation (kψ ≈ 74 s-1 for 3 at 202.5 K and kψ ≈ 300 s-1 for 4 at 197 K) of colored intermediates with broad absorption maxima near 660 and 670 nm, respectively. These values are characteristic of peroxo-to-iron charge-transfer bands and similar to that observed for the (μ-peroxo)diiron(III) intermediate (Hperoxo) in the MMO reaction cycle.

Derivatives of the energy levels of a molecular system with respect to parameters of the Hamiltonian, and their application to magnetic susceptibility calculations and least-squares fitting

Formulae are given for the first, second, and third partial derivatives, with respect to the parameters ai, of the eigenvalues of a matrix ℋ=Σaiℋi(where ℋi are Hermitian or real symmetric matrices), in terms of the eigenvalues and eigenvectors of ℋ. The matrix ℋ may also include bilinear terms of the type aiajℋij. If ℋ is the Hamiltonian matrix for a molecular system in a magnetic field, so that one of the ai is the applied field strength and the others represent features of the model such as crystal-field, spin–orbit coupling, and exchange parameters, these results can be used to obtain expressions for the paramagnetic susceptibility which are exact even at very low temperatures, within the limitations of the model and the accuracy with which the eigenvalues and eigenvectors of ℋ are known. The formulae can also be used to set up least-squares normal equations determining the values of the parameters that give the best fit to experimental susceptibility data (or other observed properties of the system), and to solve those equations iteratively. The formulae are likely to be especially useful whenever it is impossible, because of the complexity of the secular equation, to write explicit expressions for the energy levels and to calculate their derivatives by analytic differentiation, but the generality of the method may make it useful even when analytic differentiation is possible. Examples of its use in the least-squares fitting of magnetic susceptibility data are given.