DFT study of structure–properties correlations in [MnTPP][TCNE] quasi-one-dimensional molecular magnets

We report the first band structure calculations of the quasi-one-dimensional [MnTPP][TCNE] compounds (TPP = meso-tetraphenylporphyrinato, TCNE = tetracyanoethylene), based on Density Functional Theory (DFT) methods, in order to interpret the magnetic ordering in these prototypic systems. We compare and contrast the results of broken-symmetry DFT calculations for extended systems, with periodic boundary conditions, and for finite systems, magnetic dimers modeling the actual molecular magnets. By varying systematically the main angles, we are able to determine the geometry dependence of the exchange interaction. Structure–properties correlations in these charge-transfer salts reveal the determinant role of the Mn-(N≡C)_TCNE bond angle on the strength of the ferrimagnetic coupling between the S ₁ = 2 spin located on the Mn^III-porphyrin donor and the S ₂ = 1/2 spin positioned on the cyanocarbon acceptor. When the Mn-(N≡C)_TCNE angle is decreased, the intrachain magnetic coupling strengthens, correlated with the increase in the d_z² - p* d_{{z^{2} }} - \pi * orbital overlap. The exchange coupling constants resulting from DFT calculations of extended systems, with periodic boundary conditions, were found to be consistent with those obtained for the dimers, but systematically smaller. The exchange constants vary strongly with the functional used, hybrid functionals such as B3LYP leading to results that better correlate with the experimental mean-field critical temperatures. The coupling constant varies significantly with the type of broken-symmetry approach, depending on the overlap between magnetic orbitals, but weakly on the basis set once polarization effects are included. The electronic structure calculations for the extended systems provide a density of states consistent with the energy spectrum of the corresponding dimer, allowing for an intuitive explanation of the intrachain ferrimagnetic ordering.     

The DFT rationalization of exchange and anisotropy in one-dimensional d-p magnets: The [MnIII(porphyrin)][TCNE] case study

We report here numerical experiments, modeling and interpretations dealing with the magnetic interactions necessary for building nano-scale magnets in quasi-one-dimensional systems based on the assembling of [Mn(porphyrin)]⁺ magnetically anisotropic d units and TCNE-p-type spin carriers. The magnetic ordering and its coupling parameter are studied by Broken Symmetry DFT calculations for various model structures, allowing for the rationalization of geometry dependence of the effective exchange. The roles of the phenyl substituent, as well as of the basis set and the DFT functional used in the computation are discussed. The intrinsic anisotropy of these systems is studied in an original manner, extracting Ligand Field and Spin Orbit parameters by combined fits to non-relativistic and relativistic DFT calculations, allowing the explicit estimation of the Zero Field Splitting parameters.     

Selective substitution of vanadium for molybdenum in Sr2(Fe1−xVx)MoO6 double perovskites

The crystal and magnetic structures of Sr₂(Fe_1−xV_x)MoO₆ (0.03?x?0.1) compounds are refined by alternately using X-ray powder diffraction (XRD) and neutron powder diffraction (NPD) data collected at room temperature. The refinement results reveal that the V atoms selectively occupy the Mo sites instead of the Fe sites for x?0.1. The 3d/4d cation ordering decreases with the increase of the V content. Slight distortions in the lattice and metal octahedra are shown at 300 K, and the distortions increase at 4 K. The magnetic structure at 4 K can be modeled equally well with the moments aligning along [001], [110] or [111] directions. The total moments derived from the NPD data for the [110] and [111] direction models agree well with the magnetic measurements, whereas the [001] model leads to a smaller total moment. Bond valence analysis indicates that Sr ions are properly located in the structure and Mo ions are compatible with both the Fe sites and the Mo sites. The electronic effects are suggested to be responsible for the selective occupation of the V on the Mo sites due to the different distortions of the FeO₆ and MoO₆ octahedra.     

Nature of the magnetic interaction between Fe-porphyrin molecules and ferromagnetic surfaces

We have investigated computationally the magnetic spin state of free metalloporphyrins and how magnetic ordering in metalloporphyrins can be induced through contact with the metallic surface and what the origin of the exchange interaction is. To this end, we performed density functional theory (DFT) and DFT + U studies for a series of isolated, ligated as well as unligated Fe-porphyrin (FeP) molecules as well as various FeP molecules on surfaces. Our calculations for isolated FePs clearly demonstrate that the usual DFT-based exchange-correlation functionals (such as the generalized gradient approximation) cannot predict the experimental high-spin ground state of these molecules. Instead, one has to resort to DFT + U calculations with a Coulomb U of about 4 eV on the Fe atoms, to obtain the correct single-molecule spin state. The magnetic interaction between FeP and a Co surface has been studied computationally with the DFT and DFT + U approaches. Our total energy DFT and DFT + U calculations predict an optimal Fe – substrate distance of 3.5 Å and a ferromagnetic exchange coupling of FeP to the substrate, in accordance with recent experiments. For Fe-porphyrin chloride (FePCl), on the other hand, an antiferromagnetic coupling is computed to be more favorable. Our study demonstrates that due to an indirect exchange interaction, which is mediated through the four nitrogen atoms, ferromagnetic ordering on the FeP is stabilized.     

Spectroscopic study of (two-dimensional) molecule-based magnets: [M(II)(TCNE)(NCMe)2][SbF6] (M = Fe, Mn, Ni)

The M-[TCNE] (M = 3d metal; TCNE = tetracyanoethylene) system is one of the most interesting classes of molecule-based magnets, exhibiting a plethora of compositions and structures (inorganic polymer chains, 2D layers, 3D networks, and amorphous solids) with a wide range of magnetic ordering temperatures (up to 400 K). A systematic study of vibrational (both infrared and, for the first time, Raman) properties of the family of new TCNE-based magnets of M(II)(TCNE) (NCMe)(2)[SbF(6)] [M = Mn, Fe, Ni] composition is discussed in conjunction with their magnetic behavior and newly reso-lved crystal structures. The vibrational properties of the isolated TCNE(●-) anion in the paramagnetic Bu(4)N [TCNE(●-)] salt and recently characterized 2D layered magnet Fe(II)(TCNE)(NCMe)(2)[FeCl(4)] are also reported for comparison. Additionally, a linear correlation between ν(C=C) (a(g)) frequency of the TCNE ligand and its formal charge Z (the spin density on the π* orbital), Z = [1571 - ν(C=C) (a(g))]/154.5 [e], is presented. It is shown that monitoring Z by Raman spectroscopy is of great use in providing information that allows understanding the peculiarity of the superexchange interaction in M-[TCNE] magnets and establishing the structure-magnetic properties correlations in this class of magnetic material.     

Hydrothermal synthesis, characterization and composition-dependent magnetic properties of LaFe1−xCrxO3 system (0≤x≤1)

Hydrothermal synthesis, characterization and magnetic properties of a series of ABO₃-perovskites LaFe_1−xCr_xO₃ (0≤x≤1) are reported. The alkalinity in initial reaction mixtures plays a critical role in controlling the designed stoichiometry of the final compositions. Their magnetic properties are strongly dependent on the compositions and a maximum magnetic moment is found for the sample at x=0.5. Weak ferromagnetic interaction observed for the samples from x=0 to 0.9 arises from the presence of Fe-O-Fe antisymmetric exchange and Fe-O-Cr superexchange interaction. The weak ferromagnetism as well as the linear variation of the lattice parameters implies the possible random distribution of Fe and Cr ions in B sites of the perovskites. The evolution of magnetic ordering transition temperatures has a close relationship with substituent ratios, for the competition of antiferromagnetism and ferromagnetism. The saturated magnetic moment shows a great improvement compared with that for the samples synthesized by solid state method.     

First principles calculations of electronic structure and magnetic properties of Cr-based magnetic semiconductors Al1−xCrxX (X=N, P, As, Sb)

First principles calculations based on the density functional theory (DFT) within the local spin density approximation are performed to investigate the electronic structure and magnetic properties of Cr-based zinc blende diluted magnetic semiconductors Al_1−xCr_xX (X=N, P, As, Sb) for 0≤x≤0.50.The behaviour of magnetic moment of Al_1−xCr_xX at each Cr site as well as the change in the band gap value due to spin down electrons has been studied by increasing the concentration of Cr atom and through changing X from N to Sb. Furthermore, the role of p-d hybridization is analyzed in the electronic band structure and exchange splitting of d-dominated bands. The interaction strength is stronger in Al_1−xCr_xN and becomes weaker in Al_1−xCr_xSb. The band gap due to the spin down electrons decreases with the increased concentration of Cr in Al_1−xCr_xX, and as one moves down along the isoelectronic series in the group V from N to Sb. Our calculations also verify the half-metallic ferromagnetic character in Cr doped AlX.     

Organic and Organometallic Molecular Magnetic Materials—Designer Magnets

Magnets composed of molecular species or polymers and prepared by relatively low-temperature organic synthetic methodologies are a focus of contemporary materials science research. The anticipated properties of such molecular-species-based magnetic materials, particularly in combination with other properties associated with molecules and polymers, may enable their use in future generations of electronic, magnetic, and/or photonic/photronic devices ranging from information storage and magnetic imaging to static and low-frequency magnetic shielding. A tutorial of typical magnetic behavior of molecular materials is presented. The three distinct models (intramolecular spin coupling through orthogonal orbitals in the same spatial region within a molecule/ion, intermolecular spin coupling through pairwise “configuration interaction” between spin-containing moieties, and dipole—dipole, through-space interactions) which enable the design of new molecular-based magnetic materials are discussed. To achieve the required spin couplings for bulk ferro- or ferrimagnetic behavior it is crucial to prepare materials with the necessary primary, secondary, and tertiary structures akin to proteins. Selected results from the worldwide effort aimed at preparing molecular-based magnetic materials by these mechanisms are described. Some organometallic solids comprised of linear chains of alternating metallocenium donors (D) and cyanocarbon acceptors (A) that is, …?D^?+ A^?? D^?+ A^??…?, exhibit cooperative magnetic phenomena. Bulk ferromagnetic behavior was first observed below the critical (Curie) temperature T_c of 4.8 K for [Fe^III(C₅Me₅)₂]^?+ [TCNE]^?? (Me = methyl; TCNE = tetracyanoethylene). Replacement of Fe^III with Mn^III leads to a ferromagnet with a T_c of 8.8 K in agreement with mean-field models developed for this class of materials. Replacement with Cr^III, however, leads to a ferromagnet with a T_c lowered to 3.65 K which is at variance with this model. Extension to the reaction of a vanadium(o) complex with TCNE leads to the isolation of a magnet with a T_c ≈ 400 K, which exceeds the thermal decomposition temperature of the material. This demonstrates that a magnetic material with a T_c substantially above room temperature is achievable in a molecule/organic/polymeric material. Finally, a new class of one-dimensional ferrimagnetic materials based on metalloporphins is discussed.     

Structural investigation of the Zn1−xCdxSb solid solution by density-functional theory approach

A peculiar behaviour was already reported in literature from experimental investigations in the Zn_1?xCd_xSb solid solution around x = 0.5. This behaviour was assumed to be linked to an ordering in the phase; however this assumption was never confirmed. The aim of this work was to understand this behaviour from a theoretical point of view. DFT calculations were performed to calculate the energy and the lattice parameters for all the possible structures of Zn_1?xCd_xSb with several compositions (x = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0). The results show that an ordering appears in the most stable structure for x = 0.5. This ordering consists in stacked planes each containing only one chemical species.     

Magnetic properties of DyCo5 and TbCo5 intermetallics from the electronic structure calculations

LSDA and LSDA+U calculations, with spin-orbit coupling (SOC) included, were performed for DyCo₅ and TbCo₅ intermetallic compounds. In the case of magnetic moments, LSDA-SOC calculations give results in good agreement with the experimental data. However, LSDA has shown to be unable to predict relative stabilities of ferromagnetic and ferrimagnetic configurations of the 4f and 3d spin sublattices giving the wrong result that the ferromagnetic configuration is more stable. LSDA+U method cures this problem and gives correct result. Additionally, within the accuracy of available experimental data, the corresponding effective exchange fields are in reasonable agreement with experiment.     

Ab initio study of the magnetic behavior of four dithiadiazolyl radical compounds

We have studied, by means of ab initio calculations, the magnetic interaction mechanisms in four radical crystals, X–C₆F₄–CNSSN (X = O₂N, α-NC, β-NC, Br), which has allowed us to explain their different magnetic behaviour (ferromagnetism, antiferromagnetism, paramagnetism, spin frustration, etc.). First, we have identified the magnetic exchange pathways considering those with distances between two atoms of different dithiadiazolyl rings shorter than 7 Å and those with an intermolecular distance between an atom of the heterocyclic ring and an atom in a neighbouring radical shorter than 4 Å. Second, the calculations have been carried out in the framework of the DFT Broken Symmetry. Following this procedure we have determined the magnitude and the sign of the relevant coupling constants for the X–C₆F₄–CNSSN (X = O₂N, α-NC, β-NC, Br) radicals. In the cases where the radicals order magnetically, ordering temperatures determined with our ab initio calculations agree very well with the experimental ones. Thus, in the case of the O₂N derivative ferromagnetic ordering is observed below 1.3 K, in very good agreement with an ordering temperature around 1.6 K predicted from our calculated exchange constants and using a mean field approximation.     

Germanium,carbon‐germanium,and silicon‐germanium triangulenes

A series of germanium‐containing triangular molecules have been studied by density functional theory (DFT) calculations. The triangulene topology of the compounds provides for their high‐spin ground states and strong sign alternation of spin density and atomic charge distributions. High values of the exchange coupling constants witness ferromagnetic ordering of electronic structures of all studied triangulenes. The compounds bearing more electronegative atoms in a‐positions of the triangular networks possess higher aromatic character and stronger ferromagnetic ordering. © 2015 Wiley Periodicals, Inc.     

Theoretical studies on ferromagnetic behavior of [Cr(C5(CH3)5)2]+[TCNE]− and [Mn(C5(CH3)5)2]+[TCNQ]−

By using broken-symmetry hybrid-DFT (UB3LYP and UB2LYP) calculation, the effective exchange integrals (J values) of [Cr(C₅(CH₃)₅)₂]⁺[TCNE]⁻[Cr(C₅(CH₃)₅)₂]⁺ and [Mn(C₅(CH₃)₅)₂]⁺[TCNQ]⁻[Mn(C₅(CH₃)₅)₂]⁺ were determined theoretically. Those calculated models were reduced to 3-spin-sites models from X-ray crystallographic data of charge transfer 3D crystal. The calculated results showed that effective exchange integrals were positive and the signs of spin densities on the cyclopentadienyl rings were negative. These results supported the so-called McConnell I mechanism for ferromagnetism proposed by Kollmar et al. and our previous calculations. Natural orbital analysis made it clear that the orbital overlap between SOMO on metals and SOMO on TCNE or TCNQ cations was nearly zero. These results indicated that orbital orthogonality was an important key factor for explaining the ferromagnetism of those systems.     

A family of porous magnets, [M3(HCOO)6] (M = Mn,Fe, Co and Ni)

A family of porous magnets of [M₃(HCOO)₆] (M = Mn, Fe, Co and Ni) with open diamond framework based on M-centred MM₄ tetrahedral nodes, can be prepared by conventional solution chemistry method. They display permanent porosity, stability for thermal treatment, guest removal, and guest inclusion for a wide spectrum of both polar and non-polar guests of different size. The porous magnets show 3D long-range magnetic ordering and guest-modulated magnetic properties due to the subtle structure change of the magnetic framework that conforms to the guests and the nature of host–guest interaction. The dilution of [Fe₃(HCOO)₆] framework by diamagnetic zinc ion results in a mixed-metal porous [Fe_xZn_3−x(HCOO)₆] series showing gradual evolution from 3D long-range ordering to spin glass then superparamagnet and finally paramagnet.     

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), ? = ?2J?_a?_b, in a 1D chain of iron basic carboxylate cores [Fe₃O(Piv)₆(H₂O)] bridged by dicyanamide, and two related trinuclear Fe₃O moieties. The chain complex was modeled as two Fe₃O 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-Fe₃O 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.     

A tetranuclear nickel(II) heterocubane complex of a bidentate N,O-hydroxymethyl-oxazoline ligand. Synthesis,characterization, magnetic measurements and DFT investigations

Synthesis, structural, and magnetochemical characterization of the tetranuclear [Ni₄O₄] heterocubane cluster [NiCl(L1)(MeOH)]₄, 1, employing the bidentate N,O-ligand 2-hydroxymethyl-2-oxazoline, HL1, is reported. In the solid state, each nickel(II) is coordinated in a distorted octahedral environment, located on four corners of a [Ni₄(μ₃-O)₄] cubane core motif. Measurements of the magnetic susceptibility in solution (Evans method) as well as in the solid state (magnetic susceptibility balance) gave values of 5.74 and 6.08 unpaired electrons, respectively, indicating a spin ground state of S = 3. At maximum spin degeneracy (S = 4), eight unpaired electrons would be expected. Magnetic properties were further evaluated by SQUID measurements of 1, confirming the spin ground state of 1 to be S = 3. The observed deviation is caused by antiferromagnetic coupling between the four Ni atoms. In addition, broken-symmetry DFT calculations confirmed an overlap of magnetic orbitals resulting in exchange coupling between the four nickel(II) ions of 1.     

Coordination complexes with cis-TCNE radical anion ligands. models of M[TCNE]2 magnets

The synthesis and characterization of two manganese(II) complexes formally each featuring two cis-tetracyanoethylenide radical anionic ligands (TCNE*/-) are reported. In each case, tris(pyrazol-1-ylmethyl)amine serves as a capping ligand, blocking three facial coordination sites. Crystal structures show that the two TCNE anions in each molecule exhibit an intramolecular stacking interaction that forms what can be considered a coordinated (TCNE2)2- moiety. These molecules are presumed to be structural models of some of the local bonding in the family of amorphous, ferrimagnetic, M[TCNE]2.y(solvent) coordination polymer magnets. Magnetic measurements indicate that the (TCNE2)2- bridge is diamagnetic and not a good mediator of magnetic exchange, a result that might explain the observed lower ordering temperatures in some of the polymer magnets.     

Ferromagnetic anti-PbFCl-type ZnMnSb

In the Zn_xMn_2?xSb system, the tetragonal, anti-PbFCl structure occurs between Mn₂Sb and ZnMnSb. The latter is essentially an ordered compound with Zn occupying the ninefold coordinated site (II), and Mn the tetrahedral layer positions (I). Magnetic measurements indicate ferromagnetic ordering of Mn as in isostructural AlMnGe, GaMnGe, and the Mn(I) substructure of ferrimagnetic Mn₂Sb. The observed moment of ZnMnSb and the Zn_xMn_2?xSb single-phase field are consistent with the unusual low spin d⁶ configuration (+1 formal oxidation state) postulated for Mn(I) in Mn₂Sb, AlMnGe, and GaMnGe.