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).     

Exchange coupling mediated through-bonds and through-space in conformationally constrained polyradical scaffolds: calix[4]arene nitroxide tetraradicals and diradical

Calix[4]arenes constrained to the 1,3-alternate conformation and functionalized at the upper rim with four and two tert-butylnitroxides have been synthesized and characterized by X-ray crystallography, magnetic resonance (EPR and (1)H NMR) spectroscopy, and magnetic studies. The 1,3-alternate nitroxide tetraradical and diradical provide unique polyradical scaffolds for dissection of the through-bond and through-space intramolecular exchange couplings. In addition, detailed magnetic studies of the previously reported calix[4]arene nitroxide tetraradical, which possesses cone conformation in solution, reveal conformational dependence of exchange coupling. Through-bond coupling between the adjacent nitroxide radicals is mediated by the nitroxide-m-phenylene-CH(2)-m-phenylene-nitroxide coupling pathway, and through-space coupling is found between the diagonal nitroxide radicals at the conformationally constrained N...N distance of 5-6 A. Magnetic studies of the calix[4]arene polyradical scaffolds in frozen solutions show that the through-bond exchange coupling in the 1,3-alternate calix[4]arene tetraradical is antiferromagnetic, while that in cone calix[4]arene tetraradical is ferromagnetic. The through-space exchange couplings are antiferromagnetic in both cone and 1,3-alternate calix[4]arene tetraradical, as well as in the 1,3-alternate calix[4]arene diradical. The exchange coupling constants (|J/k|) are of the order of 1 K.     

Magneto-structural correlations in Cu(tn)Cl2 (tn = 1,3-diaminopropane): two-dimensional spatially anisotropic triangular magnet formed by hydrogen bonds

A novel polymeric one-dimensional compound Cu(tn)Cl2 (tn = 1,3-diaminopropane) was prepared and structurally characterized, and its spectral, magnetic, thermodynamic, and thermal properties were studied. The unique structure shows ladderlike chains composed of Cu(II) atoms and chloro bridging ligands [Cu(-mu(3)-Cl-)Cu2] running along the crystallographic c axis. The coordination geometry about copper (4 + 2) approximates that of a strongly elongated octahedron. The equatorial plane of the coordination octahedron is formed by a chelate N-bonded tn ligand and two chloro ligands. One of the chloro ligands is terminal, and the other one, mu3-Cl-, forms two additional longer bonds to the neighboring copper atoms and thus occupies the axial octahedral positions. The electronic ground state of the Cu(II) ion is of d(z)2 symmetry and suggests the activation of intraladder and interladder Cl...H-N hydrogen bonds as exchange paths that form a two-dimensional pattern of a triangular symmetry. The interaction due to the hydrogen bonds seems to play an important role in molecular packing and magnetic coupling. The studies of magneto-structural correlations including electron paramagnetic resonance measurements and thermodynamic and magnetic properties revealed a two-dimensional character of magnetic correlations with the effective intralayer exchange coupling J/k(B) approximately -3 K. No phase transition to the ordered state has been observed down to 60 mK. Cu(tn)Cl2 with the interlayer coupling J' approximately 10(-3)J and moderate intralayer interaction represents an excellent example of a two-dimensional magnetic system.     

Physical analysis of the through-ligand long-distance magnetic coupling: spin-polarization versus Anderson mechanism

The physical factors governing the magnetic coupling between two magnetic sites are analyzed and quantified as functions of the length of the bridging conjugated ligand. Using wave-function-theory based ab initio calculations, it has been possible to separate and calculate the various contributions to the magnetic coupling, i.e. the direct exchange, the spin polarization and the kinetic exchange. It is shown in model systems that while the Anderson mechanism brings the leading contribution for short-length ligands, the spin polarization dominates the through-long-ligand couplings. Since the spin polarization decreases more slowly than the kinetic exchange, highly spin polarizable bridging ligands would generate a good magneto-communication between interacting magnetic units.     

Origin of the magnetic bistability in molecule-based magnets: a first-principles bottom-up study of the TTTA crystal

The magnetic bistability present in some molecule-based magnets is investigated theoretically at the microscopic level using the purely organic system TTTA (1,3,5-trithia-2,4,6-triazapentalenyl). The TTTA crystal is selected for being one of the best-studied molecule-based systems presenting magnetic bistability. The magnetic properties of the high- and low-temperature structures (HT and LT phases, respectively) are accurately characterized by performing a First-Principles Bottom-Up study of each phase. The changes that the magnetic exchange coupling constants (J(AB)) undergo when the temperature is raised (LT → HT) or lowered (HT → LT) are also fully explored in order to unravel the reasons behind the presence of these two different pathways. The triclinic LT phase is diamagnetic due to the fact that the nearly eclipsed π dimer is effectively magnetically silent and not to formation of a covalent bond between two TTTA molecules. It is also shown that bistability in TTTA results from the coexistence of the monoclinic HT and triclinic LT phases in the temperature range studied.     

Broken-symmetry density functional theory investigation on bis-nitronyl nitroxide diradicals: influence of length and aromaticity of couplers

A series of nitronyl nitroxide (NN) diradicals with linear conjugated couplers and another series with aromatic couplers have been investigated by the broken-symmetry (BS) DFT approach. The overlap integral between the magnetically active orbitals in the BS state has been explicitly computed and used for the evaluation of the magnetic exchange coupling constant (J). The calculated J values are in very good agreement with the observed values in the literature. The magnitude of J depends on the length of the coupler as well as the conformation of the radical units. The aromaticity of the spacer decreases the strength of the exchange coupling constant. The SOMO-SOMO energy splitting analysis, where SOMO stands for the singly occupied molecular orbital, and the calculation of electron paramagnetic resonance (EPR) parameters have also been carried out. The computed hyperfine coupling constants support the intramolecular magnetic interactions. The nature of magnetic exchange coupling constant can also be predicted from the shape of the SOMOs as well as the spin alternation rule in the unrestricted Hartree-Fock (UHF) treatment. It is found that pi-conjugation along with the spin-polarization plays the major role in controlling the magnitude and sign of the coupling constant.     

Intramolecular spin alignment in photomagnetic molecular devices: a theoretical study

Ground- and excited-state magnetic properties of recently characterized pi-conjugated photomagnetic organic molecules are analyzed by the means of density functional theory (DFT). The systems under investigation are made up of an anthracene (An) unit primarily acting as a photosensitizer (P), one or two iminonitroxyl (IN) or oxoverdazyl (OV) stable organic radical(s) as the dangling spin carrier(s) (SC), and intervening phenylene connector(s) (B). The magnetic behavior of these multicomponent systems, represented here by the Heisenberg-Dirac magnetic exchange coupling (J), as well as the EPR observables (g tensors and isotropic A values), are accurately modeled and rationalized by using our DFT approach. As the capability to quantitatively assess intramolecular exchange coupling J in the excited state makes it possible to undertake rational optimization of photomagnetic systems, DFT was subsequently used to model new compounds exhibiting different connection schemes for their functional components (P, B, SC). We show in the present work that it is worthwhile considering the triplet state of anthracene, that is, P when promoted in its lowest photoexcited state, as a full magnetic site in the same capacity as the remote SCs. This framework allows us to accurately account for the interplay between transient ((3)An) and persistent (IN, OV) spin carriers, which magnetically couple according to a sole polarization mechanism essentially supported by phenyl connector(s). From our theoretical investigations of photoinduced spin alignment, some general rules are proposed and validated. Relying on the analysis of spin-density maps, they allow us to predict the magnetic behavior of purely organic magnets in both the ground and the excited states. Finally, the notion of photomagnetic molecular devices (PMMDs) is derived and potential application towards molecular spintronics disclosed.     

The dilemma of CrIIINiII exchange interactions: ferromagnetism versus antiferromagnetism

The sign of the exchange interaction in dinuclear Cr(III)Ni(II) complexes was analyzed using theoretical methods based on density functional theory. This approach allowed us to reproduce the experimental J values correctly. In addition, the Kahn-Briat model, which uses the square of the sum of the overlaps between the magnetic orbitals to correlate with the exchange coupling constant, provided a reasonable correlation between the different types of Cr(III)Ni(II) complexes when using biorthogonalized orbitals. We also examined the exchange interactions in two polynuclear Cr(III)Ni(II) complexes: a Cr(7)Ni ring and an S-shaped Cr(12)Ni(3) complex. We concluded that both systems exhibit antiferromagentic interactions, and that the Cr(III)···Ni(II) interactions are similar in value to the C(III)···Cr(III) exchange couplings.     

α-SrMnO3电子结构的第一性原理研究

采用平面波赝势方法对钙钛矿型锰酸盐氧化合物α-SrMnO3的电子结构进行了第一性原理研究. 六方钙钛矿型结构α-SrMnO3化合物为磁性绝缘体, 磁基态对应于共面八面体及共顶点八面体间的磁性交换作用均为反铁磁性(AFM), 其禁带宽度为1.6 eV; 费米能级附近的Mn3d态与O2p态存在很强的杂化作用, 属于共价绝缘体, 这种强共价性使得Mn4+的自旋磁矩偏离理想值. 采用Noodleman的对称性破缺方法, 根据α-SrMnO3不同磁有序态的总能量拟合出α-SrMnO3中的自旋交换耦合常数. α-SrMnO3的局部微结构(Mn—O—Mn)决定了整个体系的特殊磁性交换作用. 共面及共顶点的八面体间均存在AFM交换作用, 并且共顶点八面体间的AFM作用比较强.     

SmCo磁记录薄膜中磁耦合作用的研究

采用磁控溅射方法,在玻璃基片上制备了Cr/SmCo/Cr结构的SmCo薄膜,实验结果表明:在低Sm含量(20.5%(原子分数))和高Sm含量(大于30.7%)的SmCo薄膜中都能形成SmCO_5磁性相,在Sm含量较高的SmCo薄膜中同时还形成了SmCo_2等非磁性相,非磁性相的存在对磁性相有隔离作用,从而降低了磁性晶粒之间的磁耦合作用.因此可以用提高Sm含量的方法来降低SmCo薄膜磁性晶粒之间的磁耦合作用.     

Magnetic circular dichroism study of a dicobalt(II) methionine aminopeptidase/fumagillin complex and dicobalt II-II and II-III model complexes

The dicobalt form of the metallohydrolase methionine aminopeptidase from Escherichia coli (CoCo EcMetAP) has an active site with one 5-coordinate Co (II) and a more weakly bound 6-coordinate Co (II). These metal ions are bridged by two carboxylate amino acid side chains and water or hydroxide, potentially enabling magnetic exchange coupling between the metals. We used variable-temperature, variable-field magnetic circular dichroism to determine whether such coupling occurs. CoCo EcMetAP's MCD spectrum shows distinct d-d transitions at 495 and 567 nm caused by 6- and 5-coordinate Co (II), respectively. The magnetization curves for 5- and 6-coordinate Co (II) are very different, indicating that their electronic ground states vary considerably, ruling out any coupling. When the fungal metabolite fumagillin binds to the CoCoEcMetAP, the qualitative MCD spectrum is unchanged; however, VTVH MCD data show that 5- and 6-coordinate Co (II) ions have similarly shaped magnetization curves, indicating that the Co (II) ions now share the same electronic ground state. Fitting the VTVH MCD data to a model in which dimer wave functions are calculated using a spin Hamiltonian with zero-field splitting showed the Co (II) ions to be weakly ferromagnetically coupled, with J = 2.9 cm (-1). Ferromagnetic coupling is unusual for dinuclear Co (II); therefore, to support the CoCoEcMetAP/fumagillin complex results, we also analyzed VTVH MCD data from a matched pair of dinuclear cobalt complexes, 1 and 2. Complex 1 shares the carboxylate and hydroxide-bridged dicobalt(II) structural motif with the active site of CoCo EcMetAP. Complex 2 contains a nearly isostructural Co (II) ion, but the Co (III) is diamagnetic, so any magnetic coupling is switched off, while the spectral features of the Co (II) ion remain. Magnetization data for 1, fitted to the dimer model, showed that the Co (II) ions were weakly ferromagnetically coupled, with J = 1.7 cm (-1). Magnetization data for Co (II) ions in 2, however, reflect loss of magnetic exchange coupling.     

EPR of layered magnetic metal-amino acid salts. II. Cu(L-Met)2

Single crystals of bis(L-methioninato)copper(II), Cu(L-Met)₂, were studied by EPR at 9.7 and 33.6 GHz, at 300 K. The position and the peak-to-peak linewidth of the single observed EPR line were measured in three perpendicular planes of the samples. This single resonance is due to the collapse of the resonances of the two magnetically inequivalent copper ions in the lattice caused by the exchange interaction. The components of the molecular g tensor for isolated copper ions were obtained using a model which assumes axial symmetry. The results indicate that the unpaired electron occupies the d(x² − y²) orbital, and the orientation of the molecule obtained from the EPR data agrees with the crystallographic result. The linewidth data support a model which assumes exchange narrowing of the magnetic dipolar interaction in a two-dimensional magnetic lattice, an incomplete collapse of the hyperfine structure, and a frequency-dependent contribution in the planes where the g factors for the two sites of copper are different. An analysis of this latter contribution, allows to evaluate an exchange coupling constant |J′| = 0.10 K between inequivalent copper neighbors. Besides, the analysis of the hyperfine contribution to the linewidth gives |J| = 0.18 K for the average value of the exchange interaction of one copper ion with its six nearest neighbors within the layer. Concerning the possible superexchange paths between inequivalent copper ions, we suggest they can be of two types: the Cu---N---H…O---Cu one, involving hydrogen bonds between equatorial nitrogens and equatorial oxygens, and the other consisting of Cu---O---C---O---Cu carboxylate bridges involving apical and equatorial oxygens. They are discussed in view of the experimental results.     

Theoretical insights into the magnetostructural correlations in Mn3-based single-molecule magnets

Density functional theory (DFT) and the valence bond configuration interaction (VBCI) model have been applied to the oximato-based Mn(III)(3)O single-molecule magnets (SMMs), allowing one to correlate the Mn(III)-Mn(III) exchange coupling energy (J) with the bridging geometry in terms of two structural angles: the Mn-O-N-Mn torsion angle (γ) and the Mn(3) out-of-plane shift of O (angle δθ). Using DFT, a two-dimensional (γ, δθ) energy surface of J is derived and shown to yield essentially good agreement with the reported J values deduced from magnetic susceptibility data on trigonal oximato-bridged Mn(3) SMMs. VBCI is used to understand and analyze the DFT results. It is shown that the exchange coupling in these systems is governed by a spin-polarization mechanism inducing a pronounced and dominating ferromagnetic exchange via the oximato bridge as opposed to kinetic exchange, which favors a weaker and antiferromagnetic exchange via the bridging oxide. In the light of these results, a discussion of the exchange coupling in the Mn(6) family of the SMM with a record demagnetization barrier is given.     

Magnetic and redox properties in hydroxo‐ and alkoxo‐bridged Fe(III) binuclear complexes: A density functional study

DFT calculations were carried out in order to deduce the dependence of magnetic coupling on the structure of doubly hydroxide/alkoxide‐bridged diiron(III) dimers. The broken‐symmetry formalism was employed to calculate the magnetic exchange parameter J. The potential surfaces of the ground state display a geometrical minimum at an Fe O(H) Fe angle of 105° and FeFe distance of 3.2 Å, in good agreement with experimental values. The calculated correlation between the magnetic coupling with the geometrical structure agrees well with the experimental literature data, although always overestimated. Electrochemical measurements show that a one‐electron reduction is likely to cause dissociation into pseudooctahedral, monomeric subunits, and, consequently, no calculations were made for the reduced dimeric species. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 61–71, 1999     

Magnetic interactions in two heterobridged dinuclear copper(II) complexes: orbital complementarity or countercomplementarity?

The mechanisms of magnetic exchange interactions in two heterobridged mu-hydroxyl-mu-X dicopper complexes A and B (X = azaindole for A and X = pyrazole for B) are investigated by the calculations based on density functional theory combined with the broken-symmetry approach (DFT-BS). It is found that although the coordination circumstances of the copper centers in the two complexes are very similar, the magnetic magnitudes and signs are diametrically opposed. By the theoretical analyses of magnetic orbital interaction and spin distribution, it is indicated that the difference between the magnetic properties of the two complexes is due to the distinction of orbital interaction of two bridge ligands. Namely, the weak ferromagnetic coupling for complex A arises from the orbital countercomplementarity of the hydroxo and azaindole bridges while the strong antiferromagnetic coupling for complex B arises from the orbital complementarity of the hydroxo and pyrazolato bridges.     

Experimental and theoretical study of the antisymmetric magnetic behavior of copper inverse-9-metallacrown-3 compounds

Use of PhPyCNO (-)/X (-) "blends" (PhPyCNOH = phenyl 2-pyridyl ketoxime; X (-) = OH (-), alkanoato, ClO 4 (-)) in copper chemistry yielded trinuclear clusters that have been characterized as inverse-9-metallacrown-3 compounds and accommodate one or two guest ligands. The magnetic behavior showed a large antiferromagnetic interaction and a discrepancy between the low-temperature magnetic behavior observed experimentally and that predicted from a magnetic model. The discrepancy between the Brillouin curve and the experimental result provides clear evidence of the influence of the antisymmetric interaction. Introducing the antisymmetric terms derived from the fit of the susceptibility data into the magnetization formula caused the simulated curve to become nearly superimposable on the experimental one. The EPR data indicated that the compound [Cu 3(PhPyCNO) 3(mu 3-OH)(2,4,5-T) 2] ( 1), where 2,4,5-T is 2,4,5-trichlorophenoxyacetate, has isosceles or lower magnetic symmetry (delta not equal 0), that antisymmetric exchange is important ( G not equal 0), and that Delta E > hnu. The structures of the complexes 1 and [Cu 3(PhPyCNO) 3(mu 3-OH)(H 2O)(ClO 4) 2] ( 2) were determined using single-crystal X-ray crystallography. Theoretical calculations based on density functional theory were performed using the full crystal structures of 1, 2, [Cu 3(PhPyCNO) 3(OH)(CH 3OH) 2(ClO 4) 2] ( 3), and [Cu 3(PhPyCNO) 3(mu 3-OMe)(Cl)(ClO 4)] ( 4). The geometries of the model compounds [Cu 3(kappa (3) N, N, O-HNCHCHNO) 3(mu 3-OH)(mu 2-HCOO)(HCOO)] ( 5), [Cu 3(kappa (3) N, N, O-HNCHCHNO) 3(mu 2-HCOO)(HCOO)] (+) ( 6), [Cu 3(kappa (3) N, N, O-HNCHCHNO) 3(mu 3-O)] (+) ( 7), and [Cu 3(kappa (3) N, N, O-HNCHCHNO) 3] (3+) ( 8) were optimized at the same level of theory for both the doublet and quartet states, and vibrational analysis indicated that the resulting equilibrium geometries corresponded to minima on the potential energy surfaces. Both e g and t 2g magnetic orbitals seem to contribute to the magnetic exchange coupling. The latter contribution, although less important, might be due to overlap of the t 2g orbitals with the p-type orbitals of the central triply bridging oxide ligand, thereby affecting its displacement from the Cu 3 plane and contributing to the antiferromagnetic coupling. The crucial role of the triply bridging oxide (mu 3-O) ligand on the antiferromagnetic exchange coupling between the three Cu(II) magnetic centers is further evidenced by the excellent linear correlation of the coupling constant J with the distance of the mu 3-O ligand from the centroid of the Cu 3 triangle.     

First-row transition-metal complexes based on a carboxylate polychlorotriphenylmethyl radical: trends in metal-radical exchange interactions

We report the synthesis, crystal structures, and magnetic properties of a series of mononuclear, metal-radical complexes with first-row transition-metal ions using a new class of radical-based ligands, the polychlorinated triphenylmethyl (PTM) radicals. Crystal structures of three new PTM-based complexes of general formula M(PTMMC)2(py)4-x(H2O)x [PTMMC = PTM radical functionalized at the para position with one carboxylic group; M = Zn(II), x = 2 (1); M = Ni(II), x = 1 (2); M = Co(II), x = 1 (3)] show similar molecular structures in which mononuclear complexes are formed by an octahedral metal ion coordinated by two monodentated PTMMC units. From a magnetic point of view, these similar configurations describe a quasilinear, trimeric magnetic model (PTMMC-M(II)-PTMMC), in which the metal [Ni(II) or Co(II)]-radical magnetic-exchange coupling constants have been determined for the first time. In all of these complexes, the temperature dependence of the magnetic susceptibility reveals moderate antiferromagnetic-exchange coupling constants between the PTMMC radicals and Ni(II) (2J/kB = -47.1 K) and Co(II) ions (2J/kB = -15.2 K) based on the exchange Hamiltonian H = -2JSM(Srad1 + Srad2).     

Effect of magnetic exchange,double exchange,vibronic coupling,and asymmetry on magnetic properties in d2–d3 mixed‐valence dimers

The effect of magnetic exchange, double exchange, vibronic coupling, and asymmetry on magnetic properties of d²–d³ systems is discussed. The temperature‐dependent magnetic moment was calculated with the semiclassical adiabatic approach. The results show that the vibronic coupling from the out‐of‐phase breathing vibration on the metal sites (Piepho, Krausz, and Schatz [PKS] model) and the vibronic coupling from the stretching vibration between the metal sites (P model) favor the localization and delocalization of the “extra” electron in mixed‐valence dimers, respectively. The magnetic properties are determined by the interplay among magnetic exchange, double exchange, and vibronic coupling. The results obtained by analyzing d²–d³ systems can be generalized to other full delocalized dinuclear mixed valence systems with a unique transferable electron. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005