Introduction to Magnetic Exchange: Dimers and Clusters

Abstract

Energy Levels and Specific Heats 71configurational mixing of states such as M+ F M2+. The electron on Fin (c) and (d) can now couple with the lone electron in a d z 2 orbital on an adjoining Ni2+ . The preferred coupling is to give a singlet state [(c), called antiferromagnetic] rather than a triplet, (d). This in turn stabilizes the singlet state (a) with respect to the triplet (b). The strength of the interaction will depend on the amount of overlap, and we present here only a model of 180° superexchange. Metal ion orbitals can also overlap with p" ligand orbitals at a 90° angle, and much recent research effort has gone into finding the factors which influence this superexchange interaction.This model, which has been applied to a variety of systems [1,2] is somewhat similar to that which is used for explaining spin-spin coupling in NMR spectroscopy [3]. The Hamiltonian in use for metal-metal exchange interaction in magnetic insulators is of the form (5.2) where the sum is taken over all pair-wise interactions of spins i and j in a lattice. For the moment, we shall restrict our attention to dimers, and thereby limit the summation to the two atoms 1 and 2 in the dimeric molecule, so thatThis is called an isotropic (note the dot product between the two spins, S) or Heisenberg Hamiltonian, and we adopt the convention that negative J refers to antiferromagnetic (spin-paired or singlet ground state in a dimer) interactions, and positive J refers to ferromagnetic (spin-triplet ground state) interactions. The exchange constant J is given in energy units (Kelvins) and measures the strength ofthe interaction. The reader must be careful in comparing different authors, for a variety of conventions (involving the negative sign and even the factor of 2) are in use. (The symbol J now takes a different meaning from its earlier use as the quantum operator for total angular momentum.) Energy Levels and Specific HeatsAn antiferromagnetic interaction ofthe type given in Eq. (5.3), when applied to two ions each of!/ = t gives a spin-singlet ground state and a spin-triplet 2J in energy above the singlet ( Fig. 5.2). Naturally, ifthe interaction were ferromagnetic, the diagram is simply inverted. For an external field applied along the z-axis of the pair, the complete Hamiltonian will be taken as

An Investigation of Halogen Bonding as a Structure-Directing Interaction in Dithiadiazolyl Radicals

“…Elemental analysis calc. for C 7 BrF 4 N 2 S 2 : C 25.32%, H 0.00%, N 8.44%; found: C 25.30%, H 0.00%, N 8.43%; EPR (X-band, CH 2 Cl 2 , 298 K); g = 2.0097, a N = 4.9 G; MS(EI+) m/z = 330.8622 (M + ), 284.9 (M + − SN), 252.9 (M + − SSN), 226.9 (M + − CNSSN) [all peaks quoted for the 79 Br isotopomer]; IR (ν max , cm −1 , nujol): 1639(s), 1502 (s), 1416(s), 1361(s), 1246(s), 1170(m), 1059(m,sh), 977(s), 854(m), 819(s), 796(s), 751(s, sh), 724 (s, sh), 643 (m, sh).…”

“…The dominant exchange pathway, J 1 , is a factor of 2−3 larger than J 2 and J 3 at the B3LYP/6-31G*/LAV3P* level of theory. Initial attempts to model the system as a simple dimer model using the Bleaney−Bowers expression 79 required large mean field terms θ, comparable to |J intra /k|, to provide a satisfactory fit to the data. This is unsurprising as such mean field approximations tend to only hold well when the interdimer interactions are a magnitude smaller than J intra .…”

“…This is unsurprising as such mean field approximations tend to only hold well when the interdimer interactions are a magnitude smaller than J intra . We also investigated a one-dimensional alternating chain mode,l 79 but again a large mean field constant was required, reflecting a more complex magnetic system (see SUP-5). Since the magnitudes of the computed exchange couplings are similar for all three communication pathways, it is not possible to approximate this system to a simpler model.…”

Transmission of Magnetic Interactions through an Organometallic Coupler: A Novel Family of Metallocene-Substituted α-Nitronyl Aminoxyl Radicals

“…DC magnetic susceptibility measurements of radicals 1 (M = Fe, Ru) (Figure ) show quasi-paramagnetic behaviors which can be fitted to the Curie−Weiss law [Weiss constants of θ = −0.7 K for 1 (M = Fe) and −3.0 K for 1 (M = Ru)], indicating the existence of very weak antiferromagnetic intermolecular interactions in both monoradicals. The fitting of the experi-mental data can be considerably improved by using the Bleaney−Bowers equation 47 with a magnetic exchange interaction of J/k B = −0.8 K for 1 (M = Fe) and J/k B = −0.7 K for 1 (M = Ru) 9 Temperature dependence of the molar paramagnetic susceptibility, χ, of monoradicals 1 (M = Fe, Ru) and diradicals 2 (M = Fe, Ru).…”

Low coordinate iron derivatives stabilized by a β-diketiminate mimic. Synthesis and coordination chemistry of enamidophosphinimine scaffolds to generate diiron dinitrogen complexes

“…This observation also explains the lower magnetic moments measured in solution for the less sterically crowded complexes in C 6 D 6 , as they are likely solubilized as dimers and can experience weak anti-ferromagnetic coupling across the bridging bromide ligands via superexchange pathways. [30][31][32] A comparison of the 1 H NMR spectra for complexes 4a-c in d 8 -THF is provided in Fig. 2.…”