Exchange Coupling Model Research Articles

Exchange Mixing at LII,III X-Ray Edges

The Onodera model of electron-hole exchange coupling at an L II,III X-ray edge is extended (i) giving a lineshape formula expressed in terms of experimentally accessible quantities, and (ii) providing a means of accounting approximately for the energy dependences of both the absorption spectrum above threshold and the exchange interaction. The experimental implications are discussed.

Formal approach to various properties of antiferromagnets

The formal representation of thermal and magnetic properties of moderately anisotropic antiferromagnets in the presence and absence of a constant, uniform external magnetic field is discussed both in selective ordered configurations and in the paramagnetic phase. The mean-field-theoretical formalism is shown to give a satisfactory account of the magnetic properties of a class of two-sublattice antiferromagnets in those ordered configurations where the applied magnetic field is at a right angle to the direction of the spontaneously evolving sublattice magnetic moments. Predictions of mean-field theory on the linearity of the magnetic moment in the applied field strength and the attendant invariant molar susceptibility throughout the relevant portions of the configuration phase diagrams, phase-boundary lines included, are seen to be well satisfied. This is verified in detail on the typical antiferromagnet MnCl2 · 4H2O, where the Mn2+ ions in their6S5/2 ground state determine the magnetic properties and for which numerous magnetic and thermal measurements have been accumulated in both the ordered and paramagnetic phases. The experimentally explored low-temperature properties of this antiferromagnet refer to the liquid3He and4He and liquid H2 bath-temperature intervals 0.3≤T≤4.2 K and 15≤T≤21 K, respectively. In contrast with the magnetic properties, mean-field theory is less successful in accounting for the thermal properties of antiferromagnets, but its qualitative predictions agree well with the observations. In the paramagnetic phase, the isotropic nearest-neighbor exchange-coupled model system is used, wherein the data on the manganese compound are assigned approximately to an effective simple-cubic distribution of the Mn2+ ions, with an effective empirical exchange-energy parameter,J<0, derived from magnetic and heat capacity data at asymptotically high temperatures. Here the formal approach corresponds to a series expansion of the various properties in ascending powers of ‖J‖/kT, in the absence of magnetic field, with an additional magnetic-field-exchange double series in the presence of an external field. In those temperature and field-strength regions where convergence is satisfactory, the above approach is shown to give a good account of the observed thermal properties of the manganese compound in the absence of magnetic field, as well as of the low-field paramagnetic susceptibility. The hitherto observed field-dependent properties are confined to a much too narrow temperature interval outside the region of convergence of the series-expansion formalism. Experimental control of this approach requires acquisition of new data in the appropriate temperature range of convergence of the model formalism.

EPR determination of the Co(II)-free radical magnetic geometry of the “doubleT” species arising in a coenzyme B-12-enzyme reaction

The physical significance of the observed structure of the EPR signal, commonly known as the “doublet” spectrum, is that it contains information not only about the exchange coupling but also about the geometry of the magnetic dipole-dipole spin-spin coupling. We can show this because we have developed a general method of analysis applicable to this type of system and because we demand a quantitative fit of theory to experiment at two microwave frequencies. We have chosen the “doublet” free radical signal, which arises in the ribonucleotide reductase-5′-deoxyadenosylcobalamin system (from Lactobacillus leichmannii, see Hamilton et al., Biochemistry 11, 4696–4705 (1972)), for study, for the particular reason that the 35 GHz “doublet” spectrum has three components (in this case) rather than two, which provides an important test of the recently proposed model of isotropic exchange coupling by Schepler et al. ((1975) Biochim. Biophys. Acta 397, 510–518). We find that a quantitative fit to the EPR “doublet” lineshape can be obtained with a model of isotropic exchange, and a “point” magnetic dipole-dipole interaction acting over a distance of 9.9 Å with the radical located approx. 34° off the principal g zz axis and <1° off the principal g xx axis of the Co(II) in the corrin ring. Quantitative fits of the doublet portion of the observed lineshape at both 9 and 35 GHz were achieved with this model, assuming an axially symmetric free radical signal and a Gaussian spin-packet lineshape with isotropic linewidth.

On Singlet-Triplet Transitions Induced by Exchange with Paramagnetic Molecules and the Intermolecular Coupling of Spin Angular Momenta

The theoretical basis of the singlet-triplet transition mechanism by exchange coupling with neighboring paramagnetic molecules is examined. Attention is drawn to the two implicit assumptions of this exchange coupling model: (1) the validity of ``perfect'' permutational exchange of electrons between the neighboring molecules, and (2) the validity of the conservation of total spin angular momentum of the two neighboring molecules. With respect to the first assumption, it is found that the finiteness (vs perfection) of exchange overlap has not been sufficiently allowed for in the conventional (electrostatic) exchange mixing of allowed singlet and charge-transfer states and in the conventional transitions only among the composite states of the same total spin angular momentum (e.g., triplet← triplet). It is derived that there exists a direct transition moment (between the two molecules) weighted by overlap integrals, which may not be much smaller than the allowed transition moment weighted by (the indirect) exchange mixing coefficients, and which may exhibit interference effect with the latter. It is pointed out that if exchange energy is finite and spin interactions are sizable, transitions to other states of different spin multiplicities (e.g., singlet← triplet and quintet← triplet), which are not split sufficiently far apart, may contribute to intensity through spin interactions. With respect to the second assumption, it is shown that the small but finite spin interactions, especially interelectronic spin interactions, which do not commute with the assertedly conserved total angular momentum S2, have not been accounted for. A comprehensive formalism is developed to treat simultaneously exchange interaction along with spin interactions and to provide for various ranges of their relative magnitudes. These spin interactions are also shown to exhibit interference effects with the exchange interaction in the total intensity expression. All transitions, including Δ S ≠ 0 and Δ MS ≠ 0,, are considered. Matrix elements of the direct transition, of the exchange mixing of allowed singlet and charge-transfer states, and of the spin-orbit, spin-other-orbit, and spin-spin interactions are computed for general molecular orbitals and for the case of three and four electrons. The commutation and noncommutation of spin operators with S2 are traced to permutation symmetry and are treated by isomorphism to C3v (for three electrons) and Td (for four electrons) point groups. Irreducible representations of the linear as well as quadratic forms of spin and orbital operators and their interaction tensors are derived. Their relationship to spin eigenfunctions of given permutational symmetries is discussed.

Models of Exchange Coupling in Ferromagnetic Media

Models of Exchange Coupling in Ferromagnetic Media