Showing papers on "Exchange interaction published in 1977"

Kinetic exchange interaction in a narrow S-band

Abstract: A new canonical transformation is applied to the Hubbard Hamiltonian under strong correlation with arbitrary n to obtain an effective Hamiltonian which consists of both the itinerant property of electrons in split sub-bands and the Heisenberg-type spin-spin coupling. It reduces to that for a Heisenberg antiferromagnet as t/U to 0, but the intrasub-band electron hopping becomes important as t/U increases. This effective Hamiltonian is suitable for investigating the antiferro-paramagnetic transition.

On the multipole structure of exchange dispersion energy in the interaction of two helium atoms

Abstract: The exchange dispersion energy for the interaction of two helium atoms is expressed as a sum of multipole components. In contrast to the analogous expansion for the dispersion energy the derived series converges very slowly and the rate of convergence does not improve with an increasing interatomic distance. Numerical calculations show that at the van der Waals minimum the first term of the series, referred to as dipole-dipole exchange energy, represents merely 17 per cent of the exchange dispersion energy. Moreover, even the inclusion of dipole-quadrupole and quadrupole-quadrupole terms can account for only half of the total exchange dispersion interaction. The above difficulty can be avoided by expanding the dispersion pair function in terms of ionic type or explicitly correlated functions.

Long range exciton percolation and superexchange: Energy denominator study on 3B1u naphthalene

Abstract: The long-range exciton percolation model is found to describe the lowest triplet exciton superexchange (“tunneling”) migration at low temperature (2 K), in our model alloy system: Binary isotopic mixed naphthalene crystals with dispersed exciton sensors (supertraps) consisting of small concentration of betamethylnaphthalene (−10 −3 mole fraction) or isotopic substituted naphthalene molecules (with lower excitation energies than the partially deuterated naphthalene guest species). While the “host” is C 10 D 8 throughout, the “guest” species in our five experimental systems are: C 10 H 8 , 2-DC 10 H 7 . 1-DC 10 H 7 , 1,2-D 2 C 10 H 6 and 1,4,5,8-D 4 C 10 H 4 . The variation in guest—host (and supertrap—guest) energy denominator in the above systems enables a quantitative test of our physical exciton superechange (tunnelling) migration model. In conjunction with a mathematical long-range percolation model (J. Hoshen, E.M. Monberg and R. Kopelman, unpublished). The experimental monitoring of the exciton migration dynamics consists of refined phosphorescence measurements to our systems, under highly controlled conditions (crystal quality, purity, concentration, temperature and excitation). Using only the known nearest neighbor (interchange-equivalent) exciton exchange interaction, quantitative agreement with the experimental dynamic percolation concentration is achieved, without adjustable parameters, for four of the five investigated systems. The fifth one is known to involve a cooperative percolation—thermalization exciton migration, and is effective in qualitative agreement with the predicted upper limit for the exciton percolation concentration. The nearest-neighbor 3 B 1u excitation exchange interactions, and their square lattice topology, play the dominant role in determining the guest triplet exciton energy transfer and migration. This energy conduction involves an extremely narrow “impurity band”, on the order of 10 to 10 3 Hz, formed by the superexchange (tunneling) exciton interactions resulting from the above mentioned exciton exchange interactions (integrals). The latter are thus confirmed as the major contributors to the 3 B 1u exciton transfer, migration and energy bond (3 × 10 11 Hz) in the ordinary naphthalene crystal. Just below the percolation concentration the “impurity conduction band” further shrinks by one or two orders of magnitude, resulting in a bandwidth of about one hertz or less, and thus practically resulting in the “switching off” of the exciton transport. The tunneling radius is about 30 A or larger, depending on the system, but essentially in the ab plane.

Crystalline and amorphous rare-earth transition metal alloys

Abstract: A large body of experimental data is available on the magnetic properties of crystalline and amorphous rare-earth transition metal compounds or alloys. These include the results of measurements of magnetization, nuclear magnetic resonance and Mossbauer effect and also results of measurements of magnetovolume effects. Some of the experimental data point to strongly localized 3d moments; others, however, point to itinerant 3d electron magnetism. In this paper we show that the 3d electron interaction between nearest neighbour atoms has a dominating influence on the magnetic properties of the crystalline compounds and amorphous alloys. Implications of this on the 3d electron bandwidth and the exchange interaction between the 3d electrons are discussed.

Theory of magnetic field modulation of radical recombination reactions.1

Abstract: The recently observed magnetic field effects in the geminate recombination of radical ions in polar solvents are treated theoretically by solving the stochastic Liouville equation for a radical pair under the influence of the hyperfine interaction between the unpaired electrons and the nuclei. Decomposing this solution, for non-viscous solvents, into contributions from the first, second, etc. re-encounter of the radical pair a natural, rapidly converging series expansions is obtained. Non-reactive exchange collisions contribute to the second order terms in this series. The solution is presented in such a form that the calculation of the triplet and free radical yields can be performed in two steps: first the magnetic field dependent spin hamiltonian of the radical pair has to be diagonalized, and a number of functions of the magnetic field have to be calculated which depend otherwise only on the hyperfine coupling constants of the radicals. In the second step these functions - one in first order, two additional ones in second order - are inserted into simple analytic expressions, containing all the information on diffusion constants, the initial condition, exchange interaction and reaction rates.

Effects of exchange energy and orbital orthogonality on barriers to internal rotation

Abstract: In order to determine the effect of the Pauli principle on internal rotation barriers, we have calculated exchange and orbital orthogonality contributions to barriers for a small group of molecules: ethane, methanol, acetaldehyde, and hydrogen peroxide. To evaluate exchange contributions it was necessary to formulate variation equations and to energy‐optimize simple product wavefunctions of orthogonal orbitals (Hartree‐product wavefunctions). The resulting orbitals resemble very closely the Edmiston–Ruedenberg localized Hartree–Fock orbitals. Our results indicate that exchange contributions to the barriers in ethane and acetaldehyde are quite small. For methanol and hydrogen peroxide, our calculated contributions are considerably larger and suggest that, at least in some molecules, exchange contributions cannot be ignored. For all of the molecules, however, the exchange contribution is greatly overshadowed by that of end‐to‐end orbital orthogonality.

Exchange interactions in polynuclear complexes

Abstract: We present detailed optical and magneto-optical data on Cs3Cr2Cl9 as a single crystal containing only pairs of Cr3+ ions. Measurements have been carried out in a wide range of temperatures down to pumped helium and in the whole spectral region covering all singly and several doubly excited states. MCD helped considerably in resolving the absorption spectra into their numerous components, and proved especially useful in demonstrating the occurrence of a double excitation to 4 T 2. It provides also parallel g factors for several excited terms. The main conclusions of our work are: (i) all transitions are electric dipole allowed; (ii) transitions to singly excited doublet states are essentially promoted via a single ion mechanism; (iii) vibronic interaction must be invoked to understand the absorption data on sharp lines; (iv) the trigonal plus spin-orbit interaction competes favourably with exchange interaction to produce excited states splittings. We present also a new non-phenomenological model to describ...

Energy of cohesion in transition metals

Abstract: The energy of cohesion in transition metals is calculated on the basis of Hubbard Hamiltonian with exchange interaction. The Coulomb correlation term is treated in the statistical (0,1) approximation. The calculations are performed in the limits of weak and strong Coulomb correlations in both paramagnetic and ferromagnetic states using the CPA technique. It is shown that the decrease in energy of cohesion near half-filled 3d bands in the first transition series is due to the strong Coulomb correlations resulting in 3d band splitting. Such a decrease is not observed in other transition metal series, where these correlations seem to be smaller in comparison to the bandwidth.

Supertransferred hyperfine interaction in magnetic insulators (II)

Abstract: Two additive contributions to the supertransferred hyperfine (STHF) interaction are suggested to be taken into account in its semi-quantitative analysis of the N-O-M chain: (i) that of bonding molecular orbitals, (ii) that of antibonding orbitals, by calculation of spin-polarization of s-electrons in the N-ion due to the superexchange interaction with d-electrons of the M-ion. Generalized forms of the operator and angular dependence of the STHF interaction were considered due to the use of irreducible tensor operators to the point Oh group. Analytical expressions for the value of the hyperfine fieldHSTHF at the nucleus of the N-ion induced by the magnetic M-ion (both in non-degenerateA1,A2 ground states and in degenerateE, T1,T2 states as well) are derived. The value ofHSTHF is dependent upon the type of the M-ion ground state and the geometry of the N-O-M bond. The value ofHSTHF induced by M-ions ofA1,A2,E states was shown to depend only on the bond angle θ, and that ofT1,T2 states on the combinations sin2θ cos 2ϕ, sin2θ sin 2ϕ. The importance of orbital anisotropy in the STHF interaction is emphasized. The orbital anisotropic contribution toHSTHF is drastically dependent on the ground state and its splitting in the crystalline field of low symmetry: the isotropic contribution is determined mainly by the occupation numbers of thet2g andeg subshells.

Optical observation of spin reorientation in ErCrO3

Abstract: The absorption spectra of ErCrO3 due to the transitions from the groundstate 4I15/2 of Er3+ to one of its excited multiplets 4I9/2 have been measured, where spin reorientation induced by temperature and by magnetic field has been observed. The Kramers splitting energies and the g-values are obtained for the ground and excited states. The effective fields acting on Er3+ are deduced to come from the erbium-chromium exchange interaction.

Spin wave spectrum in ordered Pd3Fe alloy

Abstract: The spin wave spectrum in a combined system of itinerant electron spins and localised spins is calculated. Spin waves with wavevector q propagating in itinerant electrons and those propagating on localised spins are coupled together by the exchange interaction between the itinerant electrons and the localised spins. Acoustical and optical modes appear at q qc and they decay with a life time. The spin wave spectrum observed by Holder (1976) for an ordered ferromagnetic Pd3Fe alloy can be well explained by the present calculated results.

Wannier-mott polaritons in magnetic fields

Abstract: A review of recent theories of excitons in magnetic fields in cubic, semi-conductors is given. The valence band degeneracy and anisotropy and the exchange interaction which are taken into account in these theories create a number of typical effects (like an (mj)-dependent diamagnetism) which are verified experimentally in several materials. Consistent sets of band structure parameters are determined from a best fit of magneto-reflection results to the high field theory. A proper interpretation of the reflection experiments demands a correct line shape analysis, including the effects of an exponentially decreasing exciton free surface layer and spatial dispersion: The polariton picture has to be used. The anisotropic compression of the exciton wavefunction in high magnetic fields is directly observed via the anisotropic reduction of the exciton free surface layer. A strong increase of the oscillator strength and of the exchange interaction is another consequence of this compression. The enhanced long range part of the exchange interaction and the Magneto-Stark-Effect could explain the recently observed dependence of the transverse exciton energies on the direction of the magnetic field.

Magnetic properties of amorphous metallic alloys containing rare earth impurities

Abstract: Presents an extension of the theoretical model of Harris et al. (1974) to describe the magnetic properties of DyCo3.4 alloys. The d band is treated in terms of a Hubbard Hamiltonian and the Dy moments, which are coupled with the d band through a local exchange interaction, are subject to a random anisotropy. The Hamiltonian is treated in the mean field approximation. A fit of the magnetization against temperature curve of DyCo3.4 is presented and the magnetization curves of DyNi3.4 and DyFe3.4 are discussed in the light of the same theoretical model.

Annealed Ising Ferromagnet of Binary Alloys. II

Abstract: Annealed Ising ferromagnetic Binary alloys of arbitrary concentrations are solved by use of the Takagi approximation. The atom ordering energy as well as the exchange energy are taken into account. In the present paper the case that one of the component atoms is non-magnetic is studied. Since the exchange energy and the atom ordering energy disturb each other, the onset of order tends to destroy the magnetization and vice versa. Therefore several critical concentrations are found. The complete phase diagram is obtained in which a tetra-critical point exists. Complicated calculations are carried out by the analytical method as much as possible and the rest is supplemented by the natural iteration method developed by Kikuchi using the computer.

Pair exchange interaction in a crystalline nitroxide radical ESR study of dimers in the triplet state

Abstract: The dimerization of the 9-aza-bicyclo (3,3,1) nonan-3-one-9-oxyl in the solid state is investigated by use of ESR spectroscopy. The ESR spectrum of a single crystal is characteristic of symmetric pairs of exchange-coupled radicals in a thermally accessible triplet state. The presence of well-resolved hyperfine structure is evidence for strongly localized excitations with a jumping rate lower than 107 Hz. The ESR spectrum is well described by the spin hamiltonian At 35 GHz the observed splitting of the m s=+ 1↔0 transition has been found to be slightly different from that of the m s=0↔-1 one; this anomaly is explained by the mixing of the m s electronic states. The parameters and the principal directions of the zero-field splitting, spectroscopic and hyperfine tensors are determined and discussed. The principal directions of the dipolar tensor indicate a nearly equal spin density on the nitrogen and oxygen atoms; from the fine structure parameters D and E, determined to be (-0·0723 ± 0·0005) cm-1 and (-0·0...

Recombination of alkali positive and halogen negative ions

Abstract: The process of mutual neutralization of alkali positive and halogen negative atomic ions is considered at low energies (0.01 eV–10 keV). The exchange interaction between ionic and covalent states at the diabatic curve‐crossing point is calculated for each alkali–halogen pair using the Landau–Herring method. The neutralization cross sections, as well as the rate constants for these reactions, are calculated.

Interaction of a magnetic monopole with a ferromagnetic domain

Abstract: We calculate the interaction energy of a magnetic monopole with a single ferromagnetic domain, taking into account the ferromagnetic exchange interaction in a linear approximation. In vacuum at 400 A from the surface a monopole of strength 137e/2 is bound by 35 eV in magnetite, and for iron at 300 A from the surface the binding energy is 50 eV. We expect the binding energy to increase at smaller distances. The attractive force on a slow monopole approaching the surface of a ferromagnet from the vacuum differs, at these large distances, only slightly from that computed by simple classical image methods treating the magnet as a medium with an isotropic and wavelength-independent permeability equal to the long-wavelength transverse permeability of the ferromagnetic material. We consider the apparent contradictions with energy and momentum conservation in the problem of a monopole in the field of an electron. The exclusion of s-wave scattering largely resolves the contradictions. The effective field on a monopole in a ferromagnetic is H and not B. (AIP)

Thermal expansion measurements near the antiferromagnetic phase transitions in K 2 ReCl 6 and K 2 IrCl 6

Abstract: Measurements of the anomalous behavior in the linear thermal expansion coefficient near the antiferromagnetic phase transitions in K2ReCl6 and K2IrCl6 are reported. The results for the two compounds, which have the same crystal structure but different magnetic structures, clearly demonstrate that the contribution of the next-nearest-neighbor exchange interaction to the thermal strain is of opposite sign for the two compounds. In agreement with sublattice magnetization measurements, a spin contribution is found to persist to within10% of the Neel temperature in K2ReCl6. The relevance of the results to this unusual magnetic behavior is discussed in terms of the important role played by the next-nearest-neighbor superexchange.

Critical behaviour of a structurally and chemically disordered ferromagnet

Abstract: A classical Heisenberg ferromagnet with fluctuations in the nearest-neighbour exchange interaction is investigated by the Bethe-Peierls-Weiss method. The fluctuations, assumed to arise from the structural disorder, depress the values of the Curie temperature, the high-temperature magnetic susceptibility and the magnetization relative to the corresponding values for the average crystal. For small values of the fluctuation parameter, explicit expressions for the amount of decrease in the above quantities are obtained. The critical indices are, however, found to be unaffected by fluctuations. The same formalism is employed to study the chemical disorder introduced by substituting magnetic impurities in a non-magnetic structurally disordered host. It is shown that the critical concentration of magnetic atoms for the appearance of long-range magnetic order is not influenced by fluctuations.

Application of multiband CPA to the ferromagnetic BCC Fe-V alloys

Abstract: The results of polarized neutron diffraction measurements on ferromagnetic BCC Fe-V alloys are analysed within the multiband CPA theory. A Hubbard Hamiltonian with intra- and interatomic exchange interaction is used. Both Hubbard and exchange terms are treated in the Hartree-Fock approximation. A good agreement for the magnetic moment and asphericity of its distribution is found. It is shown that the increase of the asphericity parameter with vanadium content is caused by the transfer of eg electrons from vanadium to iron sites. This transfer is responsible also for the occurrence of a negative moment on vanadium confirmed in diffuse scattering measurements.