Table of contents

Empirical tight binding has proven to be very popular in recent years on account of its computational efficiency and accuracy. However, it has limitations, notably the difficulties associated with fitting parameters and improving models when the desired accuracy cannot be achieved. In the light of this, a number of efforts have been made to derive tight-binding models from first principles. Here are described a number of formalisms based on density functional theory which span the range of approaches currently being used.

An averaged-field approach is suggested for obtaining the explicit form of the dispersion equation for electromagnetic waves propagating in a three- or two-dimensional dielectric photonic crystal when the dimension of the inclusions is small compared with the longest period of the rectangular lattice of the photonic crystal. The band structure is obtained in an explicit and simple way. The method is verified numerically by comparing with the conventional plane-wave expansion method for a special case.

We have performed ab initiocalculations of the electronic structure and exchange couplings in the layered vanadates CaV₂ O₅and MgV₂ O₅ . On the basis of our results we provide a possible explanation of the unusual magnetic properties of these materials, in particular the large difference in spin gap between CaV₂ O₅and MgV₂ O₅ .

We have measured the energy- and momentum-resolved band structure, and ground state of occupation of the bands, for a crystalline silicon sample along the 100 and 110 directions. Band structures were determined directly by the technique of electron momentum spectroscopy (EMS) for a self-supporting Si membrane with a thickness of approximately 7 nm. We compare our experimental results with ab initiocalculations for bulk crystalline silicon performed within the linear muffin tin orbital approximation. Qualitative agreement is seen between experiment and theory for the main valence band peak. Additional intensity is observed in the measurement on either side of the main peak and is attributed mainly to multiple-scattering events. Satellite structure could also be present in these additional features, although there is no direct evidence for this.

A general solution of the model for positrons which diffuse inside a grain and then can be trapped and detrapped at a grain boundary of arbitrary shape is presented. The closed-form relations for the mean positron lifetime and the positron lifetime spectrum are obtained for a grain of spherical shape. The obtained results slightly differ from those presented in 1996 Phil. Mag.731489 where a similar problem was considered and they extend the consideration given in that paper in J. Phys.: Condens. Matter10L547.

A detailed tight-binding analysis of the electron band structure of the CuO₂plane of layered cuprates is performed within a σ -band Hamiltonian including four orbitals - Cu 3d_{x² -y²}and Cu 4s, O 2p_xand O 2p_y . Both the experimental and theoretical indications in favour of a Fermi level located in a Cu or O band, respectively, are considered. For these two alternatives, analytical expressions are obtained for the linear combination of atomic orbitals (LCAO) electron wave functions suitable for the treatment of electron superexchange. Simple formulae for the Fermi surface and electron dispersions are derived by applying the Löwdin downfolding procedure to set up the effective copper and oxygen Hamiltonians. They are used to fit the experimental angle-resolved ultraviolet photoelectron spectroscopy (ARUPS) Fermi surface of Pb_0.42 Bi_1.73 Sr_1.94 Ca_1.3 Cu_1.92 O_8+xand both the ARPES and local density approximation (LDA) Fermi surface of . The value of presenting the hopping amplitudes as surface integrals of ab initioatomic wave functions is demonstrated as well. The same approach is applied to the RuO₂plane of the ruthenate Sr₂ RuO₄ . The LCAO Hamiltonians including the three in-plane π -orbitals Ru 4d_xy , O_a2p_y , O_b2p_xand the four transverse π -orbitals Ru 4d_zx , Ru 4d_yz , O_a2p_z , O_b2p_zare considered separately. It is shown that the equation for the constant-energy curves and the Fermi contours has the same canonical form as the one for the layered cuprates.

This is the first systematic study of the spin excitations around the MBZ boundary points in -Mn alloy. The magnetic inelastic neutron scattering was measured in the antiferromagnetic Mn(13.7% Ni) alloy in a sample with unequal domain distribution in the temperature range 0.025 T_N -1.15 T_N . The evidence of the magnetic excitations around the MBZ boundary points equivalent to the MBZ centres in -Mn alloy is presented. At low temperatures these excitations differ from excitations observed around the MBZ centres; they are rather similar to excitations observed above T_N . When the temperature increases up to T_Nthe excitations observed around MBZ centres become more similar to those around the MBZ boundary equivalent points. The results of the analysis are consistent with the general features of spin fluctuations.

Polycrystalline Fe₂ BO₄prepared by solid-state reaction was investigated over a wide temperature range using Mössbauer spectroscopy and magnetization and resistivity measurements. The Mössbauer data below 270 K reveal four iron sites (two Fe²⁺and two Fe³⁺ ) in a 1:1:1:1 ratio. Above this temperature, electron delocalization sets in between the divalent-trivalent iron ions and up to 400 K both delocalized and localized iron states are observed. The magnetization and Mössbauer data indicate that this oxoborate mixed-valence system is an L-type ferrimagnet below T_c= 155 K, with the iron atoms in each sublattice having different point symmetries and different magnetic interactions. The resistivity data show the first-order nature of the charge-ordering transition (T_co= 316 K).

Optical experiments, involving photoluminescence (PL), the PL excitation and quenching spectra, as well as transmission and its quenching, were used to analyse the photochromic behaviour of some vacancy-related complexes in diamond. The 2.156 eV, 1.945 eV and 1.68 eV optical centres in CVD diamond are attributed to the neutral nitrogen-vacancy, negative nitrogen-vacancy and neutral silicon-vacancy ([Si-V]⁰ ) centres, respectively. Oscillatory behaviour in the excitation spectrum of the 1.68 eV luminescence is observed and from the threshold of the oscillations a position of E_C- 2.05 eV is suggested for the ground state of the [Si-V]⁰centre.