The D band in copper and the transition metals

• Main Author: Edwards, David Murray
• Published: Imperial College London 1963
• Subjects: 546
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.602184

The first part of the thesis deals with the tight-binding method of band structure calculations particularly as applied to 8 bands' end the second part with the role of the d band in magnetism. A fundamental error in the tight-binding method arises from the use of a restricted set of trial fumigates A method of calculating an upper bound to this error is given and an exact calculation at the error is made for a chain of d-functions. The general conclusion is that the tight-binding method is only accurate when the nearest neighbor's approximation is a good one. A method of calculating correction terms is given which is valid in cases of strong bindings the use of a 'muffin-tin' crystal potential is advocated. A criterion for choosing the 'atomic' functions is applied to the problem of calculating d bands. A correct choice ensures reasonable accuracy for states which do not interact with the sp band. A tight-binding calculation of the d band in copper is described; this employs a convenient method of reducing the energy integrals to the smallest number of independent ones and a new method of calculating three-centre integrals. A band treatment of spin waves in metals is averts The thermo-dynamic, properties of a ferromagnetic metal are discussed in terms of spin wave excitations and independent particle excitations. Herring's and Kittel's conjecture on the additivity of the two contribution to the specific heat, and to the deviation of the magnetization from saturation, is confirmed. The status of Stoner's collective electron theory is discussed. A formal proof is given of the existence of spin craves of long wavelength and a general method of calculating their energies, which depend strongly on the band structure, is outlined. Herring's and Izuyama's results on spin-wave energies are obtained as special cases.