Phan, Minh Son (1989). Dynamic Response Function and the Theory of Spin Waves in Metallic Overlayers. (Unpublished Doctoral thesis, City, University of London)

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Abstract
A general recursion method (method of adlayers) for calculating the exact Green function in an arbitrary overlayer is developed. The method as presented applies to an sband tightbinding Hamiltonian with hopping between nearestneighbours only. The general.isation of the method to a multiorbital band structure is described. The
overlayer we consider is deposited above the (100) surface of a simple cubic semiinfinite nonmagnetic metallic substrate occupying the halfspace z<O. The aim of the present thesis is twofold: firstly, the ground state of a ferromagnetic overlayer is investigated. In particular, the local densities of states (LOOS) of an overlayer are calculated using the method of adlayers. The method of adlayers is very simple, computationally stable and extremely accurate. The numerical results for the LOOS and the HartreeFock (HF) occupation numbers of a singleadlayer and a sevenadlayer overlayer are presented. The surface and bulk DOSs for an overlayer of seven atomic planes are compared. The presence of an adlayer may induce surface states if a strong enough perturbation occurs at the surface. Such surface states are automatically included in our method of adlayers. Secondly, spin waves in a transition metal overlayer are investigated within the framework of the itinerant theory of magnetism. The overlayer is modelled by a singleorbital tightbinding band with a strong intraatomic repulsion U (one band Hubbard model). All the matrix elements of the HF dynamic unenhanced susceptibility in the overlayer are computed from the HF oneelectron Green functions. Spin waves are then poles of the full dynamic enhanced susceptibility which is determined in the random phase approximation (RPA). It is demonstrated that a very high accuracy in solving the HF ground state is needed to determine correctly spin wave modes. When this requirement is fulfilled, the Goldstone theorem at zero wavevector and zero frequency is very well satisfied. Numerical results for the spin wave spectra of a singleadlayer are presented for a range of values of U. Spin wave energies for a singleadlayer, for an unsupported layer and the exchange stiffness constant 0 of an unsupported layer are compared. Finally, all the computed spin wave branches of an overlayer of seven atomic planes are presented and discussed. The disappearance of spin waves in the Stoner continuum is illustrated and the possibility that a surface spin wave mode might occur is briefly discussed.
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