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Abstract

A layer within a magnetic multilayer may exhibit properties radically different from its bulk properties, when the thickness of the layers is very small. It has been found experimentally that the magnetic moments of magnetic layers separated by a thin non-magnetic spacer spontaneously align either ferromagnetically or antiferromagnetically, depending on the thickness of the spacer layer. This type of magnetic interaction is called exchange coupling J(N) and is observed to oscillate as a func-tion of the spacer thickness N. The purpose of this thesis is to give details of one theoretical approach which can be used to model exchange coupling in magnetic multilayers. Currently three different models have been employed and we start by giving a brief details of these three methods. In the remaining Chapters we develop our preferred model, the Quantum well theory. A theory for the one band model at zero temperature is developed by expressing J(N) in terms of the local Green’s functions of the trilayer. The local Green’s functions are obtained using a very versatile method which can be applied to obtain the local Green’s function of any atomic plane in any type of multilayer. The band structure used to describe the trilayer is the tight-binding model. A numerical approach is developed to compute the ex-change coupling. This requires a considerable amount of time to compute rendering it impractical to use. Therefore we develop an asymptotic expansion of J(N) which relates the exchange coupling to the spacer layer and enables us to compute J(N) in a reasonable amount of time. We consider a single example of exchange coupling for a one band trilayer to ensure the two methods are in agreement with each other. The one band model is useful to help understand the physical mechanisms in exchange coupling but its applications are limited. We therefore generalize all the models and methods of computation so that we can compute the exchange coupling for a two band trilayer. Here we can fully take into account the hybridization between the bands. An investigation into what effect the hybridization in the ferromagnetic and spacer layers has on the exchange coupling is given. Due to the possibility the exchange coupling may oscillate with two periods for the two band trilayer we finally consider a single example of double-period exchange coupling.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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