4 Multi-Layer Structures

Figure 3: Reflection Paths for an Electron Wave in a Single Magnetic Layer

We propose to extend this analysis to magnetic multi-layer structures, by using the theory of Fabry-Perot etalons, as is [2,3] already the practice in PNR. There are infinitely many possible paths for reflection from a multi-layer structure, indexed by how many times the electron wave ``bounces'' within each layer. In the diagram (figure 3,) we can see paths with no bounces, with one bounce, and with two bounces. For a given, pure incident wave, the reflected waves from the various paths are superposed coherently to build the reflected wave, each term in the coherent superposition including an amplitude factor due to the amplitude reflection or transmission coefficient at each interface which it has encountered, and a phase factor due to the path length which it has traversed in the magnetic layers. This will result in a spin-dependent amplitude reflection coefficient for the whole multi-layer system, which will provide the weightings to go into the incoherent superposition over an unpolarized incident beam. This incoherent superposition, as for the bulk sample, will give the reflected polarization. We expect working through the maths for this to be trivial, but time-consuming.