Perhaps the best way to explain that there are also quite a few physical reasons to distinguish between capped surfaces and spin valves is to go back to Table 11.2, from which a direct comparison between these two cases can be found. As can be seen from the last two rows, for a thin film consisting of 7 Fe ML on Cu(100) the magnetic moment in the surface layer (m7) is oriented antiparallel to the one neighboring the Cu substrate. In the case of a spin valve (infinitely thick Cu cap) m7 is parallel to the first one, since symmetric boundary conditions apply:


⎧ ⎨ ⎩ Vac m7 = −2.232

Cu(100) m7 = 2.520

If the substrate and the cap are very much thicker than the actual film as is the case, e.g., when viewing these two parts of the system as leads in measurements of electric transport properties, then the term spin valve is justified. Of course there is another more practical difference between free magnetic surfaces and spin valves, namely in spin valves interdiffusion between spacer and substrate can occur at two interfaces, while interdiffusion effects for free surfaces of magnetic thin films on top of a substrate are in principle restricted to one interface. It was already shown in the last chapter and will be again discussed in

this one that interfaces and boundaries are rather important for the physical properties of systems nanostructured in one dimension. In particular a proper use of boundaries in any kind of theoretical description has perhaps unforeseen consequences. Take for example the case of Fe/Cr trilayers, Fen1CrmFen2 with fixed numbers n1 and n2 of Fe layers on both sides of the Cr slab. Treated as a "free standing" thin film for each combination of n1, n2 and m in principle a different Fermi energy F (n1, n2,m) applies. If m becomes large, sayM , then


F (n1, n2,m) tends to the Fermi energy of "bulk Cr", F (Cr). Considered as a semi-infinite system with Fe serving as substrate, e.g., Fe(100)/Fen1CrmFen2 , the Fermi energy is always that of the substrate (electron reservoir), namely F (Fe), i.e., remains constant for all finite m:

vac/Fen1CrmFen2/vac : limm→M F (n1, n2,m) ∼ F (Cr)

Fe(100)/Fen1CrmFen2/V ac


⎫ ⎬ ⎭ = limm→MF (n1, n2,m) ≡ F (Fe) .