Intrinsic periodicity associated with quantum-well states in a magnetic sandwich

From a simplified quantum-well model for a magnetic sandwich, it can be shown that in the variation of the number of occupied levels with the spacer layers, there exists an intrinsic periodicity, which leads the Fermi level to oscillate periodically. The intrinsic periodicity does not depend on the magnetic alignment but only on the quantum-well states themselves. The oscillation period can be approximately given by T=(1/ beta ) exp 3 root Pi mu sub parallel to /(3n sub 0 mu sub perpendicular ), where mu sub parallel to and mu sub perpendicular are the effective masses of the electron in the lateral and perpendicular directions respectively, beta is the distance between the two neighboring atomic layers, and n sub 0 is the electron density in the spacer layers. This makes one speculate that the long periodicity of the oscillatory coupling could be a result of the intrinsic periodicity, if mu sub parallel to / mu sub perpendicular > > 1 and a small s-electron density are assumed. On the other hand, from the calculated energy bands for a thin film, it is found that the electronic structure is highly anisotropic, which is in agreement with this assumption. Therefore, it can be confirmed that the intrinsic periodicity plays an important role in the oscillatory coupling. An inverse photoemission experiment on Cu(100) films over Co can be explained quite well using this physical picture.