Conductance modulation in a normal metal/ferromagnet/normal metal junction

Spin-dependent quantum transport in a NM1/FM/NM2 planar junction is studied, where FM and NM1,2 are a ferromagnet and two different normal metals, respectively. In this work, the oscillatory conductance depending on thickness of FM is studied by focusing on the scattering of the Schrüdinger electrons at the interfaces. The conductance modulation due to the energy of the mobile electrons split in FM layer occurs when FM and NM2 have both the Fermi energies much higher than that of the Fermi energy EF in NM1 and the exchange energy h1 in FM is much smaller than its Fermi energy EF1, h1/EF1⪡1h1/EF1⪡1. Comparing with the conductance modulation due to massless Dirac electron, recently investigated by Soodchomshom et al. [Phys. Lett. A 372 (2008) 5054], electrons in a conventional system, governed by Schrüdinger equation, always carry the modulated conductance with decaying amplitude when thickness of FM increases. This Schrüdinger conductance modulation is quite different from the massless Dirac modulated conductance with holding constant amplitude.