Etudes par microscopie en champ proche des phénomènes de ...

secondary electrons. Because of the spin-dependence ofthe electron mean free path in a magnetic metal layer,we will consider separately three electron distributions:the primary electron distribution with spin parallel to themajority spin, the primary electron distribution with spinparallel to the minority spin, and the secondary electrondistribution. We may somehow “distinguish” betweenprimary and secondary electrons because primaries arespin-tagged and we assume that there is no spin relaxationalong the transport. We also assume that the polarizationof the secondary electrons does not depend onthe incident polarization (no exchange integral effect), sothat we do not have to separate spin-up and spin-downsecondary electron distributions. Then, for an incidentbeam of spin polarization ±P 0 (wetakehereasaconventionthat the incident spin polarization is positive whenit is parallel to the majority spins in the ferromagneticlayer), the electron distribution F (ε, ±P 0 )thatformsinthe metal layer and reaches the metal /oxide interfacemay be written as the superposition of the three distributionsdefined above:8FIG. 6: (a) Calculated (full line) and experimental (symbols)variations with the injection energy E 0 of (a) the transmissionT , (b) the spin-dependent transmission ΔT , (c) the transmissionspin-asymmetry A C. For the three quantities T , ΔTand A C, the two contributions of the current transmittedabove the barrier φ SC (dotted lines) and above the barrierφ Ox (dashed lines) have been calculated.B. Spin-polarized electron transport through amagnetic metal/oxide/semiconductor junctionThe electronic distribution F (ε) that forms during thetransport through the metallic layer mixes primary andF (ε, ±P 0 )= 1 ± P 0f p + (ε)+ 1 ∓ P 0fp − (ε) (22)[221 ± P0 (+ M + − 1 ) + 1 ∓ P 0(M − − 1 )] f s (ε)22In this expression, f p + (ε) andfp − (ε) arethenormalizeddistribution of primary electrons with a spin parallelto, respectively, the majority spin and the minorityspin in the magnetic metal, and f s (ε) is the normalizeddistribution of secondary electrons. Because of the spinasymmetry of the electron mean-free-path in the magneticmetal, primary electrons have a different number ofcollisions across the magnetic layer depending on whethertheir spin is parallel to the majority spins or to the minorityspins. This has two consequences. The first one isthat majority- and minority-spin primary electrons havedifferent distributions f p + (ε) andfp − (ε): this is in fact thespin filtering effect. The second one is that majority- andminority-spin primary electrons have different secondaryelectron multiplication factors which are noted respectivelyM + and M − in Eq.(22). Indeed, if we note E p + ,Ep− and E s the respective mean energies of the three distributionsf p + (ε), fp − (ε) andf s (ε), the total energy lostby a primary electron is E 0 − E p± and this amount ofenergy is shared by M ± − 1 secondary electrons of meanenergy E s . Therefore, M + and M − are simply given by:M ± − 1= E 0 − E p± (23)E sNote that, majority spin electrons are better transmittedthan minority spin electrons, but consequently theyexcite less secondary electrons (M + is then smaller thanM − ). So the contribution of the secondary electron multiplicationspin asymmetry to the spin-dependent transmissiongoes against that of the spin filtering effect.