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

14multiplication. The variation of A Ep obtained from thecalculated values of E + M and E− Mis plotted in Fig.11. Below100eV injection energy, A Ep is almost constant andclose to 0.5. Beyond 100eV, A Ep decreases very slowly:over the entire probed energy range, the value of A Epranges from 0.25 to 0.5. Note that, if minority-spin pri-For the evaluation of A p (ε), we use Eqs.(31) and (32).Fig.12(a) shows the variation of A p (ε) for three values ofthe mean energy E M :0.15eV, 0.45eV and 0.9eV, whichcorrespond to three different values of the injection energy.The positions of the two barrier heights are indicatedby vertical dotted lines. It is clear that for smallvalues of the mean energy E M , A p (ε) maybeconsideredas constant and equal to unity for both contributionsto the transmission, above φ SC . and above φ Ox .But for higher values of E M , A p (ε) cannot be taken asequal to 1 above φ SC . As a consequence, the spin dependenttransmission should tend to decrease. The plot of(ε/EM A p (ε) − 2A Ep)f (ε) for the same three values ofE M(Fig.12(b)) clearly shows that, the spin-dependenttransmission above φ SC should even become negativewhen E M increases.FIG. 11: Variation of A Ep =(E + M − E− M )/(E+ M + E− M), thespin-asymmetry of the electron mean-energy and of the ratio(E + M + E− M)/2EM with injection energy E0. These quantitiesare obtained from the variation of E M , E + M and E− M whichhave been independently calculated as described in Sec.III.A.2using respectively λ(ε), λ + and λ − for the variation of theelectron mean-free-path versus energy.mary electrons had, in average, one more collision thanmajority-spin primary electrons, the spin-asymmetry ofthe primary electron mean energy would be equal to 2/3.FIG. 12: Variation with electron energy (a) of A p(ε), thespin[asymmetry of]the electron distribution, and (b) ofA p(ε) εE M− 2A Ep f(ε) the argument of the integral in theexpression of ΔT [Eqs.(29 and (B2]. Three calculated curvesare shown corresponding to three different values of the electronmean energy E M (0.15eV, 0.45eV, and 0.9eV) at themetal/oxide interface. The two vertical dotted lines indicatethe positions of the two barrier heights φ SC and φ Ox.