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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.
15∗ Electronic address: Yves.Lassailly@polytechnique.edu1 J. Unguris, D. T. Pierce, A. Galejs, and R. J. Celotta,Physical Review Letters 49, 72 (1982).2 E. Kisker, W. Gudat, and K. Schroder, Solid State Communications44, 591 (1982).3 H. Hopster, R. Raue, E. Kisker, G. Guntherodt, andM. Campagna, Physical Review Letters 50, 70 (1983).4 D. R. Penn, S. P. Apell, and S. M. Girvin, Physical ReviewB 32, 7753 (1985).5 D. P. Pappas, K. P. Kamper, B. P. Miller, H. Hopster,D. E. Fowler, C. R. Brundle, A. C. Luntz, and Z. X. Shen,Physical Review Letters 66, 504 (1991).6 M. Getzlaff, J. Bansmann, and G. Schonhense, Solid StateCommunications 87, 467 (1993).7 G. Schonhense and H. C. Siegmann, Annalen Der Physik2, 465 (1993).8 E. Vescovo, C. Carbone, U. Alkemper, O. Rader,T. Kachel, W. Gudat, and W. Eberhardt, Physical ReviewB 52, 13497 (1995).9 Y. Lassailly, H. J. Drouhin, A. J. Vandersluijs, G. Lampel,and C. Marliere, Physical Review B 50, 13054 (1994).10 A. van der Sluijs, Ph.D. thesis, Ecole Polytechnique (1996).11 J. C. Grobli, D. Guarisco, S. Frank, and F. Meier, PhysicalReview B 51, 2945 (1995).12 H. J. Drouhin, A. J. vanderSluijs, Y. Lassailly, andG. Lampel, Journal Of Applied Physics 79, 4734 (1996).13 D. Oberli, R. Burgermeister, S. Riesen, W. Weber, andH. C. Siegmann, Physical Review Letters 81, 4228 (1998).14 C. Cacho, Y. Lassailly, H. J. Drouhin, G. Lampel, andJ. Peretti, Physical Review Letters 88, 066601 (2002).15 D. J. Monsma, J. C. Lodder, T. J. A. Popma, and B. Dieny,Physical Review Letters 74, 5260 (1995).16 T. Kinno, K. Tanaka, and K. Mizushima, Physical ReviewB 56, R4391 (1997).17 P. N. First, J. A. Bonetti, D. K. Guthrie, L. E. Harrell,and S. S. P. Parkin, Journal Of Applied Physics 81, 5533(1997).18 A. Filipe, H. J. Drouhin, G. Lampel, Y. Lassailly, J. Nagle,J. Peretti, V. I. Safarov, and A. Schuhl, Physical ReviewLetters 80, 2425 (1998).19 W. H. Rippard and R. A. Buhrman, Applied Physics Letters75, 1001 (1999).20 S. van Dijken, X. Jiang, and S. S. P. Parkin, AppliedPhysics Letters 83, 951 (2003).21 X. Jiang, S. van Dijken, R. Wang, and S. S. P. Parkin,Physical Review B 69, 014413 (2004).22 N. Rougemaille, H.-J. Drouhin, G. Lampel, Y. Lassailly,J. Peretti, T. Wirth, and A. Schuhl, AIP Conference Proceedings675, 1001 (2003).23 A. Filipe and A. Schuhl, Journal Of Applied Physics 81,4359 (1997).24 A. Filipe, Ph.D. thesis, Ecole Polytechnique (1997).25 D. Lamine, Ph.D. thesis, Ecole Polytechnique (2007).26 As discussed in Refs.24 − 25, the oxide layer formed onGaAs is most probably Ga 2O 3. The value of the oxideband gap measured on our samples is of about 4.6eV (seeRef.25). This is comparable with the values between 4eVand 5.2eV that can be found in the literature for the bandgap of various gallium oxides : see for instance, M. Passlak,E. F. Schubert, W. S. Hobson, M. Hong, N. Moriya,S. N. G. Chu, K. Konstadinidis, J. P. Mannaerts, M. L.Schnoes, and G. J. Zydzik, J. Appl. Phys. 77, 686 (1995);Z. Ji, J. Du, J. Fan, and W. Wang, Optical Materials 28,415 (2006).27 M. P. Seah and C. P. Hunt, Surface And Interface Analysis5, 33 (1983).28 It is sometimes considered that the primary and secondaryelectron distributions have identical shapes. This wouldonly be the case if all the electrons had the same number ofcollisions along the transport whatever their final emergingenergy (like in a thermalized electron distribution). Thisis not the case here and we consider that the number ofcollisions n that an electron undergoes during the transportacross the metal layer depends on its exit energy ε.This assumption seems reasonable since, for instance, itis clear that electrons transmitted at the injection energyE 0 (i.e. with no energy loss) had no collision while electronstransmitted with an energy very close to the barrierheight have certainly suffered in average many collisions.Then, according to the energy relaxation equation that wehave used [Eq.(5)], we obtain n (ε) =Ln (E 0/ε) /Ln (2).Consequently, at energy ε, the ratio of the total number ofelectrons (primaries and secondaries together) to the numberof primary electrons is F (ε) /f p (ε) =2 n(ε) = E 0/ε.29 In the configuration of the present experiment, we can onlymeasure the transmission asymmetry related to the primaryelectron polarization. Therefore, the polarization ofthe secondary electrons can not be evidenced since its orientationis determined by that of the magnetic layer magnetizationand not by the primary electron polarization.To evidence the spin-filtering of secondary electrons oneshould either use a spin-valve structure or measure the polarizationof the transmitted electrons.
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RésuméDRISS LAMINEEffet de filtre
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AbstractDRISS LAMINESpin filter eff
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RemerciementsRemerciementsJ’ai r
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Table des matièresTABLE DES MATIER
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Table des matières4.A. Notion de r
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PréambuleChapitre IPréambuleL’u
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PréambuleRougemaille03 : Rougemail
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Chapitre II - Concepts généraux a
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Chapitre V - Modélisation du trans
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Page 166 and 167: Conclusion et perspectivesFig.VI.1
Page 168 and 169: 156Conclusion et perspectives
Page 170 and 171: BibliographieHopster83 : Hopster et
Page 172 and 173: BibliographieWeber01 : Weber W. et
Page 174 and 175: BibliographiePierce75 :Pierce D.T e
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Page 190 and 191: 12APPENDIX A: VARIATION OF THE ELEC
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