GDR-Physique Quantique Mésoscopique, 8-11 Décembre 2008 Microscopic Origin of CPP-GMR… SPIN ACCUMULATION & SPIN DIFFUSION Henri JAFFRES Unité Mixte de Physique CNRS/Thales et Université Paris Sud 11 a terrific example of how fundamental research can lead to cutting-edge technology, which in turn feeds back into fundamental research -- in this case, possibly enabling future breakthroughs in nanotechnology and quantum computing. GDR-Physique Quantique Mésoscopique, 8-11 Décembre 2008

Spin-polarized transport in 3d Ferromagnet *) two current model by Mott M Ex: Co Transport du courant en parallèle pa un canal d’ ⓔ de spin  et un canal de spin  Résistivité dans chaque canal proportionnelle au nombre de transition sd EF s d *) Equivalent resistor scheme *) Bulk spin asymetry coefficient

CPP-GMR & SPIN ACCUMULATION NANOWIRES : Co Co H(kG) (NiFe50Å)/Cu40Å) (Co100Å/Cu50Å) Piraux et al.; Appl. Phys. Lett. 65, 2484 (1994) Blondel et al.; Appl. Phys. Lett. 65, 3019 (1994) First measurements of CPP-GMR in 2-D multilayers, see Schroeder, Bass, Pratt (MSU) For a review see Barthélémy et al., Handbook of Magn. Mat., vol.12, edt by K.J.Buschow , Elsevier(1999)

CPP-GMR & SERIES RESISTANCE MODEL P configuration AP configuration M NM M M NM M   CONDITIONS : thickness << Spin Diff. Length lsf & Spin relaxation negligible in Cu   r R R  = (r+R)/2 R  = (R+r)/2 R  = r r r SPIN ACC. R R Current spin polarization R  = R GMR as a probe of the current spin polarization T. Valet - A. Fert, PRB (1993)

IN MAGNETIC MULTILAYER SPIN ACCUMULATION IN MAGNETIC MULTILAYER s s d d

Ferromagnet ( ex: Fe, Co ) current Spin Polarization Interface FM/NM : mécanisme d’injection de spins Spin Polarization ex: Co = 0.46 Mott, Proc. Roy. Soc. 156, 368 (1936) Campbell-Fert, Ferrom. mater, vol.3, 717 (1982) Ferromagnet ( ex: Fe, Co ) Non magnetic ( ex: Cu, GaAs ) zone of spin accumulation Splitting of  and  Fermi levels  current Spin Polarization diffusive spin current Van Son, PRL 58 (1987)

Good conductivity matching for metals Injection métal magnétique  métal non magnétique FM NM T. Valet, A. Fert, PRB 1993 number of spin flips in F accum. spins in FM accum. spins in NM number of spin flips in NM Good conductivity matching for metals

Profile n(x) of carrier density DIFFUSIVE CURRENT Profile n(x) of carrier density Jl n(x) current J ? Jr : mean free path z Diffusion constant

(related to band filling) DIFFUSION CURRENT carrier density Fermi level density of states EF EF,0=equilibrium chemical potential (related to band filling) EF=c

DRIFT CURRENT Ohm’s law Drift current JE in the presence of an electric field E *) average velocity acquired by a particle between 2 successive diffusions Momentum relaxation time : Displacement of the Fermi surface drift velocity Electrical potential Ohm’s law

ELECTROCHEMICAL POTENTIAL relaxation term phenomenological

DIFFUSION Vs. BROWNIAN MOTION ( E=0 ) Diffusion equation S *) EXPLORATION RADIUS  mean free path *) NUMBER OF SURFACE ‘S’ CROSSINGS

SPIN ACCUMULATION & SPIN CURRENT p ,  (mean free path) sf, lsf (spin diffusion length) t=0 lsf

CHEMICAL vs. ELECTRICAL POTENTIALS d d eV zone of spin accumulation Co Cu

LINK BETWEEN SPIN CURRENT & SPIN ACCUMULATION

SPIN ACCUMULATION & SPIN CURRENT diffusive spin current FM NM Interface z=0 Current polarization continuity of spin current Co Cu = spin-polarized current at the interface

SIMPLE SCHEME FOR MAGNETORESISTANCE FM Interface z=0 NM potential drop at the interface

Positive MR CONTACT RESISTANCE Vs. SPIN ACCUMULATION SPIN ASSYMETRY Paramagnetic electrodes SPIN ASSYMETRY FERROM. RESISTIVITY  FERROM. SPIN DIFF. LENGTH  CHARACTERISTIC RESISTANCE

EFFETS DE BULK + INTERFACE FM NM

CPP-GMR & SPIN ACCUMULATION NANOWIRES : Co Co H(kG) (NiFe50Å)/Cu40Å) (Co100Å/Cu50Å) Piraux et al.; Appl. Phys. Lett. 65, 2484 (1994) Blondel et al.; Appl. Phys. Lett. 65, 3019 (1994) First measurements of CPP-GMR in 2-D multilayers, see Schroeder, Bass, Pratt (MSU) For a review see Barthélémy et al., Handbook of Magn. Mat., vol.12, edt by K.J.Buschow , Elsevier(1999)

CPP-GMR & SERIES RESISTANCE MODEL P configuration AP configuration M NM M M NM M   CONDITIONS : thickness << Spin Diff. Length lsf & Spin relaxation negligible in Cu   r R R  = (r+R)/2 R  = (R+r)/2 R  = r r r SPIN ACC. R R Current spin polarization R  = R GMR as a probe of the current spin polarization T.Valet - A. Fert, PRB (1993)

SPIN-SWITCH : DETECTION ELECTRIQUE D’UNE ACCUMULATION DE SPINS Principle : Johnson and Silsbee, PRL 55, 1790 (1985) ; PRB 37, 5312 (1988) Experiments : Jedema et al., Nature 410, 345 (2001) A. Fert & al., J. Phys. D : Appl. Phys 35, 2443 (2002) ; J.-M. George PRB (2003) spin injection into Cu (N) through a first magnetic electrode magnetic third contact  100 nm

Good conductivity matching for metals FM NM T. Valet, A. Fert, PRB 1993 accum. spins in FM accum. spins in NM number of spin flips in F number of spin flips in NM Good conductivity matching for metals

discontinuity of EF,  and EF,  at interface = (1 ) rb j, Rashba PRB 62,R16267 (2000); Fert-Jaffres PRB 64,184420 (2001) discontinuity of EF,  and EF,  at interface = (1 ) rb j, large interface resistance  large discontinuity of EF  number of spin flip in F  number of spin flip in SC  Increase of the spin diffusive current in the semiconductor

CASE OF MULTILAYERS accumulation vector at left accumulation vector Co  Cu Co  Cu accumulation vector at left accumulation vector at right propagation matrix transfer matrix interface matrix

Ferromagnet ( ex: Fe, Co ) current Spin Polarization Interface FM/NM : mécanisme d’injection de spins Spin Polarization ex: Co = 0.46 Mott, Proc. Roy. Soc. 156, 368 (1936) Campbell-Fert, Ferrom. mater, vol.3, 717 (1982) Ferromagnet ( ex: Fe, Co ) Non magnetic ( ex: Cu, GaAs ) zone of spin accumulation Splitting of  and  Fermi levels  current Spin Polarization diffusive spin current Van Son, PRL 58 (1987)

FM NM T. Valet, A. Fert, PRB 1993

discontinuity of EF,  and EF,  at interface = (1 ) rb j, Rashba PRB 62,R16267 (2000); Fert-Jaffres PRB 64,184420 (2001) discontinuity of EF,  and EF,  at interface = (1 ) rb j, large interface resistance  large discontinuity of EF  number of spin flip in F  number of spin flip in SC  Increase of the spin diffusive current in the semiconductor

Magnetic tunnel junction : Spin-dependent Interface resistance FM I SC Tunnel junction = Spin-Dependent interface resistance  P : polarisation

SPIN INJECTION : MICROSCOPIC MODEL OF DIFFUSION current polarization ? NO YES FM SC ? FM  SC FM SC FM  d Sink Sink  Probe ? ? resistive interface ( T ) Current polarization : Current polarization :

Spin Accumulation Vs. Spin Current FM I SC

EFFETS DE BULK + INTERFACE FM NM

EFFETS DE BULK + INTERFACE FM NM

+ - CoFe MgO AlGaAs(n) GaAs AlGaAs(p) Spin LED Coll., LPCNO TOULOUSE (X. Marie)

Electrical spin injection & optical detection Polarisation-resolved Electroluminescence experiments 1 3 s+ s - H s- s+ s- s+ Measure of the circular polarization(Pc) Determine the current spin-polarization injected in the Quantum well I+ - I- I+ + I- Pc (EL) = « Injection and detection of a spin-polarized current in a light-emitting diode », R. Fiederling et al., Nature 402, 787 (1999)

Zhu et al., Phys. Rev. Lett. 87, 016601 (2001) INJECTION INTO (Al)GaAs THROUGH A SCHOTTKY BARRIER : DETECTION BY ELECTROLUMINESCENCE MEASUREMENTS TG=10°C Hanbicki et al., Appl. Phys. Lett. 80, 1240 (2002) Zhu et al., Phys. Rev. Lett. 87, 016601 (2001) Ploog, J. Appl. Phys., 91 (10), 7256 (2002) TG=50°C

INJECTION INTO GaAs THROUGH AN OXIDE BARRIER (Al2O3) V.F. Mostnyi, V.I. Safarov, Appl. Phys. Lett. 81(2), 265 (2002) 1 SZ  2.5%  Pelec. >10 % P. Van Dorpe et al, Jpn. J. Appl. Phys. Part 2, vol.42, L502 (2003) SZ  8%  Pelec. >24 % sputtering MBE 100 nm Oblique Hanle Effect (OHE)

INJECTION INTO GaAs THROUGH AN OXIDE BARRIER (Al2O3) V.F. Mostnyi, V.I. Safarov, Appl. Phys. Lett. 81(2), 265 (2002) 1 SZ  2.5%  Pelec. >10 % P. Van Dorpe et al, Jpn. J. Appl. Phys. Part 2, vol.42, L502 (2003) SZ  8%  Pelec. >24 % sputtering MBE 100 nm Oblique Hanle Effect (OHE)

OPTICAL DETECTION OF SPIN ACCUMULATION IN GaAs

Injection électrique et détection optique de spin a) Croissance T° ambiante b) Croissance 300° C Circular polarization Vs. perpendicular magnetic field Y. Lu et al., Appl. Phys. Lett. 93, 152102 (2008)

Measurement of t(T) et ts (T) et F(T) by Time-Resoloved PL experiments  Lifetime and S spin relaxation time PC = F*Ps Ps is the spin-polarization of electrons injected in the QW F(T) = 1 1+(T)/ S(T))

Mg0 thickness dependence on spin-injection yield Sample Thickness (nm) A 1.4 B2 2.6 C 4.3 The EL Spin-polarization increases With MgO thickness B2 A C

MR vs. characteristic times… ‘Courant de spin de rétrodiffusion’ injection détection

HANLE EFFECT = DEPOLARIZATION BY SPIN PRECESSION AROUND A TRANSVERSE MAGNETIC FIELD

Hanle effect

A SINGLE CONTACT EXPERIMENT…… n  51018 cm-3 n  21019 cm-3 w L 2 1 W M I GaAs Co Al2O3 H Coll. LPN Marcoussis (A. Lemaitre)

VARIATION OF THE CONTACT RESISTANCE …… ( NO WEAK LOCALIZATION EFFECT ! )

Electrical measurements… B C a b

Electrical measurements… B C a b Kerr effect…

Resume : MR Vs. INTERFACIAL RESISTANCE (CPP GEOMETRY) A. Fert, H. Jaffrès. Phys. Rev. B, 64, 184420 (2001) FM SC d NO SPIN INJECTION + NO SPIN DETECTION INJECTION & DETECTION