Microscopic Origin of CPPGMR SPIN ACCUMULATION SPIN DIFFUSION

Microscopic Origin of CPP-GMR… SPIN ACCUMULATION & SPIN DIFFUSION Henri JAFFRES Unité Mixte de Physique CNRS/Thales et Université Paris Sud 11 GDR-Physique Quantique Mésoscopique, 8 -11 Décembre 2008

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

CPP-GMR & SPIN ACCUMULATION NANOWIRES : Co Co (Co 100Å/Cu 50Å) (Ni. Fe 50Å)/Cu 40Å) H(k. G) 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 M NM M AP configuration M NM M CONDITIONS : thickness << Spin Diff. Length lsf & R R = (r+R)/2 r R R =R R SPIN ACC. R = r r r R Spin relaxation negligible in Cu R r = (R+r)/2 Current spin polarization GMR as a probe of the current spin polarization T. Valet - A. Fert, PRB (1993)

SPIN ACCUMULATION IN MAGNETIC MULTILAYER s d

Interface FM/NM : mécanisme d’injection de spins Ferromagnet ( ex: Fe, Co ) Mott, Proc. Roy. Soc. 156, 368 (1936) Non magnetic Campbell-Fert, Ferrom. mater, vol. 3, 717 (1982) ( ex: Cu, Ga. As ) Spin Polarization zone of spin accumulation ex: Co = 0. 46 Splitting of and Fermi levels current Spin Polarization diffusive spin current Van Son, PRL 58 (1987)

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

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

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

DRIFT CURRENT Drift current JE in the presence of an electric field E *) average velocity acquired by a particle between 2 successive diffusions Momentum relaxation time : drift velocity Displacement of the Fermi surface 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 t=0 lsf p , (mean free path) sf, lsf (spin diffusion length)

CHEMICAL vs. ELECTRICAL POTENTIALS s d e. V Co zone of spin accumulation Cu

LINK BETWEEN SPIN CURRENT & SPIN ACCUMULATION

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

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

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

FM EFFETS DE BULK + INTERFACE NM

CPP-GMR & SPIN ACCUMULATION NANOWIRES : Co Co (Co 100Å/Cu 50Å) (Ni. Fe 50Å)/Cu 40Å) H(k. G) 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 M NM M AP configuration M NM M CONDITIONS : thickness << Spin Diff. Length lsf & R R = (r+R)/2 r R R =R R SPIN ACC. R = r r r R Spin relaxation negligible in Cu R r = (R+r)/2 Current spin polarization 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

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

Rashba PRB 62, R 16267 (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 SC Increase of the spin diffusive current in the semiconductor

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

Interface FM/NM : mécanisme d’injection de spins Ferromagnet ( ex: Fe, Co ) Mott, Proc. Roy. Soc. 156, 368 (1936) Non magnetic Campbell-Fert, Ferrom. mater, vol. 3, 717 (1982) ( ex: Cu, Ga. As ) Spin Polarization zone of spin accumulation ex: Co = 0. 46 Splitting of and Fermi levels current Spin Polarization diffusive spin current Van Son, PRL 58 (1987)

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

Rashba PRB 62, R 16267 (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 SC Increase of the spin diffusive current in the semiconductor

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

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

Spin Accumulation Vs. Spin Current FM I SC

FM EFFETS DE BULK + INTERFACE NM

FM EFFETS DE BULK + INTERFACE NM

- + Co. Fe Mg. O Al. Ga. As(n) Ga. As Al. Ga. As(p) Spin LED Coll. , LPCNO TOULOUSE (X. Marie)

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

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

INJECTION INTO Ga. As THROUGH AN OXIDE BARRIER (Al 2 O 3) V. F. Mostnyi, V. I. Safarov, Appl. Phys. Lett. 81(2), 265 (2002) sputtering MBE 100 nm Oblique Hanle Effect (OHE) 1 SZ 2. 5% Pelec. >10 % P. Van Dorpe et al, Jpn. J. Appl. Phys. Part 2, vol. 42, L 502 (2003) SZ 8% Pelec. >24 %

INJECTION INTO Ga. As THROUGH AN OXIDE BARRIER (Al 2 O 3) V. F. Mostnyi, V. I. Safarov, Appl. Phys. Lett. 81(2), 265 (2002) sputtering MBE 100 nm Oblique Hanle Effect (OHE) 1 SZ 2. 5% Pelec. >10 % P. Van Dorpe et al, Jpn. J. Appl. Phys. Part 2, vol. 42, L 502 (2003) SZ 8% Pelec. >24 %

OPTICAL DETECTION OF SPIN ACCUMULATION IN Ga. As

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) et s (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))

Mg 0 thickness dependence on spin-injection yield Sample Thickness (nm) A 1. 4 B 2 2. 6 C 4. 3 B 2 C A The EL Spin-polarization increases With Mg. O thickness

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

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

Hanle effect

A SINGLE CONTACT EXPERIMENT…… 1 I Co M Al 2 O 3 W w Ga. As 2 H L n 2 1019 cm-3 n 5 1018 cm-3 Coll. LPN Marcoussis (A. Lemaitre)

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

Electrical measurements… A A C B a b B C

Electrical measurements… A A C B a b B C Kerr effect…

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