Models in spintronics (Part I) OUTLINE : Spin-dependent transport - PowerPoint PPT Presentation

Models in spintronics (Part I) OUTLINE : Spin-dependent transport in metallic magnetic multilayers -Introduction to spin-electronics -Spin-dependent scattering in magnetic metal -Current-in-plane Giant Magnetoresistance -Modelling transport in CIP spin-valves -Current-perpendicular-to-plane Giant Magnetoresistance -Spin accumulation, spin current, 3D generalization. B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Birth of spin electronics : Giant magnetoresistance (1988) Fe/Cr multilayers Fert et al, PRL (1988), Nobel Prize 2007 Two limit geometries of measurement: I ~ 80% V I Current-in-plane I V I Magnetic field (kG) I Current-perpendicular-to-plane R R  AP P GMR  R P Antiferromagnetically coupled multilayers B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Low field GMR: Spin-valves -3 emu) (a) 1 Antiferromagnetic FeMn 90Å M (10 pinning layer 0 Ferromagnetic -1 NiFe 40Å pinned layer (b) Non magnetic spacer Cu 22Å 4  R/R (%) 3 NiFe 70Å Soft ferromagnetic layer 2 Ta 50Å Buffer layer 1 0 400 600 800 -200 0 200 substrate H(Oe) 4 (c)  R/R (%) 3 IBM Almaden 2 Ultrasensitive magnetic field sensors (MR heads) Spin engineering 1 0 B.Dieny et al, Phys.Rev.B.(1991)+patent US5206590 (1991). -40 -20 40 0 20 H(Oe) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Benefit of GMR in magnetic recording GMR spin-valve heads from 1998 to 2004 B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Two current model (Mott 1930) for transport in magnetic metals As long as spin-flip is negligible, current can be considered as carried in parallel by two categories of electrons: spin  and spin  (parallel and antiparallel to quantization axis)  1     1 1                      Sources of spin flip: magnons and spin-orbit scattering Negligible spin-flip often crude approximation (spin diffusion length in NiFe~4.5nm, 30% spin memory loss at Co/Cu interfaces) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Spin dependent transport in magnetic metals (1) Band structure of 3d transition metals In transition metals, partially filled bands which participate to conduction are s and d bands Non-magnetic Cu : Magnetic Ni : E E s  (E) s  (E) s  (E) s  (E) D  (E) D  (E) D  (E) D  (E) E E D  (E F )  D  (E F ) D  (E F ) = D  (E F ) Most of transport properties are determined by DOS at Fermi energy Spin-dependent density of state at Fermi energy B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Spin dependent transport in magnetic metals (2) m*(d) >> m*(s) J mostly carried by s electrons in transition metals Scattering of electrons determined by DOS at E F : E s  (E) s  (E) P  2    i W f D f E ( ) Fermi Golden rule : F D  (E) s  s  D  (E) d  s  s  d  Most efficient scattering channel Spin-dependent scattering rates in magnetic transition metals     10 nm ; 1 nm Example:   Co Co B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Potential experienced by conduction electrons in magnetic metallic multilayers Parallel magnetic configuration Antiparallel magnetic configuration Co/Cu majority electrons : antiparallel magnetic configuration Co/Cu majority electrons : parallel magnetic configuration Co Cu Co Cu (c) (a) Co/Cu minority electrons : parallel magnetic configuration Co/Cu minority electrons : parallel magnetic configuration Co/Cu minority electrons : antiparallel magnetic configuration U(x,z) (b) (d) x z •Lattice potential modulation due to difference between Fermi energy and bottom of conduction band (reflection, refraction) •Spin-dependent scattering on impurities, interfaces or grain boundaries (Dominant effect in GMR) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Simple model of Giant Magnetoresistance Parallel config Antiparallel config Fe Cr Fe Fe Cr Fe 2        2      1         ap        1   Equivalent resistances :               Key role of     2    scattering contrast         AP    P    2   B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current-in-plane transport (semi-classical Boltzman theory of GMR) Approach initiated by Camley and Barnas, PRL, 63, 664 (1989) Gas of independent particles described by distribution f(r, v, t), submitted to force field F (=-e E for electrons in electrical field E). Time evolution of the distribution described by Boltzman equation: Equilibrium function conserved in a volume element d r d v along a flow line. df  df   df         0 t+dt In presence of scattering, dt  dt   dt  t F scattering E Balance between acceleration due to force and relaxation due to scattering          df f f f f f f f          . v . v . v . a . a . a x y z x y z         dt  t x y z v v v F x y z       f        m a F v . f a . f with  r v  t B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

        df df f F            v . f . f  r v  dt dt t m     F scatt  f  0 In stationary regime,  t     0   df f f    In single relaxation time approximation (  )  dt   scatt Where f 0 is the equilibrium distribution (Fermi Dirac for electrons). Boltzmann equation for electron gas in electrical field E :         0 e E f f      v . f . f  r v  m B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current transport in bulk metals I               f r , v f r , v g r , v 0 V Perturbation Fermi-Dirac due to electric field 1      f r , v      0 I    exp F 1   k T   B    E      0 e E f f      v . f . f  x r v  m   f  0 Spatially homogeneous transport  r k z   eE f  g ( v ) x 0 x  m v x k x In k-space, shift in Fermi surface by  k     k eE  k y x B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current transport in bulk metals (cont’d) Current density: (     3 j e v g v ) d v x  2 ne 1     j E E E  m ne  2   m Well-known expression of conductivity in Drude model n=density of conduction electrons n~1/atom in noble metals such as Cu, Ag, Au n~0.6/atom in metals such as Ni, Co, Fe B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Typical resistivity of sputtered metals Material Measured Material Measured resistivity resistivity (ferro) 4K/300K 4K/300K 0.5-0.7  .cm Cu a 10-15  .cm Ni 80 Fe 20 a 3-5 22-25 1  .cm Ag f 9-13  .cm 7 Ni 66 Fe 13 Co 2 20-23 b 2  .cm Au g 1 8 4.1-6.45  .cm Co a,d 160  .cm 12-16 Pt 50 Mn 50 e 180 6-9  .cm Co 90 Fe 10 h 140  .cm Ni 80 Cr 20 13-18 e 140 7-10  .cm Co 50 Fe 50 h 9.5-11  .cm 15-20 Ru c 14-20 Thermal variation of resistivity due to phonon scattering and magnon scattering (in magnetic metals) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Modeling current transport in metallic thin films I               f r , v f r , v g r , v 0    z      V 0 e E f f      v . f . f  r v  I m E x Due to scattering at outer surfaces, the perturbation g is no longer homogeneous: g(z)         0 g z , v g z , v eE f v      z v mv v z z x     = elastic mean free path Integration constants determined v F from boundary conditions General solution :      f z        0   g z , v eE v 1 A exp      x    v       z +(-) refer to electrons traveling towards z>0 (z<0) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara