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Mairbek Chshiev European School on Magnetism Spintronics Conventional spintronics Spin-orbit phenomena -> Spin orbitronics Dzyaloshinskii- Magneto Spin Hall Spin-orbit Rashba Interlayer Spin GMR Spin Transfer Moriya (DMI)

  1. Mairbek Chshiev European School on Magnetism

  2. Spintronics Conventional spintronics Spin-orbit phenomena -> Spin orbitronics Dzyaloshinskii- Magneto Spin Hall Spin-orbit Rashba Interlayer Spin GMR Spin Transfer Moriya (DMI) crystalline Effect Torques Effect Exchange Filtering & Torques anisotropy (SHE) (SOT) (IEC) (SF) TMR (STT) … Ferrites AFM Layered Alloys Spin Frustrated Heusler (CoFe 2 O 4 ) Rutiles Domain walls Single & metals structures (BiCu, valves magnets alloys double Garnets IrCu …) (Pt/Co/AlOx, barrier perovskites Graphene AFM Interfaces ( Y 3 Fe 5 O 12 ) Ta/CoFe/MgO MTJs insulators … Tunnel magnetoresistance (TMR) Spin transfer torques (STT) • Quantum origin of spin transfer torque • Description of spin currents and spin transfer torques This lecture: - Free electron model - Tight-binding model • Voltage dependence of STT - symmetric MTJs - asymmetric MTJs Interlayer exchange coupling … M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  3. Spintronics Bloch state symmetry Tunnel (TMR) magnetoresistance: based Spin Filtering (SF) ||  magnetization acts on current  0 k ( k ) n Fe  M’ p z s d z 2 H M  1 in MgO TMR~600%  Fe|MgO|Fe E d xy F (Tohoku,2008)  E Huge TMR in crystalline MTJ if: F • Good epitaxial fit between FM and I(SC) • Evanescent states in I(SC) with the same Bloch state symmetry • High symmetry Bloch state (  1 ) for one of two e - d xz , d yz spin states in FM electrodes (“ half-metallic ” -like) p x , p y W. H. Butler et al, PRB (2001) The 1 st Brillouin zone with high symmetry k-points M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  4. Spintronics Bloch state symmetry Tunnel (TMR) magnetoresistance: based Spin Filtering (SF) magnetization acts on current W. H. Butler et al, PRB (2001) IEEE Trans. Mag. , 41 (2005) 2645 Sci. Technol. Adv. Mater. 9 (2008) 014106  M’ H M     -4 e   TMR~600% -8 e Fe|MgO|Fe  (Tohoku,2008) -12 e Huge TMR in crystalline MTJ if: -16 • Good epitaxial fit between FM and I(SC) e • Evanescent states in I(SC) with the same Bloch state symmetry -20 • High symmetry Bloch state (  1 ) for one of two e - e spin states in FM electrodes (“ half-metallic ” -like) W. H. Butler et al, PRB (2001) 0 5 10 15 20 25 layer Fe  Fe  MgO The 1 st Brillouin zone with high symmetry k-points M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  5. Spintronics Tunnel (TMR) magnetoresistance: magnetization acts on current   R R ( H ) R  TMR AP P  R P  ( j ) R M’ H M GMR, TMR, STT Spin Transfer Torque (STT): Field (Oe) current acts on magnetization Current (mA) ref free MTJs Logic Functional  M’ devices Si j M Logics Cu J PtMn CoFe “0” “1” (R high ) (R low ) MgO CoFe R(H) MRAM Freescale 4Mbit (Pt/Co) Cu Sensors RF components Memories M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  6. Spintronics Quantum transport theory and electronic structure of materials for spintronics Tunnel Materials Spin transfer Spin Spin Hall Giant m agnetoresistance for spintronics Effect (SHE) torque (STT), filtering magnetoresistance (TMR ) exchange coupling chalcogenides , (GMR) alloys amorphous and crystalline (IEC), anisotropy rutiles , spinels , metallic crystalline , single magnetic tunnel Heusler alloys, nanostructures amorphous and and double barrier junctions Graphene , crystalline tunnel tunnel junctions frustrated junctions magnets Keldysh formalism Kubo formalism Boltzmann approach Ab - initio (DFT ) Tight - binding model Free electron model (drift - diffusion) Calculation techniques + Condensed Matter Theory Computational Materials Science M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  7. Julliere 1975 -> Moodera 1995 Moodera et al, PRL 74, 3273 (1995) Miyazaki  Different H coercive fields Fe AlOx Co For Co, Fe Parallel configuration Antiparallel configuration  R/R~ 15% 300K  P+0.26             parallel antiparall el J D D D D J D D D D L R L R L R L R     2 ( ) ( ) R P P D E D E    ( ) ( ) L R L R F L R F TMR P  ( )   L R  1 R P P ( ) ( ) D E D E P L R L ( R ) F L ( R ) F P>0 (~50%) in Fe, Co   R/R~40 - 70% with alumina barriers at low T M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  8. Stearns’ polarization    ( ) ( ) D E D E  ( ) ( ) L R F L R F P ( )   L R  ( ) ( ) D E D E L ( R ) F L ( R ) F Julliere’s model is insufficient! Not overall density of states important but specific bands at the Fermi level and their       properties k k   ( ) ( ) L R L R P  Stearns first explanation in this way ( )   L R  ) k k L ( R ) L ( R ) M. B. Stearns, JMMM 5, 1062 (1977) M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  9. Free electron model for tunneling (no spin) Matching Boundary Conditions (4 linear equations with 4 unknowns) allows the solution for the transmission probability. y=0 y=a 1.5 1.5 Energy, Wave Function Energy, Wave Function 1 1 Energy Energy 0.5 0.5 E F at equal potential 0 0 -0.5 -0.5 -1 -1 -1.5 -1.5 -2 -2 -1.5 -1.5 -1 -1 -0.5 -0.5 0 0 0.5 0.5 1 1 1.5 1.5 2 2 2.5 2.5 3 3     y y ik y ik y ik R y t transmission amplitude e re te L L Boundary conditions :     y y Ae Be 0 0 continuity of | Y > and its derivative M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  10.      Free electron model for tunneling (no spin) T=|t|² Transmissi on probabilit y :  2 8 k k  0 1 2 T             2 2 2 2 2 2 2 2 2 ( )( ) cosh( 2 ) 4 ( )( ) k k a k k k k 0 0 0 0 0 0 L R L R L R  >> 2 a When system is thick enough tha t 1 : e 0    2 2 a 16 - Depends on barrier thickness + height k k e 0  0 L R T - k=k F     2 2 2 2 ( )( ) k k - Given by transmission probabilities L, R 0 0 L R Note that this can be written as :   4 4 k k       2 2 a a 0 0 L R T e T T e = T (k // ) 0 0     L R 2 2 2 2 ( ) ( ) k k 0 0 L R   2 I e    ( k ) Landauer Formula for Conductanc e G T || V h k || E F M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»                >>                    

  11. Slonczewski model for tunneling (with spin) Slonczewski (1989) Delocalized electrons contribute most to the current (sp states ) Localized states don’t ( d states)  free electron tunneling U E       2 2 a  16 E k k e E F 0     ' 0 ' T     2 2 2 2 ( )( ) k k   0 ' 0 for simplicity L=R material Spin  and spin  channels conduct in parallel (two current model):         and G G G G G G Parallel Antiparall el     2      2 k k k k          2 2 0 a      16 G G e 0     0 Parallel antiparall el 2 2 2 2  k k    0 0 Slonczewski Polarisation Tunnel magnetoresistance          2 2 G G 2 G P k k k k        Parallel antiparall el     0 F F F F P      ²    2 1 G G P     k k k k     Parallel parallel 0 F F F F - Depends on properties of FM and barrier! - Bandstructure details are important! M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

  12. Slonczewski model for tunneling (with spin)         2 2 ( ) k k k k m U E              2 0 F F F F k P        0 || 2 2      k k k k     0 F F F F In Julliere’s model, only the polarization within the magnetic electrodes influences the TMR. In Slonczewski’s model, the barrier height also plays a role.  >> , k k Case of high barrier:   F F  k k Electrons with highest  >   F F 0 P velocity give strongest  k k contribution to tunneling   F F mk   ( ) DOS E k Free electrons:  2 2     2 2 D D R G P    Back to Julliere formula   P   ² 1 With P defined via DOS R G P D D   Antiparall el Parallel M. Chshiev «Theory of spintronic phenomena in magnetic tunnel junctions»

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