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

Models in spintronics (Part II) OUTLINE : Spin-dependent transport in magnetic tunnel junctions -Introduction to tunnel effect -magnetic tunnel junctions and tunnel MR -Julliere model -Slonczewski’s model (free electron gas) -Crystalline barrier: Spin-filtering according to symmetry of wave functions Spin-transfer in non collinear magnetic configuration -spin-torque term and effective field term Spin-injection in semiconductors B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Magnetic tunnel junctions Structure of a magnetic tunnel junction NiFe CoFe Al(Zr)O x Storage layer: CoFe 4 Magnetic Tunnel junction CoFe nm Al 2 O 3 barrier 1.5nm or IrMn Reference layer :CoFe 3nm NiFe IrMn 7nm Acts as a couple polarizer/analyzer with the spin of the electrons. •First observation of TMR at low T in MTJ: Julliere (1975) (Fe/Ge/Co) •TMR at 300K : Moodera et al, PRL (1995);  R/R~50% Myazaki et al, JMMM(1995). in AlO x based junctions B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Giant TMR of MgO tunnel barriers S.S.P.Parkin et al, Nature Mat. (2004), nmat1256. S.Yuasa et al, Nature Mat. (2004), nmat 1257. Very well textured MgO barriers grown by sputtering or MBE on bcc CoFe or Fe magnetic electrodes, or on amorphous CoFeB electrodes followed by annealing to recrystallize the electrode. Yuasa et al, APL89, 042505(2006) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Tunneling through magnetic insulators : spin filters V Inject spin polarized electrons through spin-split insulator M 1 IF M 2 Barrier height h is spin-dependent h Tunnel current varies exponentially with e 2 mE      t ( )     P 1 e bias ,    T<T C with   , 2  E exch J J P injectée ~ 90 % if M1, M2 normal metal ~ 130 % if M1 Gd (ferromagnetic) EuS …… but T = 4.2 K (Tc EuS ~ 16 K) P. LeClair et al., Also magnetic oxides (Fe 3 O 4 , Fe 2 CoO 4 …) Appl. Phys. Lett. 80, 625 (2002) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Tunnel effect Quantum mechanical origin  F x A classical particle cannot enter the barrier zone if  F <E 0 In quantum mechanics, electrons obey Schrödinger equation (1D model): 2 2 d        V ( x ) E 2 2 m dx 2 2 d      E Off the barrier Plane waves 2 2 m dx 2 mE   k   ikx e 2  2 2 d   In the barrier     ( E E ) Evanescent waves 0 2 2 m dx  2 m E e    qx   q 2  B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Tunneling through a simple rectangular barrier 1.5 Energy, Wave Function 1 Energy 0.5 0   -0.5 ik x ik x e re re - + ikx ikx e 1 1 e k ± ik x x te ikx te 2   qx qx -1 Ae Be -1.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 x Continuity of wave function and derivative through interfaces  qa 4 qe k 1  t      ik q ik q 1 2 B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Transmission through a simple rectangular barrier Probability of tunneling = t.t*  2 2 qa 16 q e k   1 * P tt       2 2 2 2 q k q k 2 1 Typically,  E~1eV, m~free electron  1/q~0.2nm Tunnel barrier must be at most a few nm thick to get reasonable tunneling rate through it B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Case of more general barrier 2 2 d        V ( x ) E 2 2 m dx 2 d 2 m          2 V ( x ) E q ( x ) 2 2 dx x   q ( u ) du   W.K.B approximation: e 0  d ( x )    What is neglected?: q ( x ) ( x ) dx   2 d ( x ) dq ( x ) d ( x )     ( x ) q ( x ) 2 dx dx dx  2 d ( x ) dq ( x )     2  ( x ) q ( x ) ( x ) 2 dx dx dq    2 m V ( x ) E  2 q ( x ) WKB OK if i.e. smoothly varying barrier  q ( x ) dx 2  B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

How to calculate electrical current through barrier? At zero bias voltage, same current from left to right and right to left.  F  F J e (V=0)=0 Need to apply a bias voltage, to create a dissymetry in tunneling current  F eV  F B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

How to calculate electrical current through barrier? Cont’d The probability for an electron to tunnel through the barrier is (WKB): x   2 q ( u ) du   * P ( E ) tt e 0 Nb of electrons tunneling per unit time: Fermi-Dirac distribution 1    E     dN 4 m ²  f r , v   P ( E ) dE f ( E ) dE      0    x x // exp F 1 3 dt h   k T   0 0 B Electrical current:  E    dN dN 4 e m ²            J e  1 2 2 1  P ( E ) dE f ( E ) f ( E eV ) dE e x x // 3  dt dt  h 0 0 B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Approximate expressions of J(V) in free electron model from Simons (1963)  0  F For low bias: still rectangular barrier s V     1 . 02 s 10 J 3 . 16 10 e 0  Linear J(V) at low bias 0 s  0 For intermediate bias 0<V<  0 : trapezoïdal barrier  F Conductance  when V  s       1 / 2 1 / 2 10         6 . 2 10 V V V V                           J exp 1 . 025 s exp 1 . 025 s     0 0 0 0 2 s  2   2   2   2           0 For large bias V>  0 : Fowler Nordheim  F Injection in conduction band s B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Exemple of experimental I(V) characteristics in tunnel junction Tunnel barrier of MgO Dynamic conductance=dI/dV T.Dimopoulos et al B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Julliere model of TMR Insulator Jullière,Phys. Lett. Ferro 1 A54 225 (1975) 1 F F E F Isolant eV E F 0 Ferro 2 P  2    i W f D f E ( ) Fermi Golden rule: proba of tunneling F  D i E ( ) Nb of electrons candidate for tunneling F       tunneling current in each spin channel J D ( E ) D ( E ) 1 F 2 F Parallel configuration Antiparallel configuration         antiparall el J parallel     D D D D J D D D D 1 2 1 2 1 2 1 2  R 2 P P   TMR 1 2  R 2 P P    D ( E ) D ( E )  R 1 P P   TMR 1 2  F F P AP 1 2    R 1 P P  D ( E ) D ( E ) F F P 1 2 P~50% in Fe, Co  R/R~40 - 70% with alumina barriers B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Spin polarization of 3d metals E Metals s  (E) s  (E) Parkin et al D  (E) D  (E) E NiMnSb (Ristoiu et al.) Half metals Half metals are Photoemission intensity E 100% spin polarized ! Heussler alloys Intensité (u.a.) LaSrMnO 3 Fe 3 O 4 300K E  CrO 2 D  (E) D  (E)   spin up …  spin down  - Exchange spliting -1 0 1 2  - half metallic gap E-E F (eV) B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara

Slonczewski’s model (1989) Model of band structure derived from M.B.Stearns JMMM 5, 167 (1977). Hybridization between s and d electrons. « Itinerant free electrons » ie free electrons (parabolic bands) but with band splitting. Schrödinger equation solved for both spin d   channels assuming continuity of and dx through the interfaces q For each spin channel:  2 2 qa 16 q e k k   '   ' J      2 2 2 2 q k q k   '  ’ refer to spin state in the left and right electrodes B.Dieny « Models in spintronics » 2009 European School on Magnetism, Timisoara