Part 2 Tunneling Magnetorezistance (TMR) in Magnetic Tunnel Junctions (MTJ) Prof. Dr. Coriolan TIUSAN UTCN ‐ CNRS
Tunneling Magnetorezistance (TMR) consequence of spin ‐ dependent tunneling Tunnel effect (1928 George Gamow): NONZERO transmission of particle ‐ associated wave across a thin potential barrier Incident wave The nature of particles as waves Transmitted wave (de Broglie) determines the tunnel effect Pure QM approach Reflected wave No Classical approach M2 Tunnel junction: = two metallic layers separated by a thin insulator: => electron propagation by tunneling M1 2
Some quantum mechanics Schrödinger 2 0 metal U B U E U Re ikx ikx 2 e U barrier m B ikx Te E 2 m k E metal 2 Free electrons => Plane wave 2 m U d d Ae Be ( ) E 2 barrier B ~ exp( 2 ) T d Transmission probability: Tunnel current (conductivity): ( ) ( ) ( ) ( ) 1 ( ) FD FD I n E f E T E n E f E dE LR L L R R lead R T L Total (net) current when biasing the junction V I I I LR RL ( ) ( ) ( ) FD ( ) FD ( ) n E T E n E eV f E f E eV dE L R L R 3
MAGNETIC TUNNEL JUNCTION – elementary brick of spintronics Spin dependent Metallic layers = ferromagnetic density of states n (E) • FM 1 / I / FM 2 trilayer • potential profile in the ferromagnet M 2 2 , , h FM U E U 2 m FM2 U barrier B I M 1 FM1 QM T (E) Spin dependent transmission probability Spin dependent current ( ) ( ) ( ) ( ) ( ) J n E T E n E f E f E dE 1 2 1 2 4
Mechanisms of TMR Spin transport by quantum tunneling U E F +eV E F 1 2 eV Two current model (2 independent channels) Spin conservation during tunneling Quantum spin up: J Mechanics spin down: J J J J tot ( ) ( ) ( ) ( ) ( ) ( ) J V n E T E n E eV f E f E eV dE 1 2 1 2 T OK ( ) ( ) ( ) J V n E n E eV 1 2 F F 5
MAGNETIC TUNNEL JUNCTION – Tunnel Magnetoresistive (TMR) effect Tunnel magnetoresistance: R R R R AP P TMR R R R AP P R p 2 R R R P P 1 2 AP P – 1 R R P P 1 2 P n n Hrot Hrot Hrot 1 ( 2 ) 1 ( 2 ) with P R=f ( cos( ) ) R=f ( cos( ) ) 1 ( 2 ) n n 1 ( 2 ) 1 ( 2 ) M2 M2 M2 Spin-valve effect FM2 FM2 FM2 I I I R R R R p ap p ap M1 M1 M1 cos( θ ), R 2 2 0 0 2 2 FM1 FM1 FM1 θ , ) M 1 M 2 Slonczewski : Phys. Rev. B39 , 6995, (1989) Slonczewski : Phys. Rev. B39 , 6995, (1989) 6
MAGNETIC TUNNEL JUNCTION – Large spin valve effect Field, rotation Current I=f( ) => sensors Spin ( ) I f dependent tunnel current M 2 Analyzer FM2 I: Spin dependent I tunneling HD ‐ Read HDD M 1 FM1 Polarizer n E n E P n E n E 7
Key parameters for MTJ FM2 Isolant FM1 e ‐ R=f( )=R(H) Hc 1 Hc 2 exp T d U U U E F E F E F 1 1 1 2 2 2 eV eV eV R anti parallel R parallel Control of barrier structure at nanometer Control of magnetic properties of scale electrodes 8
(I) Control of magnetic properties M (1) (2) M 1 +M 2 Hc Hc 2 1 H – M 1 + M 2 (3) ? Operating at low fields: H C1 <H<H C2 – M 1 – M 2 R (2) R high Hard ‐ soft architecture (3) (1) R low Operating an MTJ: H M(H ) <=> R(H) Hc 2 Hc 1 9
(I) Control of magnetic properties |H|<H C2 M (1) Minor loop: Hc 1 Hc 2 M 1 +M 2 (2) • Layer M 2 blocked H • Layer M 1 mobile – M 1 + M 2 R (2) R high Hard ‐ soft architecture (1) R low JTM: M(H )<=> R(H) H Hc 2 Hc 1 10
Hardening : difficult task in 3d FM thin films Exchange biased SyAF reduces stray ‐ fields and Hard/soft dipolar coupling (1) Clasically (2) Exchange biasing low K ‐ soft low K ‐ soft low K ‐ soft large K ‐ soft F1 F1 RKKY 2 materials K F2 cristalline phase Fe(bcc) vs Co(hcp) aspect ratios of FM electrodes Complex micromagnetic problems Typical Magnetoresistance versus magnetic fi eld exchange ‐ biased MTJ hard–soft MTJ For applications Beyond static => Complex micromagnetic problems Dynamic magnetic properties related to fast and homogeneous magnetization switching have to be optimized: Pillar shape, aspect ratio, FM material, switching mechanisms (field, spin ‐ current/torques, thermal assisted…). 11 E. Tsymbal et al, J. Phys.: Condens. Matter 15 (2003) R109–R142
(II) Control of barrier structure T exp d U Control of d Control of U Tunnel cartography Image AFM Image TEM C D' 0.7 nm A A' C' D 0 nm 50nm 50nm 50nm courant 0.5 nm AA' 100 nA DD' CC ’ 0.1 nA 0 nm inhomogène homogenuous Optimisation of buffer layer ==> small roughness Homogeneity of tunnel current C. Tiusan et al, JAP 85 , 5276 (1999) V.DaCosta, C. Tiusan, T. Dimopoulos, K. Control of epitaxial growth in Ounadjela, PRL 85 , 876 (2000) epitaxial (single crystal or textured) MTJs 12
Magnetic tunnel junction – underlying Physics Polycrystalline MTJs : random distribution of crystallographic axes (amorphous barrier) r ( ) ikr free electron model (constant potential + plane waves) e Tunnel transport independent of propagation direction C. Tiusan et al, Phys. Rev. Lett. 85, 876 (2000); Phys. Rev B 61, 580, (2000) Single crystal MTJs Single crystal electrodes : anisotropy of space properties dependent of propagation direction potential : crystal periodicity ( ) ( ) ikr beyond the free ‐ electrons model: Bloch waves r e u r nk nk Fully epitaxial systems Conservation of symmetry across the stack ! Model systems where theory and experiment confront C. Tiusan et al, Appl. Phys. Lett. 82, 4507, (2003) 13 J. Phys. Cond. Mat. 19, 165201, (2007).
(I) Polycrystalline MTJs (Al2O3 based) Hystorically, first MTJ systems 1995 discovery of the TMR effect at RT The fi rst observation of reproducible, large room temperature magnetoresistance in a CoFe/Al2O3/Co MTJ Moodera J S, Kinder L R, Wong T M and Meservey R Phys. Rev.Lett. 74, 3273, ( 1995) 14
Early experiments and models Measure the spin polarization of the tunnelling current originating from various ferromagnetic metals 1. Experiments on spin ‐ dependent tunnelling across an alumina insulating barrier in ferromagnet/insulator/superconductor (FM/I/S) Tedrow and Meservey tunnel junctions superconducting Al fi lm which acts as a spin detector The results of these early experiments on SDT were interpreted in terms of the DOS of the ferromagnetic electrodes at E F n n P FM n n Applied H II plane inconsistency between measured P and P FM The inconsistency between the experimental and theoretical SP = consequence of the fact that the tunneling conductance depends not only on the number of electrons at the Fermi energy but also on the tunneling probability , which is different for various electronic states in the ferromagnet 15
Takes into account features of band structure in 2. Stearns’ model tunneling transmission probability depends on the effective mass which is different for different bands localized d electrons => large effective mass and therefore decay very rapidly into the barrier region the dispersive s ‐ like electrons decay slowly the nearly free ‐ electron (most dispersive bands) dominate the tunnelling current The heavy curves show the free ‐ electron ‐ like bands which dominate tunnelling. k ↑ and k ↓ are the Fermi wavevectors which determine the spin Electronic bands in bulk fcc Ni in the [110] polarization of the tunnelling current: direction for the majority ‐ spin (a) and minority ‐ spin (b) electrons. Using an accurate analysis of the electronic band structure, Stearns found that P FM = 45% for Fe and 10% for Ni, which are consistent with the experimental data Stearns: introduces the notion of TDOS (tunneling density of states) early indication that the understanding of SDT requires detailed knowledge of the 16 electronic structure of MTJs
3. Julliere’s experiments and model M. Jullière, Phys. Lett. A54, 225, (1975). 1975, first observation of TMR effect in Fe/Ge/Co MTJ (4.2K) Correlates TMR and polarization P Assumptions: two independent current model (up, dn spin) tunneling from DOS up1 ‐ up2, dn1 ‐ dn2 in P and up1 ‐ dn2, dn1 ‐ up2 in AP G n n n n 1 2 1 2 P G n n n n 1 2 1 2 AP 2 G G R R PP 1 2 P AP AP P TMR 1 with G R PP 1 2 AP P Consistency between measured SP (Tedrow ‐ Meservey) and TMR values 17
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