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Spin Dependent Electron Transport in Nanostructures

Spin Dependent Electron Transport in Nanostructures. A. Ali Yanik † Dissertation † Department of Physics & Network for Computational Nanotechnology Purdue University, West Lafayette, IN 47907 April 2007. Spin + Electronics = Spintronics. Spintronic Devices. Field Controlled Spintronics.

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Spin Dependent Electron Transport in Nanostructures

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  1. Spin Dependent Electron Transport in Nanostructures A. Ali Yanik† Dissertation †Department of Physics & Network for Computational Nanotechnology Purdue University, West Lafayette, IN 47907 April 2007 A. Ali Yanik, Purdue University

  2. Spin + Electronics = Spintronics A. Ali Yanik, Purdue University

  3. Spintronic Devices Field Controlled Spintronics Magnetoelectronics Devices: Spin-FET (Datta), etc.. Devices: GMR (read heads), TMR(MRAM), BMR Devices, etc.. Contact Injection/Detection Gate Contact External B Field Spin Dephasing Gate Voltage Control / Rashba Effect S. Datta & B. Das, APL. 56, 665 (1990) Non volatile RAM, Freescale,2006 A. Ali Yanik, Purdue University

  4. NEGF Formalism Motivation-I Concepts Devices • Engineering Community • Transport + QM • Non-Equilibrium • Physics Community • Spin Decoherence + QM • Equilibrium Decoherence Physics Quantum Transport Ph.D. Thesis: First formalized treatment of Quantum-Transport with Spin-Decoherence in NEGF A. Ali Yanik, Purdue University

  5. Channel Electrons Phonons Contacts Spin-lattice relaxation time Localized Spins Motivation-II NEGF FORMALISM (Inelastic Transport) Ballistic Transport / NEGF FORMALISM Electron-phonon relaxation time • Challenges: • Physics Based Unified Treatment (not specialized for each device, geometry, etc) • Conservation Laws (angular momentum, total energy, particles) • Numerically Treatable • Benchmark against experiment. • State of Art Modelling • Averaging of Coherent Processes • Doesn’t Capture the Physics • Not straightforward to include dissipative interactions NON-EQUILIBRIUM TRANSPORT EQUILIBRIUM PHYSICS EQUILIBRIUM PHYSICS A. Ali Yanik, Purdue University

  6. A Unified Quantum Transport Model A. Ali Yanik, Purdue University

  7. Gate Quantum Device Drain Source Scatterer Unified Approach to Nanoscale Devices MOSFET (Damle et al) Nanotubes (IBM, Kosawatta et al) Nuclear Spin Polarization (Salahuddin et al) RTD (Klimeck et al) MTJ (Yanik et al) Molecule (Gosh et al) Spin Torque (Prabhakar et al) A. Ali Yanik, Purdue University

  8. Magnetic Tunnel Junctions Availability of Experimental Data Technological Importance A. Ali Yanik, Purdue University

  9. Coherent Regime A. Ali Yanik, Purdue University

  10. Stearns M. B., J. Magn. Magn. Mater. 5, 167 (1977) Junction Magnetoresistance • Potential Barrier + Magnetic Contacts • Soft Layer & Hard Layer (fixed) • Exchange shifted two current model Parallel Contacts Antiparallel Contacts T.M. Maffit et al IBM J. Res. & Dev. 50, 25 (2006) A. Ali Yanik, Purdue University

  11. Slonczewski’s Formula: • Spin polarization is conserved • Rectangular potential barrier & exchange shifted parabolic bands. • Qualitatively correct and widely used by experimentalists Junction Magnetoresistance • Potential Barrier + Magnetic Contacts • Soft Layer & Hard Layer (fixed) • Exchange shifted two current model Parallel Contacts Antiparallel Contacts Practical Interest T.M. Maffit et al IBM J. Res. & Dev. 50, 25 (2006) Fails for Thin Tunneling Barriers!!! J.C. Slonczewski PRB 39, 6995 (1989) A. Ali Yanik, Purdue University

  12. Coherent Regime (NEGF) JMR for Different Incoming Energies Weighting Factor ω(Ez) shifts towards higher energies with increasing barrier thicknesses EF=2.2eV, ∆=1.45eV and Vbias=1meV after Stearns et al. A. Ali Yanik, Purdue University

  13. Coherent Regime (NEGF) EF=2.2eV, ∆=1.45eV and Vbias=1meV after Stearns et al. JMR for Different Incoming Energies Weighting Factor ω(Ez) shifts towards higher energies with increasing barrier thicknesses Experimentally Measured JMR ω(Ez) shifts towards higher energies with increasing barrier thicknesses A. Ali Yanik, Purdue University

  14. Incoherent Regime Impurity Concentration Barrier Thickness Barrier Height A. Ali Yanik, Purdue University

  15. Tunneling Oxide Tunneling Oxide Soft Layer Impurity Layer F Hard Layer F MTJs with Magnetic Impurity Layers R. Jansen & J. S. Moodera, J. Appl. Phys. 83, 6682 (1998) A. Ali Yanik, Purdue University

  16. MTJs with Magnetic Impurity Layers JMR(Ez) ratios reduces at all energies Elastic spin scattering doesn’t effect normalized ω(Ez) Decreasing JMRs with increasing impurity concentrations Normalized JMR ratios are barrier thickness independent A. Ali Yanik, Purdue University

  17. MTJs with Magnetic Impurity Layers A universal trend independent from the barrier heights Minimal Fitting Parameters A. Ali Yanik, Purdue University

  18. Pd & Ni Impurity Layers • <J2>2D exchange coupling used as a fitting parameter • Minimal temperature dependence • Close <J2>2D coupling constants estimated for Pd and Ni impurities • +1 spin state is believed to be the dominant state. A. Ali Yanik, Purdue University

  19. High-Spin/Low-Spin Phase Transition • J exchange coupling used as a fitting parameter • Large temperature dependence • Thermally driven low-spin/high-spin phase transitions S. W. Biernacki et al, PRB. 72, 024406 (2005). Crystal Field Theory -The Pairing energy (P) Coulombic repulsion Exchange Energy -The eg - t2g Splitting d4-d7 systems: t2g set → low spin state eg set →high spin case. A. Ali Yanik, Purdue University

  20. Details of the Theory A. Ali Yanik, Purdue University

  21. Analogous to the Electron/Hole Density Rate at which electrons/holes are scattered in/out of a state Exchange Interaction Spin Scattering • Magnetic Impurity • Magnon Scattering • Aranov-Bir-Pikus (Electron-Hole) • Nuclei (Hyperfine Interaction) Hamiltonian: Effective mass description Modeled through contact self energy Modeled using self consistent Born approximation A. Ali Yanik, Purdue University

  22. Spin Exchange Interaction Channel Spin Scattering Self Energy Interaction Hamiltonian: Preserves Angular Momentum Jordan-Wigner Electron Operators Impurity Operators A. Ali Yanik, Purdue University

  23. Inelastic Spin Flip Scattering Impurity Density Matrix Spin Flip Scattering Non-Spin Flip Scattering A. Ali Yanik, Purdue University

  24. Elastic Spin Flip Scattering 2-D Translational Symmetry Elastic Spin Flip Scattering A. Ali Yanik, Purdue University

  25. Magnetic Impurity Layer Unpolarized Spin Ensemble A. Ali Yanik, Purdue University

  26. Self-consistent Solution Hamiltonian Channel: Regular Contacts: Fixed at the Outset Incoherent Scattering: Self-consitent Sol. Green’s Function Transport Equations: Direct Sol A. Ali Yanik, Purdue University

  27. Summary • Challenges: • Physics Based Unified Treatment • Conservation Laws (angular momentum, total energy, particles) • Numerically Treatable • Benchmarking against experiment • Contributions: • A Non-Equilibrium Quantum Transport model with Spin Decoherence is developed. • A Self Energy Calculation scheme is derived for Exchange Interaction Scattering. • A numerical implementation is shown in MTJ devices. A. Ali Yanik, Purdue University

  28. Acknowledgement • Professors Supriyo Datta and Gerhard Klimeck • Dr. Dmitri Nikonov – Intel corporation • Sayeef Salahuddin, Prabhakar Srivastava • NSF funded Network for Computational Nanotechnology (NCN) and MARCO A. Ali Yanik, Purdue University

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