1. 12/8/2015A. Ali Yanik, Purdue University1 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

2. 12/8/2015A. Ali Yanik, Purdue University2 Spin + Electronics = Spintronics

3. 12/8/2015A. Ali Yanik, Purdue University3 Spintronic Devices Non volatile RAM, Freescale,2006 Devices: GMR (read heads), TMR (MRAM), BMR Devices, etc.. Magnetoelectronics S. Datta & B. Das, APL. 56, 665 (1990) Gate Voltage Control / Rashba Effect Field Controlled Spintronics Devices: Spin-FET (Datta), etc.. Contact Injection/Detection Gate Contact External B Field Spin Dephasing

4. 12/8/2015A. Ali Yanik, Purdue University4 NEGF Formalism Motivation-I DevicesConcepts  Physics Community  Spin Decoherence + QM  Equilibrium  Engineering Community  Transport + QM  Non-Equilibrium Decoherence PhysicsQuantum Transport Ph.D. Thesis: First formalized treatment of Quantum-Transport with Spin-Decoherence in NEGF

5. 12/8/2015A. Ali Yanik, Purdue University5 Motivation-II Contacts Channel Electrons Ballistic Transport / NEGF FORMALISM Phonons NEGF FORMALISM (Inelastic Transport) Electron-phonon relaxation time Localized Spins Spin-lattice relaxation time EQUILIBRIUM PHYSICS 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

6. 12/8/2015A. Ali Yanik, Purdue University6 A Unified Quantum Transport Model A Unified Quantum Transport Model

7. 12/8/2015A. Ali Yanik, Purdue University7 Unified Approach to Nanoscale Devices Quantum Device Source Drain Gate Scatterer Molecule (Gosh et al) MTJ (Yanik et al) Spin Torque (Prabhakar et al) Nanotubes (IBM, Kosawatta et al) Nuclear Spin Polarization (Salahuddin et al) MOSFET (Damle et al) RTD (Klimeck et al)

8. 12/8/2015A. Ali Yanik, Purdue University8 Magnetic Tunnel Junctions Availability of Experimental Data Technological Importance

9. 12/8/2015A. Ali Yanik, Purdue University9 Coherent Regime

10. 12/8/2015A. Ali Yanik, Purdue University10 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) Stearns M. B., J. Magn. Magn. Mater. 5, 167 (1977)

11. 12/8/2015A. Ali Yanik, Purdue University11 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)  Spin polarization is conserved  Rectangular potential barrier & exchange shifted parabolic bands.  Qualitatively correct and widely used by experimentalists Slonczewski’s Formula: Fails for Thin Tunneling Barriers!!! J.C. Slonczewski PRB 39, 6995 (1989) Practical Interest

12. 12/8/2015A. Ali Yanik, Purdue University12 Coherent Regime (NEGF) Weighting Factor JMR for Different Incoming Energies E F =2.2eV, ∆=1.45eV and V bias =1meV after Stearns et al. ω (E z ) shifts towards higher energies with increasing barrier thicknesses

13. 12/8/2015A. Ali Yanik, Purdue University13 Coherent Regime (NEGF) Weighting Factor JMR for Different Incoming Energies E F =2.2eV, ∆=1.45eV and V bias =1meV after Stearns et al. ω (E z ) shifts towards higher energies with increasing barrier thicknesses Experimentally Measured JMR ω (E z ) shifts towards higher energies with increasing barrier thicknesses

14. 12/8/2015A. Ali Yanik, Purdue University14 Incoherent Regime Impurity Concentration Barrier Thickness Barrier Height

15. 12/8/2015A. Ali Yanik, Purdue University15 MTJs with Magnetic Impurity Layers R. Jansen & J. S. Moodera, J. Appl. Phys. 83, 6682 (1998) Hard Layer F Tunneling Oxide Impurity Layer Tunneling Oxide Soft Layer F

16. 12/8/2015A. Ali Yanik, Purdue University16 MTJs with Magnetic Impurity Layers Normalized JMR ratios are barrier thickness independent JMR(E z ) ratios reduces at all energies Elastic spin scattering doesn’t effect normalized ω(E z ) Decreasing JMRs with increasing impurity concentrations

17. 12/8/2015A. Ali Yanik, Purdue University17 MTJs with Magnetic Impurity Layers A universal trend independent from the barrier heights Minimal Fitting Parameters

18. 12/8/2015A. Ali Yanik, Purdue University18 Pd & Ni Impurity Layers  2D exchange coupling used as a fitting parameter  Minimal temperature dependence  Close 2D coupling constants estimated for Pd and Ni impurities  +1 spin state is believed to be the dominant state.

19. 12/8/2015A. Ali Yanik, Purdue University19 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 d4-d7 systems: t 2g set → low spin state e g set → high spin case. S. W. Biernacki et al, PRB. 72, 024406 (2005). Crystal Field Theory -The Pairing energy (P) Coulombic repulsion Exchange Energy -The e g - t 2g Splitting

20. 12/8/2015A. Ali Yanik, Purdue University20 Details of the Theory

21. 12/8/2015A. Ali Yanik, Purdue University21 Exchange Interaction Spin Scattering Hamiltonian: Effective mass description Modeled through contact self energy Modeled using self consistent Born approximation  Magnetic Impurity  Magnon Scattering  Aranov-Bir-Pikus (Electron-Hole)  Nuclei (Hyperfine Interaction) Analogous to the Electron/Hole Density Rate at which electrons/holes are scattered in/out of a state

22. 12/8/2015A. Ali Yanik, Purdue University22 Spin Scattering Self Energy Interaction Hamiltonian: Channel Spin Exchange Interaction Impurity Operators Electron Operators Preserves Angular Momentum Jordan-Wigner

23. 12/8/2015A. Ali Yanik, Purdue University23 Inelastic Spin Flip Scattering Spin Flip Scattering Non-Spin Flip Scattering Impurity Density Matrix

24. 12/8/2015A. Ali Yanik, Purdue University24 Elastic Spin Flip Scattering 2-D Translational Symmetry Elastic Spin Flip Scattering

25. 12/8/2015A. Ali Yanik, Purdue University25 Unpolarized Spin Ensemble  Magnetic Impurity Layer

26. 12/8/2015A. Ali Yanik, Purdue University26 Self-consistent Solution Regular Contacts: Channel: Incoherent Scattering: Hamiltonian Transport Equations: Green’s Function Fixed at the Outset Self-consitent Sol. Direct Sol

27. 12/8/2015A. Ali Yanik, Purdue University27 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.

28. 12/8/2015A. Ali Yanik, Purdue University28 Acknowledgement Professors Supriyo Datta and Gerhard Klimeck Professors Supriyo Datta and Gerhard Klimeck Dr. Dmitri Nikonov – Intel corporation Dr. Dmitri Nikonov – Intel corporation Sayeef Salahuddin, Prabhakar Srivastava Sayeef Salahuddin, Prabhakar Srivastava NSF funded Network for Computational Nanotechnology (NCN) and MARCO NSF funded Network for Computational Nanotechnology (NCN) and MARCO