Electron spin transport in Magnetic Multilayers and Carbon Materials. Kurt Stokbro CEO, Founder QuantumWise A/S (Copenhagen, Denmark)

Transcription

1 Electron spin transport in Magnetic Multilayers and Carbon Materials Kurt Stokbro CEO, Founder QuantumWise A/S (Copenhagen, Denmark)

2 Outline Methodology Example 1: Spin filtering in Ni-Graphene-Ni Example 2: Spin filtering in Graphene ribbon with adsorbed Fe/V atom Example 3: Spin filtering in Graphene ribbon with V-shaped notch Towards large scale transport simulations

3 Calculation of coherent transport in nanostructures Propagation of wave function in nanoscale structure, Calculation of transmission amplitudes t Calculation of current,

4 One-electron Hamiltonian from DFT using ATK/TranSIESTA Interaction region Bulk region Bulk region D Electronic structure Density Functional Theory Numerical orbitals w. finite range (SIESTA) Pseudopotentials Transport Full description of electrodes using self-energies Non-equilibrium electron distribution using NEGF Calculation of electron current H M. Brandbyge, K. Stokbro, J. Taylor, J. L. Mozos, P. Ordejon,, MRS proceedings 636, D9.25 (2001). M. Brandbyge, J.-L. Mozos, P. Ordejon, J. Taylor, K. Stokbro, Phys. Rev. B. 65, (2002). J. Soler, J. Phys. Cond. Mat. 14, 2745 (2002).

5 Magnetic tunnel junctions (MTJ) Fe(Co) MgO Fe(Co) Ni graphite Ni Co Cu Cu

6 Fe MgO Fe: basic research Fe MgO Fe (, ( W. H. Butler et al., PRB 63, (2001) TMR arises in magnetic tunnel junctions (MTJs) due to spin filtering Key to production of» magnetoresistive random-access memory (MRAM)» programmable logic elements» magnetic sensors TMR I I I

7 TMR in Fe MgO Fe MTJs TMR saturates and decreases with incresed # of MgO layers agrees with experimental data (Hitachi, private communication) 6 MgO layers is a reasonable practical limit Modeling can guide for R&D efforts

8 The k-dependent transmission coefficient Majority Spin WKB theory 2m T + h 2 2 ( E, kx, k y ) exp( ( ε ) 2 v E + kx k y Decay of wave function through the MgO semiconductor Minority Spin W. H. Butler et al., PRB 63,

9 Scattering states P-config up down up AP-config down

10 K-dependent transmission coefficient (parallel) Majority spin Majority Spin Minority Spin Majority Spin Transport at the Fermi energy is dominated by barrier tunneling of Bloch states with wave vectors near the Γ-point No correlation between transmission and DOS Minority spin Minority Spin Transport at the Fermi energy is dominated by resonant tunneling through interface states Strong correlation between transmission and DOS

11 TMR for Fe-Co system Fe lattice parameter All TMR s show tendency for saturation for large # of MgO layers In the region 2-6 layers FeCo(Co) system has highest TMR Same material but different interface layer => huge difference in TMR Implication for fabrication? Can one control composition of the interface in FeCo?

12 Interlayer exchange coupling (IEC) Antiferromagnetic IEC Ferromagnetic IEC Experiment: Katayama, APL 89, IEC changes sign vs. MgO thickness Why? Suggestion: oxygen vacancies in MgO layer play a role IEC decreases exponentially with the # of MgO layers IEC depends critically on the chemistry of terminating layer for FeCo system

13 Discrepancy between theory and experiment!? Calc.: TMR= 2300% Exp. : TMR= 280% Fe MgO Fe (, ( Hitachi Advanced Research Lab. Reported TMR > 1100% in MRS Spring Meeting 2008 Are the theoretical and experimental structures the same?

14 Crystalline magnetotunnel junctions for MRAM Proposal: FeO layer may form at the Fe/MgO interface X.-G. Zhang, et al., PRB 68, (2003) TMR (%) R A (Ω μm²) Fe-MgO-Fe Fe-FeOMgO-Fe M. Stilling et al., Molecular Simulation 33, 557 (2007)

15 Crystalline magnetotunnel junctions for MRAM Can we avoid oxidation? Introducing a Au layer in the Fe/MgO interface may avoid the oxidation J. Mathon and A. Umerski, PRB 71, (2005) TMR (%) R A (Ω μm²) Fe-MgO-Fe Fe-FeOMgO-Fe Fe-AuMgOAu-Fe M. Stilling et al., Molecular Simulation 33, 557 (2007) Fe-NiOMgO-Fe Fe-MnOMgO-Fe

16 Fe MgO Fe: process optimization Modeling allows to understand which structural defects must be minimized to maximize the TMR Ideal Vacancy Boron

17 Oxygen site defects: vacancy & B substitution Defects introduced in one of Fe/MgO interfaces 25% of interface oxygen was replaced by vacancies or B On volumetric basis the model presents ~ 6% defects Model TMR (%) Ideal structure 2700 Interface O vacancy 50 Interface B 47 Qualitatively both kinds of defects dramatically decrease the TMR

18 Heusler alloys Heusler alloys suggested as new materials for MTJs A. Thomas et al., APL 89, (2006) E.g. Co 2 MnSi Semi-metallic: majority spin is metallic, minority is semiconducting Mn Co Mg Si O Parallel or Anti-Parallel 1.0E+05 0 TMR [%] 1.0E E E E+01 TMR Spin Torque E Bias voltage [V] Spin Transfer Torque [mev]

19 Co Cu Co spin valve Current perpendicular to plane (CPP) GMR in Co-Cu-Co (111) The current in the parallel spin configuration dominates the spin torque behavior In the anti-parallel spin configuration, a quadratic bias dependence is found ATK can handle complex magnetic electrodes to search for optimum material properties for spintronics (for example Heusler alloys FeCoAl) Model Co Cu Co

20 Ni Graphite Ni spin filter (1) In-plane lattice constant of graphite matches the surface lattice constants of Ni(111) almost perfectly Lattice parameters (exp.): Graphite Co Ni Cu a hex = 2.46 Å a hex = 2.42 Å a hex = 2.49 Å a hex = 2.57 Å C Ni Ni-Gr mismatch only 1.3% V. M. Karpan et al., PRL 99, (2007)

21 Ni Graphite Ni spin filter (2) Ni(111) Ni(111) 3 graphite monolayers 5 graphite monolayers 7 graphite monolayers

22 Ni Graphite Ni spin filter (3) Ni Graphene Ni is basically an ideal spin filter TMR ~ 100% (pessimistic) (optimistic) for 5-7 graphite monolayers Similar results obtained for Co (one or both sides), and the TMR is only reduced slightly by interface defects V. M. Karpan, PRL 99, (2007) TMR (tunnel magneto-resistance) 1 layer = 38% R.A (Ωμm 2 ) = layer = 10 5 % R.A (Ωμm 2 ) = layer = 10 7 % R.A (Ωμm 2 ) = 0.5

23 Ni Graphite Ni spin filter (4) Conduction takes place through minority spin channel K-point resolved transmission spectrum Majority spin Minority spin

24 Ni Graphite Ni spin filter (5) Spin resolved transmission spectrum Surface Ni 3d-density of states

25 Transport throughcarbonnanoribbon with Fe/V adatom PB Joachim A. Fürst, Mads Brandbyge, Antti-Pekka Jauho, and Kurt Stokbro, Phys. Rev. B 78, (2008)

26 Spin-resolved Transmission (GPB) Fürst, PRB 78, (2008)

27 Transmission analysis Clear correspondance between d-orbital PDOS and dips. Scattering depends on d- state filling (iron: minority spin, vanadium: majority spin). d-orbitals act as Fano scattering resonances. Fürst, PRB 78, (2008)

28 Eigenchannel analysis Fürst, PRB 78, (2008)

29 V-shaped notch in graphene nanoribbon Transmission spectrum Spin Up Spin Down Y. Hancock, K. Saloriutta, A. Uppstu, A. Harju and M.J. Puska, J Low Temp Phys 153: (2008)

30 Towards real devices, goal= 1 million atoms. Tight binding DFT

31 ATK-SE: Semi-empirical module Electronic structure H,S parametrized Extended Huckel Model User defined model Total energy Generic pair potentials Module for optimizing potentials to database Forces and stress Electrostatics CNDO parameters for adding electron density Parallel Poisson solver Dielectric and metallic regions General features Works with periodic and two probe systems New more efficient algorihtms for two-probe systems, speedup 2-10 times Continiuum model of electrostatic gates and dielectrics

32 Band to Band tunneling in CNT Avouris et. al. PRL 93, (2004).

33 (8,4) nanotube with simple metal electrodes H.H. Sørensen, et. Al. xxx.lanl.gov v3

34 Semiempirical module, new algorithms Krylov method for calculating electrode self-energies H. H. Sørensen et al., arxiv: v3 Parallel Greens function calculator 128 blocks, 16 processors D.E. Petersen et. Al, submitted

35 Acknowledgments Davide Riccie (Atomistix A/S) Morten Stilling (Atomistix A/S) Mads Brandbyge (DTU) Joachim Furst (DTU) Hans Henrik Sørensen (Århus University) QuantumWise A/S Dan Erik Petersen Søren Smidstrup Anders Blom Mads Peter Ipsen