Semiconductor and Graphene Spintronics Jun-ichiro Inoue Nagoya University, Japan Spintronics applications : spin FET role of interface on spin-polarized current in FM/SC, FM/graphene junctions KITPC2010

Collaborators Syuta Honda PD, Kansai University A.Yamamura T. Hiraiwa R. Sato MC students, Nagoya University, Japan Hiroyoshi Itoh Asc. Prof., Kansai University, Japan (computer codes)

Outline Introduction - role of junction interface on GMR, TMR - spin MOSFET and issues for SC, graphene Spin injection and MR in spin MOSFET - some experiments - role of Schottky barrier on spin polarized current Two-terminal lateral graphene junctions - a simple model for MR - band mixing at interface; effects on DPs - more realistic models

Spintronics Usage of both charge and spin of electrons Phenomana and applications - GMR, TMR, CIMS  sensors, MRAM - GMR: spin dependent scattering at interfaces - TMR: matching/mismatching of band symmetry between two electrodes (  1 symmetry) Semiconductor spintronics - spin FET, spin MOSFET with semiconductors - or graphene

Spin MOSFET Spin transistor - Monsma et al.: hot electron spin transistor - Datta-Das: gate control of SOI Sugawara-Tanaka - Spin MOSFET with half-metals - logic + memory device Many proposals - Flatté-Vignale: Unipolar spin diodes &transistors - psuedospintronics, valleytronics in graphene gate 2DEG with SOI FM Conventional MOSFET - Unipolar transistor

Issues and materials - Si: promising candidate, compatible with Si CMOS technology, weak spin-orbit interaction (SOI) - GaAs: high mobility, gate controllable SOI many experiments on spin injection - Graphene: high mobility, weak SOI long spin diffusion length, Spin injection, transport and detection Materials gate FM Electrons Role of interface on spin-dep. Transport in GaAs and graphene junctions

Some Experiments Spin injection into GaAs: - Schottky barrier or tunnel barrier - spin polarization 40 ~ 50 % - optical detection - GaMnAs as spin injector  high ratio only at low T e.g. O. M. van’t Erve et al., APL 84, 4334 (2004) X. Jiang et al., PRL94, (2005) Van Dorpe et al. PRB (2005) Spin injection into Si: - spin polarization 10~20% B. T. Jonker et al., Nature (2007)

Imaging of spin injection S. A. Crooker et al., Science 309, 2192 (2005) Positive spin accumulation in GaAs - Lateral Fe/GaAs/Fe, Kerr effect  Negative spin polarization in current from GaAs to Fe see also: Kotissek et al., Nat. phys. 3, 872 (2007) Lou et al., Nat. phys (2007) Negative spin polarization - Fe/GaAs/Fe junctions, negative TMR Moser et al., APL 89, (2006) - Current induced by photo-excited electrons Kurebayashi et al., APL 91, (2007) e-e- P>0 P<0

Band structure of GaAs Electronic states at interface of GaAs FeGaAs ECEC Conduction band Valence band IRS (Schokley state) at interface IRSs mix with Fe bands - ↑spin bands; strong mixing - ↓spin bands; weak mixing due to band symmetry  spin ECEC ↑ spin

Ls = 200ML,  s = 0.5 eV  DOS [eV  1 ] EFEF Ga contact GaAs bulk As contact  spin  spin  02 E  E C [eV] Interfacial resonant states (IRSs) : local DOS Spin dependent IRSs appear in SB. ↓spin IRSs in Fe-As contact are sharp. Fe n-GaAs  spin ECEC  spin 200 ML SS Fe As As contact Fe Ga Ga contact Exp. barrier height ~ 0.49 – 0.44 eV

   Bias [V]  S =0.3eV P Bias dependence of spin polarization Fe GaAs Zero bias: large I ↑ due to  1 band symmetry Negative bias: Contribution from ↓spin IRSs Spin polarization of current becomes negative for small Schokley barrier height. V Shift of IRSs

(  S =0.3eV, Bias=0.3V)  point 0 8  spin  spin D(k || ) [eV  1 ] Log  k   [e 2 /h] DOS  Momentum resolved conductance IRSs spread over whole Brillouin zone, but those near the  point contribute to the conductance due to small Fermi surface of GaAs assumed.  Large P

Fe –As contact  [e 2 /h] [  10  5 ] Bias [V] PP PP Fe/GaAs/Fe tunnel junctions MR Bias [V]    S [eV] 0.75(without Schottky barrier) SS Fe GaAs Potential profile Bias~0.6V Bias~0.0V P↑1P↑1 P↓P↓ AP  1

several issues, - Conductivity mismatch vs spin relaxation by SOI Semiclassical model by Fert-Jaffres (2001) for FM/I/SC/I/FM - roughness - stacking direction SC layer - half-metallic electrodes - spin injection into Si Fe/GaAs with Schottky barrier and Fe/GaAs/Fe - Interfacial resonant states are spin dependent and give large positive and negative spin polarization.  Control of Schottky barreir is crucial. Conductivity mismatch SOI (barrier resistivity) Summary of first part

E kxkx kyky     E K Γ M  Graphene Structure 2-D Honeycomb lattice of C Electronic states s, p x, p y orbitals   bands p z orbital   bands (zero-gap semiconductor) Linear dispersion : Dirac points  Zero effective mass x y zig-zag edge armchair edge

Characteristics of Graphene Massless fermions  High mobility, low resistivity New material for electronics Carbon atoms : light element  Weak spin-orbit interaction Long spin diffusion length application to spintronics 2-dimensionality  Gate control Possible applications Graphene transistor, spin-FET, terra-hertz wave, …

FM/G/FM spin FET Spin injection / MR effect Current: on/off by gate – energy gap nano-ribbon bilayer graphene Hydrogenation - graphane Magnetization control Fabrication method Top gate Back gate FM Graphene sheet Exp. MR ratios a few % Non-local measurement Shiraishi’s group (2007)

E [eV] k || 0123 EE 0123   E [eV]   [e 2 /h] 1 MR 0 Dirac point of Graphene E(k // ) for nano-ribbon with zigzag edge k // : momentum along the edge Matching of the conduction pass with DP A simple model of MR MR appears when momentum matching is spin-dependent, and when the band width of conduction band is narrow. However, usual transition metal FM  Wide conduction band  no MR

MR in lateral FM/graphene/FM junctions A single orbital tight-binding model + Kubo formula  DP shifts due to contact with leads  tunneling via states near DP L=12[ML] L t I =sp  W = ∞ Zigzag edge contact with electrodes (square lattice)  k ||  [e 2 /h] Effective DP EFEF k // DP Tunnel barrier

s-□ 20ML Graphene s-□ 50ML k // E(k) Large band mixing Small band mixing Energy states of finite size junction probability density of graphene

More details Shift of DP with - Graphene length - Band mixing at the contact  spin dependent G for FM electrodes

Realistic contacts 4ML sp 3 d 5 sp 3 x y z sp 3 d 5 L Zigzag edge aa Electrodes with fcc (111) lattice or triangular lattice wide overlap region between graphene and electrodes

LL=LR=1 LL=1 LR=400 LL=LR=400 k //  [e 2 /h/atm] k // 1000 [ML] L R [ML] k // L L [ML] 5 [ML] S+P Shift of DP with - overlap of graphene and electrodes (triangular lattice) - band mixing Some preliminary results

MR L [ML] MR PP PP  AP  [e 2 /h] L=  8 10  6 10  4 10  PP PP  AP  [e 2 /h] k || K’K’ MR in bccFe/graphene/bccFe Spin dependent band mixing at interface  MR Bcc lattice on leads W = ∞ L sp 3 d 5 sp 3 tgtg tItI

MR in graphene junctions with Fe alloys Materials dependence of MR – shifting the up spin band  Ferromagnetic alloys for lead  2.0   E  [eV] MR Fe 0.7 Co 0.3 Fe 0.9 Cr 0.1 Fe Change in the electronic state of Fe alloys at the contact  matching of conduction channel becomes worse in up spin state

Summary of the second part MR in FM/graphene/FM junctions - Spin dependent shift of Dirac points appears in zigzag edge contact.  moderate MR effect - MR can be large for some FM alloy electrodes. Importance of electronic structure near the interface on spin injection and MR Other effects unconsidered should be examined to confirm the present results.

 of n-type graphene/graphene/n-graphene junctions Zigzag edge vs Armchair edge