Ferromagnetic and non-magnetic spintronic devices based on spin-orbit coupling

1. Ferromagnetic and non-magnetic spintronic devices based on spin-orbit coupling Tomas Jungwirth University of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds, Andrew Rushforth, Devin Giddings et al. Institute of Physics ASCR Alexander Shick Hitachi Cambridge University of Texasand Texas A&M Jorg Wunderlich, Bernd KaestnerAllan MacDonald, Jairo Sinova David Williams

2. SO-coupling and electric field controlled spintronics: 1.Coulomb-blockade anisotropic magnetoresistance 2.Spin-Hall effect Spintronic SET in thin-film GaMnAs Electric-field induced edge spin polarization in GaAs 2DHG

3. I Bptp B0 B90 1. Coulomb blockade AMR Spintronic transistor- magnetoresistance controlled by gate voltage Strong dependence on field angle hints to AMR origin Huge hysteretic low-field MR Sign & magnitude tunable by small gate valtages Wunderlich, Jungwirth, Kaestner et al., cond-mat/0602608

4. AMR nature of the effect Coulomb blockade AMR normal AMR

5. Single electron transistor Narrow channel SET dots due to disorder potential fluctuations (similar to non-magnetic narrow-channel GaAs or Si SETs) CB oscillations low Vsd blocked due to SE charging

6. magnetization angle  CB oscillation shifts by magnetication rotations At fixed Vg peak  valley or valley  peak  MR comparable to CB negative or positive MR(Vg)

7. M [010] [110] F [100] [110] [010] Q0 Q0 e2/2C Coulomb blockade AMR SO-coupling  (M) magnetic electric & control of Coulomb blockade oscillations

8. Different doping expected in leads an dots in narrow channel GaMnAs SETs • CBAMR if change of • |(M)| ~ e2/2C ~ 10Kelvin from exp. •  consistent • In room-T ferromagnet change of |(M)|~100Kelvin • CBAMR works with dot both ferro • or paramegnetic Calculated doping dependence of (M1)-(M2)

9. CBAMR SET • Huge, hysteretic, low-field MR tunable • by small gate voltage changes • Combines electrical transistor action • with permanent storage Other FERRO SETs • Non-hysteretic MR and large B - • chemical potential shifts due to Zeeman effect • Ono et al. '97, Deshmukh et al. '02 • Small MR - subtle effects of spin-coherent and • resonant tunneling through quantum dots • Ono et al. '97, Sahoo '05

10. 2. Spin Hall effect Spin-orbit only & electric fields only induced transverse spin accummulation Detection through circularly polarized electroluminescence x applied electrical current y z spin(magnetization) component Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05 Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05

11. 2DHG 2DEG Testing the co-planar spin LED only first p-n junction current only (no SHE driving current) 20 EL EL peak 10 Bz=0 • Can detect edge polarization • Zero perp-to-plane component • of polarization at Bz=0 and Ip=0 0 Circ. polarization [%] -10 -20

12. n p LED 1 n y x LED 2 z 1.5m channel SHE experiments 10m channel - show the SHE symmetries - edge polarizations can be separated over large distances with no significant effect on the magnitude

13. =0 Ex x jyz (y)/Ex y Sz (y)/Ex 0 10 20 30 40 50 y [kF-1] Szedge Lso ~ jzbulktso Theory: 8% over 10nm accum. length for the GaAs 2DHG Consistent with experimental 1-2% polarization over detection length of ~100nm Murakami et al. '03, Sinova et al.'04, Nomura et al. '05, ...

14. skew scattering =0 Other SHE experiments: Spin injection from SHE GaAs channel Electrical measurement of SHE in Al Valenzuela, Tinkham '06 Kato et al. '04, Sih et al. '06 100's of theory papers: transport with SO-coupling intrinsic vs. extrinsic

16. Q0 Q0 e2/2C Microscopic origin Q VD Source Drain • Vg = 0 Gate VG  Coulomb blockade • Vg  0 Q=ne - discrete Q0=CgVg - continuous Q0=-ne blocked Q0=-(n+1/2)e open

17. Sub GaAs gap spectra analysis: PL vs EL ++ -- X : bulk GaAs excitons I : recombination with impurity states B (A,C): 3D electron – 2D hole recombination Bias dependent emission wavelength for 3D electron – 2D hole recombination [A. Y. Silov et al., APL 85, 5929 (2004)]

18. Circularly polarized EL In-plane detection angle Perp.-to plane detection angle  NO perp.-to-plane component of polarization at B=0  B≠0 behavior consistent with SO-split HH subband

20. total wf antisymmetric = * spin wf symmetric (aligned) orbital wf antisymmetric e- FERO MAG NET 1. Introduction Non-relativistic many-body Pauli exclusion principle & Coulomb repulsionFerromagnetism • Robust(can be as strong as bonding in solids) • Strong coupling to magnetic field • (weak fields = anisotropy fields needed • only to reorient macroscopic moment)

21. p s V e- Beff Spin-orbit coupling (Dirac eq. in external field V(r) & 2nd-order in v /c around non-relativistic limit) Beff Bex + Beff Bex FM without SO-coupling GaMnAs valence band tunable FM & large SO GaAs valence band As p-orbitals  large SO

22. M || <100> M || <010> GaMnAs ky kx  Band structure depends on M AMR (anisotropic magnetoresistance) Ferromagnetism: sensitivity to magnetic field SO-coupling: anisotropies in Ohmic transport characteristics

23. TMR (tunneling magnetoresistance) Based on ferromagnetism only spin-valve no (few) spin-up DOS available at EF large spin-up DOS available at EF

24. Magnetization [010] [110] [100]  [100] F [100] [010] Current [100] [110] [010] [010] [010] Tunneling AMR: anisotropic tunneling DOS due to SO-coupling MRAM (Ga,Mn)As Au Au - no exchange-bias needed - spin-valve with ritcher phenomenology than TMR Gould, Ruster, Jungwirth, et al., PRL '04, '05

25. y jt z x y jt z x Wavevector dependent tunnelling probabilityT (ky, kz) in GaMnAs Red high T; blue low T. thin film Magnetization perp. to plane Magnetization in-plane Magnetisation in plane constriction Giddings, Khalid, Jungwirth, Wunderlich et al., PRL '05

26. TAMR in metals ab-initio calculations Shick, Maca, Masek, Jungwirth, PRB '06 NiFe TAMR TMR Bolotin,Kemmeth, Ralph, cond-mat/0602251 TMR ~TAMR >>AMR Viret et al., cond-mat/0602298 Fe, Co break junctions TAMR >TMR

27. 2DEG VT 2DHG VD EXPERIMENT Spin Hall Effect

28. Q0 Q0 e2/2C Single Electron Transistor Q VD Source Drain • Vg = 0 Gate VG  Coulomb blockade • Vg  0 Q=ne - discrete Q0=CgVg - continuous Q0=-ne blocked Q0=-(n+1/2)e open

29. Coulomb blockade anisotropic magnetoresistance Spin-orbit coupling Band structure (group velocities, scattering rates, chemical potential) depend on If lead and dot different (different carrier concentrations in our (Ga,Mn)As SET) magnetic electric & control of Coulomb blockade oscillations

30. Wunderlich, Jungwirth, Kaestner, Shick, et al., preprint • CBAMR if change of |(M)| ~ e2/2C • In our (Ga,Mn)As ~ meV (~ 10 Kelvin) • In room-T ferromagnet change of |(M)|~100K • Room-T conventional SET • (e2/2C>300K) possible

31. CBAMR  new device concepts

32. Electrically generated spin polarization in normal semiconductors SPIN HALL EFFECT

33. Ordinary Hall effect Lorentz force deflect charged-particles towards the edge B _ _ _ _ _ _ _ _ _ _ _ FL + + + + + + + + + + + + + I V Detected by measuring transverse voltage

34. V=0 Spin Hall effect Spin-orbit coupling “force” deflects like-spin particles _ _ _ FSO _ non-magnetic FSO I Spin-current generation in non-magnetic systems without applying external magnetic fields Spin accumulation without charge accumulation excludes simple electrical detection

35. Microscopic theory and some interpretation experimentally detected spin * velocity non-conserving (ambiguous) theoretical quantity - weak dependence on impurity scattering time - Szedge ~ jzbulk/ vF tso=h/so: (intrinsic) spin-precession time Lso=vF tso: spin-precession length Szedge Lso ~ jzbulktso Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05

36. n LED 1 p y m 1.5 m x n channel LED 2 z SHE experiment in GaAs/AlGaAs 2DHG Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05 10m channel - shows the basic SHE symmetries - edge polarizations can be separated over large distances with no significant effect on the magnitude - 1-2% polarization over detection length of ~100nm consistent with theory prediction (8% over 10nm accumulation length) Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05

37. n p y m 1.5 m x n channel z Conventionally generated spin polarization in non-magnetic semiconductors: spin injection from ferromagnets, circular polarized light sources, externalmagnetic fields SHE: small electrical currents in simple semiconductor microchips SHE microchip, 100A high-field lab. equipment, 100 A

38. majority _ _ _ FSO _ FSO I minority V Spin and Anomalous Hall effects Spin-orbit coupling “force” deflects like-spin particles InMnAs Simple electrical measurement of magnetization

39. skew scattering Skew scattering off impurity potential (Extrinsic SHE/AHE)

40. SO-coupling from host atoms (Intrinsic SHE/AHE) bands from l=0 atomic orbitals  weak SO (electrons in GaAs) bands from l>0 atomic orbitals  strong SO (holes in GaAs)

41. Intrinsic AHE approach explains many experiments • (Ga,Mn)As systems [Jungwirth et al. PRL 02, APL 03] • Fe [Yao, Kleinman, Macdonald, Sinova, • Jungwirth et al PRL 04] • Co [Kotzler and Gil PRB 05] • Layered 2D ferromagnets such as SrRuO3 and pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 01,Taguchi et al., Science 01, Fang et al Science 03, Shindou and Nagaosa, PRL 01] • Ferromagnetic spinel CuCrSeBr [Lee et al. Science 04] Experiment sAH  1000 (W cm)-1 Theroy sAH  750 (W cm)-1

42. Hall effects family • Ordinary: carrier density and charge; magnetic field sensing • Quantum: text-book example a strongly correlated many-electron system with e.g. fractionally charged quasiparticles; universal, material independent resistance • Spin and Anomalous: relativistic effects in solid state; • spin and magnetization generation and detection