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Spin-orbit coupling based spintronics: Extraordinary magnetoresistance studies in semiconductors

Spin-orbit coupling based spintronics: Extraordinary magnetoresistance studies in semiconductors. Tom as Jungwirth. Universit y of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds, Andrew Rushforth, Devin Giddings et al. Institute of Physics ASCR

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Spin-orbit coupling based spintronics: Extraordinary magnetoresistance studies in semiconductors

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  1. Spin-orbit coupling based spintronics: Extraordinary magnetoresistance studies in semiconductors 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, Jan Mašek, Josef Kudrnovský, František Máca, Karel Výborný, Jan Zemen, Vít Novák, Miroslav Cukr, Kamil Olejník, et al. Hitachi Cambridge University of Texasand Texas A&M Jorg Wunderlich, Bernd KaestnerAllan MacDonald, Jairo Sinova, et al. David Williams, et a.

  2. _ _ _ _ _ _ _ _ _ _ _ _ FSO M _ B + + + + + + + + + + + + + I _ _ _ _ _ _ _ _ _ _ _ FL + + + + + + + + + + + + + I V p s V Beff V Extraordinary magnetoresistance Ordinary magnetoresistance: response to external magnetic field via classical Lorentz force Extraordinary magnetoresistance: response to internal spin-polarization via quantum-relativistic spin-orbit coupling anomalous Hall effect anisotropic magnetoresistance e.g. ordinary (quantum) Hall effect Discovered in the 19th century in TM ferromagnets – classical unsettled CMP field - now accessible in semiconductors

  3. Conventional ferromagnetic metals Ab initio Kubo (CPA) formula for AMR and AHE in FeNi alloys Mott’s model of transport ss sd AHE AMR ss sd Mott&Wills ‘36 Banhart&Ebert EPL‘95 itinerant 4s: no exch.-split no SO Khmelevskyi ‘PRB 03 localized 3d: exch. split SO coupled difficult to match models and microscopics

  4. Ga Mn As Mn Ferromagnetic semiconductors insulating GaMnAs As-p-like holes metallic GaMnAs Mn-d-like local moments • carriers with both strong • SO coupling and • exchange splitting • - simpler band structure • SO topology of holes dominated by As • p-orbitals as in hosts (Mn on Ga sublattice) favorable for exploring physical origins

  5. ky kx Origin of R[M  I]> R[M || I]non-crystalline AMR in GaMnAs Boltzmann eq. in relax. time approximation 1st order Born approximation 4-band spherical Kohn-Luttinger model SO-coupling – spherical model FM exchange spiitting M 1/k (M) ~(k . s)2 ~Mx . sx ky kx M ky hot spots for scattering for states moving  M  R[M  I]> R[M || I] (opposite to most metal FMs) kx

  6. M current  M  ) ) current [110]  ) full 6-band Hamiltonian: non-crystalline and crystalline AMR spherical model: non-crystalline AMR only theory In metallic GaMnAs: also magnitudes and relative strengths of non-crystalline and crystalline AMR terms consistent with experiment exp. Rushforth et al. ‘07

  7. AlOx Au GaMnAs [100] [100] M [010] [110] [010] F [100] [100] [110] Au [010] [010] [010] Family of new AMR effects: TAMR – anisotropic TDOS predicted and observed in metals TAMR– discovered in GaMnAs  Au Shick et al.PRB'06, Bolotin et al. PRL'06, Viret et al. EJP’06, Moser et al. 06, Grigorenko et al. ‘06 Gould, et al., PRL'04, Brey et al. APL’04, Ruster et al.PRL’05, Giraud et al. APL’05, Saito et al. PRB’05,

  8. M [010] [110] F [100]  [110] [010] Coulomb blockade AMR – anisotropic chemical potential Q VD Source Drain Gate VG magnetic electric & Predicted stronger CBAMR for metals control of Coulomb blockade oscillations Wunderlich et al. ‘06

  9. _ _ _ FSO _ FSO I V AHE mechanisms Karplus&Luttinger intrinsic AHE mechanism revived in GaMnAs Karplus&Luttinger PR ‘54 Jungwirth et al. PRL ‘02,APL ’03, Edmonds et al. APL ’03, Chun et al. PRL ‘07 Experiment sAH  1000 (W cm)-1 Theroy sAH  750 (W cm)-1 • intrinsic AHE in pure Fe: ab initio Kubo eq. Yao et al. PRL ‘04 Co[Kotzler&Gil PRB ‘05] 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]

  10. _ _ _ FSO _ non-magnetic FSO _ _ _ FSO _ I FSO I V=0 2DHG 2DEG V • AHE  SHE - All Semiconductor systems including 2D with “model” SO Cubic (2DHG) and linear (2DEG) in k Rashba model Kato Sci ’04, Wunderlich et al PRL’05, PRB’06, Sih et al. NatPhys ‘05 - Optical methods: polarized EL Solvable analytically

  11. Exploring SHE & AHE fenomenologies in 2D non-magnetic SC - + 2DHG 2DEG z x Gate 2DHG 2DHG 2DEG 2DEG + - Gate AHE SHE

  12. 2D “model” systems ideal to explore intrinsic vs. extrinsic AHE/SHE intrinsic skew scattering side jump group velocity semicalssical Boltzmann eq. distribution function quantum Kubo formula jump side int. skew sc. Extrinsic skew scattering term: - absent in 2DEG for two-band occupation - absent in 2DHG for any band occupation Borunda et al. ‘07

  13. Optical means of exploring EMR fundamentals on systems with simple yet topologically distinct SO-bands

  14. 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

  15. 1. Coulomb blockade AMR Spintronic transistor- magnetoresistance controlled by gate voltage I Bptp B0 B90 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

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

  17. 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

  18. 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)

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

  20. 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)

  21. 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

  22. _ _ _ FSO _ non-magnetic FSO I V=0 SPIN HALL EFFECT no ferromagnetism, spin-orbit coupling only all-electric spintronics Spin-current generation in non-magnetic systems without applying external magnetic fields Spin accumulation without charge accumulation excludes simple electrical detection

  23. 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

  24. 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

  25. 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

  26. =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, ...

  27. 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

  28. 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

  29. 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)]

  30. 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

  31. 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)

  32. 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

  33. 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

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

  35. 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

  36. 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

  37. 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

  38. 2DEG VT 2DHG VD EXPERIMENT Spin Hall Effect

  39. 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

  40. 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

  41. 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

  42. CBAMR  new device concepts

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

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

  45. 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

  46. 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

  47. 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

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