Electric-field controlled semiconductor spintronic devices University of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds, Andrew Rushforth, Devin Giddings et al. Institute of Physics ASCR Alexander Shick Tomas Jungwirth Hitachi Cambridge University of Texas and Texas A&M Jorg Wunderlich, Bernd Kaestner Allan MacDonald, Jairo Sinova David Williams

e- Spintronics Beff s Beff Bex + Beff spin coupled to macroscopic V Beff p s Spin-orbit coupling Dirac eq. in external field V(r) & 2nd-order in v /c around non-relativistic limit Beff Bex + Beff Ferromagnetism Coulomb repulsion & Pauli exclusion principle ky ky spin coupled to momentum and crystal fields macroscopic moment kx kx e.g. GaAs valence band As p-orbitals  large SO e.g. GaMnAs valence band FM & large SO

Current spintronics - two terminal AMR or GMR devices Au Au [010] F Magnetization [110] [100]  Current

Yamanouchi et al., Nature (2004) Electrical control of spintronic devices 1. Current driven magnetization reversal 2. Spintronic transistor 3. Electric-field induced spin-polarization in non-magnetic systems 2 orders of magnitude lower critical currents in dilute moment (Ga,Mn)As than in conventional metal FMs Sinova, Jungwirth et al., PRB (2004) Magnetic race track memory Parkin, US Patent (2004) Yamanouchi et al., Nature (2004) Coulomb blockade AMR spintronic SET in thin-film GaMnAs Spin Hall effect induced edge spin polarization in GaAs 2DHG

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

AMR nature of the effect normal AMR Coulomb blockade AMR

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

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

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

Calculated doping dependence of 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)

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

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

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

In-plane HH spin-splitting due to SO-coupling Non-zero in-plane component of EL polarization at Bx=0 and Ip=0 -5 -10 5 10 Circ. polarization [%]

SHE experiments - show the SHE symmetries 1.5m channel SHE experiments n p y x z LED 1 2 applied electrical current x z 10m channel induced transverse spin accummulation spin (magnetization) component y - show the SHE symmetries - edge polarizations can be separated over large distances with no significant effect on the magnitude

=0 Szedge Lso ~ jzbulk tso jyz (y)/Ex Ex Sz (y)/Ex x y [kF-1] 10 20 30 40 50 jyz (y)/Ex Sz (y)/Ex =0 y x Ex Szedge Lso ~ jzbulk tso 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, ...

skew scattering 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 =0 skew scattering

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

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

 NO perp.-to-plane component of polarization at B=0 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

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

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

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

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

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

TAMR in metals TAMR TMR NiFe 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

EXPERIMENT Spin Hall Effect 2DHG 2DEG VT VD

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

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) electric & magnetic control of Coulomb blockade oscillations

CBAMR if change of |(M)| ~ e2/2C 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

CBAMR  new device concepts

Electrically generated spin polarization in normal semiconductors SPIN HALL EFFECT

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

Spin-orbit coupling “force” deflects like-spin particles Spin Hall effect Spin-orbit coupling “force” deflects like-spin particles V=0 _ _ _ _ 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

Szedge Lso ~ jzbulk tso tso=h/so : (intrinsic) spin-precession time 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 ~ jzbulk tso Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05

SHE experiment in GaAs/AlGaAs 2DHG 1.5 m channel n p y x z LED 1 2 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

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

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

Skew scattering off impurity potential (Extrinsic SHE/AHE)

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) Since I am the first talk and the topic of spin-orbit coupling will come up often let me introduce its basic notion. The spin orbit coupling interactions is nothing but an effective magnetic field interaction felt by a moving charge due to a changing electric field due to its relative motion in a potential generating such an electric field. Maxwell’s equations show us that this relative motion of the charge and the electric field induces an effective magnetic field proportional to the orbital momentum of the quasiparticle. As illustrated in the equation shown the spin quantization axis for such a

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

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

e- Spintronics Beff s Beff Bex + Beff Bex Ferromagnetism Coulomb repulsion & Pauli exclusion principle V Beff p s 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 GaAs valence band As p-orbitals  large SO GaMnAs valence band FM & large SO