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

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

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/ B ptp B 90 B0B0 I

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 V sd  blocked due to SE charging

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

& electric & magnetic control of Coulomb blockade oscillations Q0Q0 Q0Q0 e 2 /2C  Coulomb blockade AMR [ 010 ]  M [ 110 ] [ 100 ] [ 110 ] [ 010 ] SO-coupling   (M)

CBAMR if change ofCBAMR if change of |  (M)| ~ e 2 /2C  |  (M)| ~ e 2 /2C  ~ 10Kelvin from exp.  consistent In room-T ferromagnet change of |  (M)|~100KelvinIn room-T ferromagnet change of |  (M)|~100Kelvin CBAMR works with dot both ferro CBAMR works with dot both ferro or paramegnetic or paramegnetic Different doping expected in leads an dots in narrow channel GaMnAs SETs Calculated doping dependence of  (M 1 )-  (M 2 )

Huge, hysteretic, low-field MR tunable by small gate voltage changes Combines electrical transistor action with permanent storage 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 CBAMR SET Other FERRO SETs

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

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

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

=0 Murakami et al. '03, Sinova et al.'04, Nomura et al. '05,... y x ExEx Theory: 8% over 10nm accum. length for the GaAs 2DHG Consistent with experimental 1-2% polarization over detection length of ~100nm y [k F -1 ] j y z (y)/E x S z (y)/E x S z edge L so ~ j z bulk t so

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

Microscopic origin SourceDrain Gate VGVG VDVD Q  Coulomb blockade V g = 0 V g = 0 V g  0 V g  0 Q=ne - discrete Q 0 =C g V g - continuous Q 0 =-ne  blocked Q 0 =-(n+1/2)e  open Q0Q0 Q0Q0 e 2 /2C 

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)] ++ --

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

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

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

AMR AMR (anisotropic magnetoresistance) Band structure depends on M  Ferromagnetism: sensitivity to magnetic field SO-coupling: anisotropies in Ohmic transport characteristics M || GaMnAs kyky kxkx

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

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

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

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

EXPERIMENT Spin Hall Effect 2DHG 2DEG VTVT VDVD

Single Electron Transistor SourceDrain Gate VGVG VDVD Q  Coulomb blockade V g = 0 V g = 0 V g  0 V g  0 Q=ne - discrete Q 0 =C g V g - continuous Q 0 =-ne  blocked Q 0 =-(n+1/2)e  open Q0Q0 Q0Q0 e 2 /2C 

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

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

CBAMR  new device concepts

Electrically generated spin polarization in normal semiconductors SPIN HALL EFFECT

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

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

Microscopic theory and some interpretation - weak dependence on impurity scattering time S z edge ~ j z bulk / v F - S z edge ~ j z bulk / v F t so =h/  so t so =h/  so : (intrinsic) spin-precession time L so =v F t so L so =v F t so : spin-precession length S z edge L so ~ j z bulk t so S z edge L so ~ j z bulk t so Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05 experimentally detected non-conserving (ambiguous) theoretical quantity spin * velocity

1.5  m channel n n p y x z LED  m channel SHE experiment in GaAs/AlGaAs 2DHG - 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) Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05 Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05

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

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

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

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

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  AH  1000 (  cm) -1 Theroy  AH  750 (  cm) -1

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