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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. Hitachi Cambridge University of Texas and Texas A&M Jorg Wunderlich, Bernd Kaestner Allan MacDonald, Jairo Sinova, et al. David Williams, et a. Institute of Physics ASCR Alexander Shick, Jan Mašek, Josef Kudrnovský, František Máca, Karel Výborný, Jan Zemen, Vít Novák, Miroslav Cukr, Kamil Olejník, et al.

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

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

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Ferromagnetic semiconductors Mn-d-like local moments As-p-like holes Mn Ga As Mn insulating GaMnAs metallic GaMnAs carriers with both strong - carriers with both strong SO coupling and SO coupling and exchange splitting 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

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Origin of R[M I]> R[M || I] non-crystalline AMR in GaMnAs ~(k. s) 2 ~M x. s x SO-coupling – spherical model FM exchange spiitting hot spots for scattering for states moving M R[M I]> R[M || I] (opposite to most metal FMs) Boltzmann eq. in relax. time approximation1 st order Born approximation 4-band spherical Kohn-Luttinger model kyky kxkx kxkx kxkx kyky kyky M M 1/ k (M)

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

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Family of new AMR effects: TAMR – anisotropic TDOS TAMR – discovered in GaMnAs Au GaMnAs Au AlOx Au predicted and observed in metals [100] [010] [100] [010] [100] [010] 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, [ 010 ] M [ 110 ] [ 100 ] [ 110 ] [ 010 ] Shick et al.PRB'06, Bolotin et al. PRL'06, Viret et al. EJP’06, Moser et al. 06, Grigorenko et al. ‘06

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& electric & magnetic control of Coulomb blockade oscillations Coulomb blockade AMR – anisotropic chemical potential Wunderlich et al. ‘06 Predicted stronger CBAMR for metals SourceDrain Gate VGVG VDVD Q [ 010 ] M [ 110 ] [ 100 ] [ 110 ] [ 010 ]

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Karplus&Luttinger intrinsic AHE mechanism revived in GaMnAs Experiment AH 1000 ( cm) -1 Theroy AH 750 ( cm) -1 AHE mechanisms intrinsic AHE in pure Fe: ab initio Kubo eq. I _ F SO _ _ _ V Jungwirth et al. PRL ‘02,APL ’03, Edmonds et al. APL ’03, Chun et al. PRL ‘07 Yao et al. PRL ‘04 Karplus&Luttinger PR ‘54 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]

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

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

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

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

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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:

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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

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AMR nature of the effect normal AMR Coulomb blockade AMR

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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

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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 )

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

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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 )

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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

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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 SPIN HALL EFFECT no ferromagnetism, spin-orbit coupling only all-electric spintronics

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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

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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

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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

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=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

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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

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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

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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)] ++ --

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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

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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

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Spin-orbit coupling (Dirac eq. in external field V(r) & 2nd-order in v /c around non-relativistic limit ) e-e-e-e- VV 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

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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

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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

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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

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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

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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

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EXPERIMENT Spin Hall Effect 2DHG 2DEG VTVT VDVD

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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

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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

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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

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CBAMR new device concepts

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Electrically generated spin polarization in normal semiconductors SPIN HALL EFFECT

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

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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

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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

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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

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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

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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

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

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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)

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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

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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

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