Spin-orbit coupling and spintronics in ferromagnetic semiconductors (and metals) Tomas Jungwirth University of Nottingham Bryan Gallagher, Tom Foxon, Richard Campion, Kevin Edmonds, Andrew Rushforth, Chris King et al. Hitachi Labs., UK & Japan Jorg Wunderlich, Byong-Guk Park, Andrew Irvine, Elisa De Ranieri, Samuel Owen, David Williams, Akira, Sugawara, et al. Institute of Physics ASCR Alexander Shick, Jan Mašek, Josef Kudrnovský, František Máca, Karel Výborný, Jan Zemen, Vít Novák, Kamil Olejník, Jairo Sinova et al.

Outline 1. Intro – spin-orbit coupling in spintronics 2. GaMnAs based spintronic devices 3. GaMnAs and other spin-orbit coupled ferromagnetic materials

SO-couping = E&M and postulated electron spin nucleus rest frame electron rest frame Lorentz transformation  Thomas precession 22 e-e-e-e- … it’s all about spin and charge of electron communicating & &  Spintronics Spin-orbit couping 2

Ferromagnetism = Pauli exclusion principle & Coulomb repulsion total wf antisymmetric = orbital wf antisymmetric * spin wf symmetric (aligned) DOS e-e-e-e- e-e-e-e- e-e-e-e- … collective communication macroscopic moment  large effects

AMR ~ 1% MR effect GMR ~ 10% MR effect < FM only (      ) TMR ~ 100% MR effect TDOS   TDOS  FM & SO-coupling  (M ) + linear sensing, low-noise - low MR, low-resistance + larger MR - low-resistance, non-linear, spin-coherence, exchange biasing or interlayer coupling, higher noise + very large MR, high resistance, bistable  memory - non-linear, spin-coherence, exchange biasing, higher noise Au AlOx Au TAMRCBAMR TDOS (M ) chem. pot. Combining “+” and eliminating “-” of AMR and TMR(GMR) & SET gating  spintronic transistor

SO-coupling  magnetocrystalline anisotropies  sensitivity to lattice distortions Ferromagnetic/magnetostrictive Ferroelectric/piezoelectric Semicondicting/gatable magneto-sensors, transducors, memory, storage electro-sensors, transducors, memory transistors, processors FeFET piezo/FM hybrids FM semiconductors Systems integrating all three basic elements of current microelectronics

Outline 1. Intro – spin-orbit coupling in spintronics 2. GaMnAs based spintronic devices 3. GaMnAs and other spin-orbit coupled ferromagnetic materials

(Ga,Mn)As: archetypical system for SO-coupling based spintronics research Mn-d-like local moments As-p-like holes Mn Ga As Mn SW-transf.  J pd S Mn. s hole Dilute Mn-doped SC: sensitive to doping; 100  smaller M s than in conventional metal FMs  weak dipolar fields Mn-Mn coupling mediated by holes in SO-coupled SC valence bands: sensitive to gating, comparable magnetocrystalline anisotropy energy and stiffness to metal FMs Model sp-d ferromagnet: kinetic-exchange (J pd ) & host SC bands provides simple yet often semiquantitative description

& electric & magnetic control of Coulomb blockade oscillations Coulomb blockade AMR – anisotropic chemical potential SourceDrain Gate VGVG VDVD Q [ 010 ]  M [ 110 ] [ 100 ] [ 110 ] [ 010 ] M ||  (M)

Tunneling AMR – anisotropic TDOS TAMR in GaMnAs GaMnAs Au AlOx Au Resistance Magnetisation in plane M perp. M in-plane ~ 1-10% in metallic GaMnAs Huge when approaching MIT in GaMnAs Anisotropc tunneling amplitudes

One  m Strain controlled micromagnetics … plus x smaller currents for DW switching and x weaker dipolar crosslinks  prospect for dense integration of magnetic microelements switchable by low currents 500 nm DW structure and dynamics directly reflecting e.g. (strain dependent) competition between uniaxial and cubic anisotropies strain ~ 10 -4

bulk ~100nm - 1  m wide bars Sensitivity of AMR to lattice distortions GaAs GaMnAs

Outline 1. Intro – spin-orbit coupling in spintronics 2. GaMnAs based spintronic devices 3. GaMnAs and other spin-orbit coupled ferromagnetic materials

Magnetism in systems with coupled dilute moments and delocalized band electrons (Ga,Mn)As coupling strength / Fermi energy band-electron density / local-moment density

VB-CB VB-IB Mn-acceptor level (IB) Short-range ~ M. s potential - additional Mn-hole binding - ferromagnetism - scattering GaAs:Mn extrinsic semiconductor GaAs VB GaMnAs disordered VB   2.2x10 20 cm -3

MIT in GaAs:Mn at order of magnitude higher doping than quoted in text books MIT (and ferromagnetism) at relatively large doping  suppressed gating effect MIT in p-type GaAs: - shallow acc. (30meV) ~ cm -3 - Mn (110meV) ~10 20 cm -3

d4d4 d Weak hybrid. Delocalized holes long-range coupl. Strong hybrid. Impurity-band holes short-range coupl. d 5  d 4 no holes InSb, InAs GaN AlAs d5d5 Search for optimal III-V host optimal combination of large SO-cupling, hole delocalization, hole-Mn coupling SO-coupling strength, band-parabolicity GaP GaAs

I(II,Mn)V dilute-moment ferromgantic semiconductors III = I + II  Ga = Li + Zn GaAs and LiZnAs are twin semiconductors Prediction that Mn-doped are also twin ferromagnetic semiconductors No limit for Mn-Zn (II-II) substitution within the same crystal structure Independent carrier (holes and electrons) doping by Li-Zn stoichiometry adjustment

+ interstitial Rock Salt FCC Zinc Blende – (III,Mn)V + interstitial I(II,Mn)V Half Heusler (NiMnSb) I(II,Mn)V as a link between DMSs and high-T c half-metalic Heuslers, all comaptible with III-V technology

High Tc large SO-coupling TM thin films and ordered alloys FM TM heavy TM spontaneous moment magnetic susceptibility spin-orbit coupling FM TM heavy TM FM TM Key: large induced moment on strongly SO-coupled heavy TM

B. G. Park, J. Wunderlich, D. A. Williams, S. J. Joo, K. Y. Jung, K. H. Shin, K. Olejnik, A. B. Shick, and T. Jungwirth: Tunneling anisotropic magnetoresistance in multilayer-(Co/Pt)/AlOx/Pt structures, submitted to Phys. Rev. Lett. (2007) Akira Sugawara, H. Kasai, A. Tonomura, P. D. Brown, R. P. Campion, K. W. Edmonds, B. L. Gallagher, J. Zemen, and T. Jungwirth: Domain walls in (Ga,Mn)As diluted magnetic semiconductor, Phys. Rev. Lett. in press (2007) A. W. Rushforth, K. Výborný, C. S. King, K. W. Edmonds, R. P. Campion, C. T. Foxon, J. Wunderlich, A. C. Irvine, P. Vašek, V. Novák, K. Olejník, Jairo Sinova, T. Jungwirth, B. L. Gallagher: Anisotropic magnetoresistance components in (Ga,Mn)As, Phys. Rev. Lett. 99 (2007) J. Masek, J.Kudrnovsky, F. Maca, B. L. Gallagher, R. P. Campion, D. H. Gregory, and T. Jungwirth: Dilute moment n-type ferromagnetic semiconductor Li(Zn,Mn)As, Phys. Rev. Lett. 98 (2007) J. Wunderlich, T. Jungwirth, B. Kaestner, A. C. Irvine, K.Y. Wang, N. Stone, U. Rana, A. D. Giddings, A. B. Shick, C. T. Foxon, R. P. Campion, D. A. Williams, B. L Gallagher: Coulomb Blockade Anisotropic Magnetoresistance Effect in a (Ga,Mn)As Single-Electron Transistor, Phys. Rev. Lett. 97 (2006) T. Jungwirth, Jairo Sinova, J. Mašek, J. Kučera, and A.H. MacDonald: Theory of ferromagnetic (III,Mn)V semiconductors, Rev. Mod. Phys. 78 (2006) 809 C. Rüster, C. Gould, T. Jungwirth, J. Sinova, G.M. Schott, R. Giraud, K. Brunner, G. Schmidt, L.W. Molenkamp: Very Large Tunneling Anisotropic Magnetoresistance of a (Ga,Mn)As/GaAs/(Ga,Mn)As Stack, Phys. Rev. Lett. (2005)