Spinorbit coupling and spintronics in ferromagnetic semiconductors and

Spin-orbit coupling and spintronics in ferromagnetic semiconductors (and metals) Tomas Jungwirth Institute of Physics ASCR Alexander Shick, Jan Mašek, Josef Kudrnovský, František Máca, Karel Výborný, Jan Zemen, Vít Novák, Kamil Olejník, Jairo Sinova et al. 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.

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

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

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

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

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

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

(Ga, Mn)As: archetypical system for SO-coupling based spintronics research SW-transf. Jpd SMn. shole As-p-like holes Ga Mn As Mn Mn-d-like local moments Dilute Mn-doped SC: sensitive to doping; 100 smaller Ms 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 (Jpd) & host SC bands provides simple yet often semiquantitative description

Coulomb blockade AMR – anisotropic chemical potential Source Q VD Drain Gate VG [110] [010] M M || <110> M || <100> F [100] [110] [010] (M) electric & magnetic control of Coulomb blockade oscillations

Tunneling AMR – anisotropic TDOS TAMR in Ga. Mn. As Au Anisotropc tunneling amplitudes M perp. Resistance Al. Ox Magnetisation in plane ~ 1 -10% in metallic Ga. Mn. As M in-plane Huge when approaching MIT in Ga. Mn. As

One Strain controlled micromagnetics 0. 1 -1 m DW structure and dynamics directly reflecting e. g. (strain dependent) competition between uniaxial and cubic anisotropies 500 nm strain ~ 10 -4 … plus 100 -10 x smaller currents for DW switching and 100 -10 x weaker dipolar crosslinks prospect for dense integration of magnetic microelements switchable by low currents One

Sensitivity of AMR to lattice distortions bulk Ga. Mn. As Ga. As ~100 nm - 1 m wide bars

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

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

Ga. As: Mn extrinsic semiconductor Ga. As VB Mn-acceptor level (IB) Ga. Mn. As disordered VB 2. 2 x 1020 cm-3 VB-IB VB-CB Short-range ~ M. s potential - additional Mn-hole binding - ferromagnetism - scattering

MIT (and ferromagnetism) at relatively large doping suppressed gating effect MIT in p-type Ga. As: - shallow acc. (30 me. V) ~ 1018 cm-3 - Mn (110 me. V) ~1020 cm-3 MIT in Ga. As: Mn at order of magnitude higher doping than quoted in text books

Weak hybrid. Delocalized holes long-range coupl. optimal combination of large SO-cupling, hole delocalization, hole-Mn coupling SO-coupling strength, band-parabolicity Search for optimal III-V host In. Sb, In. As d 5 Ga. As Ga. P Strong hybrid. Impurity-band holes short-range coupl. Al. As d 5 d 4 no holes d Ga. N d 4

I(II, Mn)V dilute-moment ferromgantic semiconductors III = I + II Ga = Li + Zn • Ga. As and Li. Zn. As 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

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

High Tc large SO-coupling TM thin films and ordered alloys heavy TM FM TM heavy TM spontaneous moment spin-orbit coupling magnetic susceptibility 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)/Al. Ox/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) 147207 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) 067202 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) 077201 T. Jungwirth, Jairo Sinova, J. Mašek, J. Kučera, and A. H. Mac. Donald: 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/Ga. As/(Ga, Mn)As Stack, Phys. Rev. Lett. (2005) 027203