Surprises from the spin Hall effect how the spin Hall effect and relativistic torques are opening new paths for information storage

Surprises from the spin Hall effect how the spin Hall effect and relativistic torques are opening new paths for information storage Jairo Sinova Johannes Gutenberg Universität Mainz 17th of September 2017 Magnetism: from fundamental to spin based technology Bad Honnef, Germany 1

Surprises from the spin Hall effect how the spin Hall effect and relativistic torques are opening new paths for information storage I. Introduction II. Spin-Orbit Torques in Ferromagnets: SHE and Inverse spin galvanic effect phenomenology Spin-Orbit Torques Intrinsic SOT in GaMnAs SOT in NiMnSb III. Antiferromagnetic Spintronics: Neél SOTs Active manipulation of Néel order by currents: Néel spin-orbit torque IV.Topological Dirac Fermion + Antiferromagnets + Neel SOTs 2

Using charge and spin in information technology Transistors CHARGE SPIN Magnets S gate insulator semiconductor substrate D HIGH tunability of electronic current All electrons line up together The first spintronics revolution comes in information storage 3

Evolution in World s Storage Capacity Digital: Hard-disks, DVDs, Analog: books, video/film, 10 15 MB 10 14 10 13 Gutenberg (1400-1468) Analog to Digital 10 12 1986 1993 2000 2007 Hilbert et al. Science (2011) 4

Discovery of Giant Magneto Resistance Low Resistance High Resistance From fundamental to practical Albert Fert Peter Grünberg GMR first observed in 1988 Stuart Parkin 2014 Humboldt Professor and 2014 Millennium Prize 5

What is next in memory storage? MRAM Magnetic Random Access Memory Spin-Transfer MRAM (2015) Heating Problems First generation did NOT combine charge and spin 6

Magnetization dynamics and Spin Transfer Torque d ˆM dt = ˆM ~ Heff + ˆM d ˆM dt + ~PJ 2e ( ˆM ˆM 0 ) ˆM Spin Transfer Torque Ferro 1 Spacer Ferro 2 Torque (proposed by Slonczewski, Berger 1996) 7

Spin-Transfer-Torque MRAM MTJ excellent scaling lower power no crosstalk problem simpler fabrication ~ 30 μa STT mechanism: 8

use SPIN CURRENTS instead of electric currents! CHARGE SPIN + particles/antiparticles & spin quantum mechanics special relativity Dirac equation e - = Connects the motion of an electron to a spin dependent force 9

spin-orbit coupling interaction (one of the few echoes of relativistic physics in the solid state) e Impurity potential V(r) Produces an electric field ~E = 1 rv (~r ) e Motion of an electron effective magnetic field in moving electron s rest frame ~B eff = ~~ k mc ~ E ~E H SO = ~µ B ~B eff ~ Beff ~ k 10

Spin-orbitronics Spin-orbit Torques New magnetic materials Caloritronics Nanotransport Spinorbitronics Spintronic Hall effects Topological transport effects 13

Anomalous Hall Effect: the basics Spin dependent force deflects like-spin particles ρ H =R 0 B +4π R s M Electrical measurement of spin polarization (n -n ) InMnA AH xy B + A xx Intrinsic (scattering independent) Nagaosa, JS, et al, Rev. Mod. Phys. 2010 Scattering dependent 14

Spin Hall effect Transverse spin-current generation in paramagnets Intrinsic `Berry Phase, interband coherence [Murakami et al, Sinova et al 2003] Extrinsic `Skew Scattering, Occupation # Response [Dyakonov 1971, Hirsch, S.F. Zhang 2000] Wunderlich, JS, PRL 05 Kato,et al Science Nov 04 15

Intrinsic spin-hall effect: the Rashba SOC example H R = ~2 k 2 2m µ B~ ~B eff ( ~ k) = ~2 k 2 2m + R( x k y y k x ) ky [010] [010] +sz Δp eet kx [100] S=0 ~E [100] ~B eff ( ~ k) / ~s eq -sz B eff pŷ 16

Current induced polarization Inverse Spin Galvanic Effect or Edelstein Effect ky kx δsy 0 δs=0 J x Wunderlich, Jungwirth, JS, et al PRL/PRB 2003/2004 17

Anomalous/Spin Hall effects: more than meets the eye Anomalous Hall Effect Spin Hall Effect spin-current generator Inverse SHE spin-current detector Intrinsic Extrinsic Topological Insulators Mesoscopic Spin Hall Effect SHE Transistor SHE/SOT MRAM HE V Intrinsi Kane and Mele PRL 05 Brune,JS, Molenkamp, et al Nature Physics 2010 Wunderlich, Irvine, JS, Jungwirth, et al, Nature Physics 09, Science 2011 Buhrman,et al., Science 2012 Kubayashi, JS, et al, Nature Nanotech. 2014 18

Spin-Transfer-Torque MRAM MTJ excellent scaling lower power no crosstalk problem simpler fabrication ~ 30 μa STT mechanism: 3" 19

in-plane-current switching MRAM MTJ If switching can be done by an in-plane current then a key issue in STT-MRAM is resolved 4" 20

Experiments of in-plane current Miron et al., Nature 11 spin-orbit torque at PM/FM interface ky Buhrman,et al., Science 12 SHE as spin-current generator + STT δs=0 δsy 0 kx J x d ~ M dt intrinsic SHE + STT! = P ˆM (ˆn ˆM) SHE STT h SOT z J d ~ M dt! SOT = J ex ~ ~ M ~s Intrinsic SHE in paramagnet acts as the external polarizer 21

Experiments of in-plane current magnetic switching spin-orbit torque at PM/FM interface SHE as spin-current generator + STT Miron et al., Nature 11 Buhrman,et al., Science 12 h SOT z J d ~ M dt! SOT = J ex ~ ~ M ~s intrinsic SHE + STT d M ~! = P dt ˆM (ˆn ˆM) SHE STT Gordon Research Conference - Jairo Sinova 22

Spin-orbit Torques in Bilayer Systems Make a ferromagnet behave like a cat: SOC (broken bulk inversion)+ferromagnetism? Spin Hall Rashba Courtesy of P. Gambardella 23

Intrinsic (Berry phase) spin-orbit torque from Bloch eq. Large exchange limit and Rashba SOC ~M [001] Δp eet [100] ~E eq B ~ M eff d ˆM dt ˆM s z ẑ B eff pŷ maximum s z ẑ for M! E! 24

Intrinsic (Berry phase) spin-orbit torque from Bloch eq. Large exchange limit and Rashba SOC [001] Δp eet [001 [100] [100 ~E M eq B ~ M eff M B eq eff d ˆM dt ~ M d ˆM dt B eff pŷ anti-damping ˆM s zero for M! E! z ẑ s z ẑ ˆM s z ẑ s z ẑ ( ~ E ẑ) ˆM cos( M E ) 25

Intrinsic (Berry phase) spin-orbit torque in GaMnAs [010] [010] [110] [110] GaMnAs Rashba [100] GaMnAs GaAs Dresselhaus [100] d ˆM dt! SOT = ˆM s z ( M E )ẑ angle between M and current direction current direction 26

Measuring spin-orbit fields: electrical induced/detected FMR Landau-Lifshitz-Gilbert equation h z h y h x V dc (μv) Because h so =-J pd Δs μ 0 H 0 (T) the V amplitudes contain spin-orbit fields information. 27

Torque types and line-shapes Vsym Vasy Anti-damping torque Τ in-plane (or h z ) V sym = C 1 h z (θ M-E ) sin (2θ M-E ) Kurebayashi, Sinova et al., Nature Nanotech. (2014) Fang et al., Nature Nanotech. (2011) Sample: 18 or 25 nm-thick GaMnAs 4 mm-wide 28

The out-of-plane SO field the out-of-plane field the symmetric line-shape V sym (θ M-E ) ~ h z (θ M-E ) sin (2θ M-E ) 10 5 sin2θ 100 50 I M hz V sym (µv) 0-5 -10 100 0 90 180 270 360 θ (degree) M-dependent h z sinθ symmetry for 100 direction. h z (µt) 0-50 -100 I h z M 0 90 180 270 360 θ (degree) 29

Comparison to Theory µ 0 h z [ µt ] 150 100 50 0-50 -100 [100] [010] 150 100 50 0-50 -100-150 -150 150 90 180 270 90 180 270 150 µ 0 h z [ µt ] 100 50 0-50 -100 [1-10] [110] 100 50 0-50 -100-150 -150 0 90 180 270 360 θ M-J 90 180 270 360 θ M-J 30

Comparison to Theory Dash line: Calculations replacing H KL with a parabolic model, i.e. no (J.k) 2 term µ 0 h z [ µt ] 150 100 50 0-50 -100 [100] [010] 150 100 50 0-50 -100 [010] S // M [100] -150-150 150 90 180 270 90 180 270 150 µ 0 h z [ µt ] 100 50 0-50 -100 [1-10] [110] 100 50 0-50 -100-150 -150 0 90 180 270 360 θ M-J 90 180 270 360 θ M-J 31

Discovery of anti-damping spin-orbit torques Solid line: Calculations with H KL (captures higher harmonics) µ 0 h z [ µt ] 150 100 50 0-50 -100 [100] [010] 150 100 50 0-50 -100 [010] S // M [100] -150-150 150 90 180 270 90 180 270 150 µ 0 h z [ µt ] 100 50 0-50 -100 [1-10] [110] 100 50 0-50 -100-150 -150 0 90 180 270 360 θ M-J 90 180 270 360 θ M-J Kurebayashi, JS, et al., Nat. Nanot. (2014) 32

SOT in metals: dominated by field like term NiMnSb Z&[001]& [1#10]& I [110] φ& M S (φ) I [110] Kubo Scattering Formalism Jacob Gayles Z&[001]& B y& I [110] In Plane B x& M S (ϕ) & [1/10]& Z&[001]& I [110] Out of Plane B y& B x& M S (ϕ) & [1/10]& 33

Room-temperature SOT in NiMnSb Ciccarelli, et al., Nature Physics (2016) 25 μt J 2 [110] z y x J 1 [1-10] 15 15 10 5 V asy V sym 10 5 V asy V sym V dc (µv) 0-5 V dc (µv) 0-5 -10 [1-10] -15 0 90 180 270 360 φ (deg) The driving field is linear in current: -10 [110] -15 0 90 180 270 360 φ (deg) 34

Why antiferromagnetic spintronics Ferromagnets: Antiferromagnets: Spin-order with M Spin-order with M=0 Magneto-electronics (spintronics): non-volatility, radiation-hardness, speed, energy,... Allow for manipulation and detection by magnetic fields Do not allow for direct manipulation and detection by magnetic fields B.G. Park, et al, Nature Mater. 10 (2011) 347 351 Magnetic fields not used in advanced ferromagnetic spintronics Perturbed by <Tesla Produce ~Tesla nearby stray fields Insensitive to ~10-100 Tesla Produce no stray fields X. Marti, et al, arxiv:1303.4704 X. Marti, et al, Nat. Mater. (2014) Speed limited by FM dynamics timescales Difficult to realize in semiconductors Ultrafast due to AFM dynamics timescales Many room-t semiconductors 36

Antiferromagnetic Spintronics Ordered spins Non-volatile Spin not charge based Radiation-hard No net moment Insensitive to magnetic fields, no fringing stray fields THz dynamics Ultra-fast switching Multiple-stable domain configurations Memory-logic bit cells Last issue of the International Technological Roadmap for Semiconductors in 2016 Materials range Insulators, semiconductors, semimetals, metals, superconductors 37

Antiferromagnetic AMR experiment: AFM memory SQUID experiment: AFM at room-t m (x10-3 emu) 2 1 0-1 -2 RT 400 K -1 0 1 µ 0 H (T) Negligible stray fields from the AFM Marti, Fina,Jungwirth et al. Nature Mater. 14, EP13196118, US311200012 38

Antiferromagnetic AMR experiment: AFM memory Transport experiment: AFM-AMR memory read-out R (Ω) 11.30 11.25 100 300 500 step Marti, Fina,Jungwirth et al. Nature Mater. 14, EP13196118, US311200012 39

Antiferromagnetic AMR experiment: AFM memory AFM memory with no stray fields and insensitive to magnetic field (tested up to 9 T) Comparable AMR to FM NiFeCo comparable size and read-out-time scaling Marti, Fina,Jungwirth et al. Nature Mater. 14, EP13196118, US311200012 40

Antiferromagnetic Spin-orbitronics Writing by spin-orbit torque in a single-layer ferromagnet Magnet reversing itself : SOT Néel SOT AFM J. Zelezny, H. Gao, K. Vyborny, J. Masek, J. Zemen, A. Manchon, J. Sinova, and T. Jungwirth, PRL (2014) 41

Writing by spin-orbit torque in a single-layer ferromagnet Magnet reversing itself: ky Rashba Spin-orbit Torque H SOT z J kx S=0 Sy 0 J x Broken space-inversion symmetry (GaMnAs) 42

Writing by Néel spin-orbit torque in a single-layer antiferromagnet ky kx H SOT z J S=0 Sy 0 J x ky H SOT -z J kx S=0 Sy 0 Zelezny, Gao, Jungwirth, JS December PRL (2014) Antiferromagnet with broken sublattice space-inversion symmetry: (Mn 2 Au) 43

Writing by Néel spin-orbit torque in a single-layer antiferromagnet B(mT) (per 10 7 A/cm 2 ) B(mT) (per 10 7 A/cm 2 ) 0.4 0.2 0-0.2-0.4 0.3 0.1 0-0.1 B x A B x B B y A B y B 0 45 90 135 180 Φ (Degrees) B z B B y B J x B y A B x B B x A -0.3-90 -45 0 45 90 θ (Degrees) Antiferromagnet with broken sublattice space-inversion symmetry: (Mn 2 Au) B z A Zelezny, Gao, Jungwirth, JS December PRL (2014) 44

How it works - kind of 45

!3 0 0 20 40 60 80 100 120 140 160 Experimental Observation of Néel SOT in CuMnAs $P uls e $num be r Wadley, Jungwirth et al Science (2016) CuMnAs" B" 8" 1" 2" 3" B A"D" 4" 5" ( B" $ Rashba0 field: 2 4 0!3 0 Setting 1-5 0 40 2 4 6 8 P uls e )num be r + 10 12 $ $ ΔR t+ (m Ω) $ Figure"4""10 30 (A)"Transverse"resistance"using"orthogonal"probe"curr 20 (black)"and"3h7"(red)."(b)"dependence"of"the"change"i 0 density"of"the"seung"pulse."the"dashed"line"is"a"guide 10 resistance"afer"current"pulses"alternately"along"ortho '10 1H6)"and"with"4.4"kOe"ﬁeld"applied"(pulses"7H12)."(D)"M 0 measured"by"squid"magnetometer." 5 6 7 8 9 10 44 0 6 06 8 0 81 0 0 10 120 140 160 S e tting +c urre nt+de ns ity+(ma /c m ) " be r $P uls e $num $ ( ( 30 '10 Setting 3-7 0 '40 ( ΔR t((m Ω) ΔR t(m Ω) 0!3 0 ΔR t(m Ω) ΔR t((m Ω) 6" 30 0 D '20 GaP" 10 4.4 )ko e )a pplie d ) ΔR t(m Ω) 7" A ( ) 20 CuMnAs C" N o)fie ld)a pplie d 40 + A" C" 00 220 6 8 10 PB uls~e (num r 3 mtbeper 107 Acm-2P uls e (num be r 2 N o)fie ld)a pplie d 4.4 )ko e )a pplie d 40 C" Magnetism: from fundamentals to spin based technology; Bad D" Honnef School- Jairo Sinova 0.8 ) ( 0.05 ( 46

From prediction, to observation, to device in 1 one year!! Electrical read/write antiferromagnetic memory Works like this but not done like this Wadley, TJ et al. Science 16, TJ, Marti, Wadley, Wunderlich, Nature Nanotech. 16 47

Dirac/Weyl semimetals 2016 Néel SOT SOT 3D TI 2D TI graphene 2003 QSHE SHE 53

Coexistence of Topological Dirac fermions and Néel SOT? E Relativistic fermions Topology? k Wan, PRB (2011) Magnetic order Železný, JS, Jungwirth, PRL (2014), arxiv (2016) Wadley, Science (2016) Γ X Z U Néel spin-orbit torques Smejkal, Zelezny, Sinova, Jungwirth PRL (2017) 54

Relativistic physics, topological semimetals and spin-orbitronics effects 55

Dirac and Weyl fermions Relativistic quantum field theory = spinor fields + Lorentz invariant building blocks E E k k graphene 56

Ab initio leading experiment: Topological Semimetal Dirac semimetals Na 3 Bi 2012/2013 Weyl semimetal Y 2 Ir 2 O 7 Weyl semimetal TaAs 2011 2015 13D Dirac semimetals Young, Kane, Mele et al. PRL (2012) 3Liu et al. Science (2014) 2Na 3 Bi candidate Wang Na3Bi PRB (2012) 57

Ab initio leading experiment: Topological Semimetal Dirac semimetals Na 3 Bi 2012/2013 Weyl semimetal Y 2 Ir 2 O 7 Weyl semimetal TaAs 2011 2015 Symmetry breaking Time reversal broken Noncentrosymmetric Pyrochlore iridates Wan PRB (2011) TaAs family: Hasan group (2014/15), Weng, Bernevig PRX(2015), Lv PRX(2015), C. Felser group, Nat. Phys. (2015) 58

Can we control the relativistic fermions electrically?? + 59

Model of AFM topological semimetal B A band crossing Dirac fermions? + YES! AF spintronics Overlap of symmetry conditions 1. Two sites in unit cell [001] δs J δs inversion-partner sites staggered field B A [100] [010] 2. PT symmetry spin-degeneracy Dirac point AF spin-sublattices at inversion partner sites AF spin-orbit orque 60

Minimal lattice model: construction B B A A Kane-Mele spin-orbit coupling Smejkal, Zelezny, Sinova, Jungwirth PRL (2017) 61

Minimal lattice model: local symmetries Pseudovector/axial vector PT + A, B noncentrosymmetric x z P PT P Smejkal, Jungwirth, Sinova PSS (2017) Neel spin-orbit torque 62

Symmetry protection of Dirac points Mirror Translate at Gx invariant subspace [010] [100] nonsymmorphic symmetry = point group + nontrivial translation glide mirror plane Gx={Mx/(1/2,0,0)} Mx 63

Quasi-2D effective model (½ 0 0) A U' A' B [010] PT (½ 0 0) M [100] M' x Y M +i -i X' Г X -i +i Smejkal, Zelezny, Sinova, Jungwirth PRL (2017) 64

Dirac fermions in antiferromagnets CuMnAs tetra. screw axis Sz={2z/(1/2,0,1/2)} ortho. Maca, Jungwirth et al. JMMM (2012) Tang et al. Nat.Phys.(2016) Smejkal, Zelezny, Sinova, Jungwirth PRL (2017) 65

Electrical control of Dirac fermions tetra. Demonstration of inplane Field like torque manipulation ortho. Demonstration of (001)! inplane Field like torque Nonsymmorphic symmetry: Screw axis+glide plane 66

Topological metal-insulator transition 67

Topological magnetotransport: AMR 68

SUMMARY SHE and ISGE SOT in a single-layer ferromagnet ~E Kurebayashi, et al., Nature Nanotech (2014) JS,Valenzuela, Wunderlich, Back, Jungwirth RMP (2015) M B eq eff ~ M B eff pŷ Kurebayashi, et al., Nature Physics (2016) Néel SOT in a singlelayer antiferromagnet Electrical control of Dirac fermions and topological phases Topological Dirac Semi Metal+ AFM (i) Neel SOT physics (ii) J. Zelezny, et al, PRL (2014) J. Zelezny, et al, PRB (2016) O. Gomonay, et al, PRL (2016) Wadley, et al Science (2016) Libor Smejkal, et al PRL (2017) 69

THANK YOU Smejkal, Gayles, Zeledny, Gao, Masek, Kurebayashi, Fang, Irvine, Wunderlich Zarbo, Vyborny, Ferguson, Gomonay, Abanov, and Jungwirth Institute of Physics ASCR Prague Charles Univ. Prague, Czech Rep. Univ. of Nottingham, UK Hitachi and Univ. of Cambridge, UK JGU Mainz

9 th JEMS Conference 2018 Joint European Magnetic Symposia 3 rd -7 th of September 2018 - Mainz, Germany

Spin Phenomena Interdisciplinary Center http://www.spice.uni-mainz.de/ 72