Antiferromagnetic Spintronics: Neél spin-orbit torques to Dirac fermions Jairo Sinova Johannes Gutenberg Universität Mainz 1th of October 216 Nanoscience and Quantum Transport Kiev, Ukraine Sinova et al RMP 215, Zelezny et al PRL 214/PRB 216, Ciccarelli, Gayles, et al Nature Physics 216, Gomonay, et al PRL 216, Smejkal, et al in prepration (216) Gayles, Zelezny, Smejkal, Ciccarelli, Gomonay, Jungwirth, Molenkamp, Yuan, Kurebayashi, Ferguson, Mukrausov Institute of Physics Prague Univ. of Nottingham Univ. of Cambridge Univ. of Würzburg
Antiferromagnetic Spintronics: Neél spin-orbit torques to Dirac fermions I. Spin-Orbit Torques in Ferromagnets: SHE and Inverse spin galvanic effect phenomenology Spin-Orbit Torques: Intrinsic SOT in GaMnAs SOT in NiMnSb II. Antiferromagnetic Spintronics: Neél SOTs Active manipulation of Néel order by currents: Néel spin-orbit torque III.Topological Dirac Fermion + Antiferromagnets + Neel SOTs I.Relativistic physics in solid state IV.SPICE Kurebayashi, et al., Nat. Nanot. (214) Ciccarelli, et al., Nat. Phys. (216) Sinova,et al RMP (215) Zelezny, Gao, JS, Jungwirth PRL (214) Zelazny, Gao, et al. PRB (216) Gomonay, Jungwirth, Sinova PRL (216) Smejkal, et al in prepration (216) 2
Spin-current and spin-polarization generation by currents Inverse Spin Galvanic Effect or Edelstein Effect (Reverse process of circular photo-galvanic effect, Ganichev et al., 21) ky kx δs δs= y J x Spin Hall Effect in p-gaas Effective fields 1-1 T Spin polarizations 1-1% Wunderlich et at. arxiv 4, PRL 5 3
Experiments of in-plane current switching Miron et al., Nature 11 spin-orbit torque at PM/FM interface ky Buhrman,et al., Science 12 SHE as spin-current generator + STT kx J x δs= δsy hsot z J ~ dm dt! = SOT ~ dm dt! intrinsic SHE + STT SHE ST T = P M (n M ) Jex ~ M ~s ~ Intrinsic SHE in paramagnet acts as the external polarizer 4
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 H (T) the V amplitudes contain spin-orbit fields information. 5
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 ) + Field-like/Rashba torque Τ out-of-plane (h x & h y ) V asy = C 2 sin(2θ M-E ) (-h x (θ M-E )sin(θ M-E ) +h y (θ M-E )cos(θ M-E )) Kurebayashi, Sinova et al., Nature Nanotech. (214) Fang et al., Nature Nanotech. (211) 6
Spin-orbit Torques in Bilayer Systems Spin Hall Rashba Courtesy of P. Gambardella 7
Linear response I. (condensed matter class) Boltzmann theory: non-equilibrium distribution function and equilibrium states Extrinsic (skew-scattering) SHE X 1 ~js = ~js (~k)g~ k V Field-like SOT 1 X ~ ~s = ~s(k)g~k V ~ k ~ k jc δsy J x Dyakonov and Perel 1971 Hirsch PRL 99 Kato et al., Science 4 g! n,k = f! n,k f (E )! n,k ~ dm dt! = SOT Jex ~ M ~s ~ 8
Linear response II. (condensed matter class) Perturbation theory: equilibrium distribution function and non-equilibrium states Intrinsic SHE from linear response II z ĵ y E x j z y = X ~k ~k i = ~ kie ie ~ k t + e i! h ~k (t) ĵ z y ~k if (E ~k ) X ~ kn6=n ~ kn h i ~ kn E ~ ˆv ~ kni E ~kn E ~kn + ~! e i(e ~ +!)t kn + Murakami,et al, Science 3 Sinova, et al. PRL 4 Wunderlich et al. Phys. Rev. Lett. 5 Werake et al., PRL 11 Scattering-independent anti-damping SOT from linear response II. 9
Intrinsic (Berry phase) spin-orbit torque from Bloch eq. Large exchange limit and Rashba SOC ~ M [1] Δp eet [1] ~ E eq eff B ~ M dm M sz z maximum dt Bef f py!! sz z for M E 1
Intrinsic (Berry phase) spin-orbit torque from Bloch eq. Large exchange limit and Rashba SOC [1] Δp eet [1 [1] [1 ~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 ) 11
Intrinsic (Berry phase) spin-orbit torque in GaMnAs [1] [1] [11] [11] GaMnAs Rashba [1] GaMnAs GaAs Dresselhaus [1] d ˆM dt! SOT = ˆM s z ( M E )ẑ angle between M and current direction current direction 12
Comparison of Experiment -Theory Solid line: Calculations with H KL (captures higher harmonics) µ h z [ µt ] 15 1 5-5 -1 [1] [1] 15 1 5-5 -1 [1] S // M [1] -15-15 15 9 18 27 9 18 27 15 µ h z [ µt ] 1 5-5 -1 [1-1] [11] 1 5-5 -1-15 -15 9 18 27 36 θ M-J 9 18 27 36 θ M-J Kurebayashi, et al., Nature Nanotech (214) 13
Other Materials: Half Heuslers NiMnSb Tc = 73 K in bulk 15
SOT Torque: dominated by field like term NiMnSb Z&[1]& MS(φ) I [11] φ& [1#1]& Kubo I [11] Scattering Formalism Jacob Gayles Z&[1]& I [11] By& In Plane Bx& MS(ϕ)& [1/1]& Z&[1]& I [11] By& Out of Plane Bx& MS(ϕ)& [1/1]& 15
Room-temperature SOT in NiMnSb Ciccarelli, et al., Nature Physics (216) 25 μt J 2 [11] z y x J 1 [1-1] 15 15 1 5 V asy V sym 1 5 V asy V sym V dc (µv) -5 V dc (µv) -5-1 [1-1] -15 9 18 27 36 φ (deg) The driving field is linear in current: -1 [11] -15 9 18 27 36 φ (deg) 16
Antiferromagnetic Spintronics: Neél spin-orbit torques to Diract fermions I. Spin-Orbit Torques in Ferromagnets: SHE and Inverse spin galvanic effect phenomenology Spin-Orbit Torques: Intrinsic SOT in GaMnAs SOT in NiMnSb II. Antiferromagnetic Spintronics: Neél SOTs Active manipulation of Néel order by currents: Néel spin-orbit torque III.Topological Dirac Fermion + Antiferromagnets + Neel SOTs I.Relativistic physics in solid state IV.SPICE Kurebayashi, et al., Nat. Nanot. (214) Ciccarelli, et al., Nat. Phys. (216) Sinova,et al RMP (215) Zelezny, Gao, JS, Jungwirth PRL (214) Zelazny, Gao, et al. PRB (216) Gomonay, Jungwirth, Sinova PRL (216) Smejkal, et al in prepration (216) 17
Antiferromagnetic Spintronics Need Spin-Orbit Torques Reviews: MacDonald & Tsoi Phil. Trans. R. Soc. A 369, 398 (211) Gomonay & Loktev Low Temp. Phys. 4, 17 (214) TJ, Marti, Wadley, Wunderlich Nature Nanotech. 11, 231 (216) Baltz, Manchon, Tsoi, Moriyama, Ono, Tserkovnyak http://arxiv.org/abs/ 166.4284 18
Why antiferromagnetic spintronics Ferromagnets Antiferromagnet Spin-order with M Spin-order with M= 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. 1 (211) Magnetic fields not used in advanced ferromagnetic spintronics Perturbed by <Tesla Produce ~Tesla nearby stray fields Insensitive to ~1-1 Tesla Produce no stray fields X. Marti, et al, arxiv:133.474 X. Marti, et al, Nat. Mater. (214) Speed limited by FM dynamics timescales Ultrafast due to AFM dynamics timescales Difficult to realize in semiconductors Many room-t semiconductors Reviews: Gomonay & Loktev Low Temp. Phys. 4, 17 (214); Jungwirth et al, Nature Nanotech. 11, 231 (216); Baltz, et al http://arxiv.org/abs/166.4284 19
Antiferromagnetic AMR experiment: AFM memory SQUID experiment: AFM at room-t m (x1-3 emu) 2 1-1 -2 RT 4 K -1 1 µ H (T) Negligible stray fields from the AFM Marti, Fina,Jungwirth et al. Nature Mater. 14, EP13196118, US311212 2
Antiferromagnetic AMR experiment: AFM memory Transport experiment: AFM-AMR memory read-out R (Ω) 11.3 11.25 1 3 5 step Marti, Fina,Jungwirth et al. Nature Mater. 14, EP13196118, US311212 21
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, US311212 22
Antiferromagnetic Spin-orbitronics Writing by spin-orbit torque in a single-layer ferromagnet Magnet reversing itself : SOT STT SOT Néel SOT AFM J. Zelezny, et al, PRL (214) What type of current-induced polarisation can we generate? 23
Néel spin-orbit torque in a single-layer antiferromagnet ky HSOT z J kx S= Sy J x ky HSOT -z J kx S= Sy Zelezny, Gao, JS, Jungwirth, PRL (214) Antiferromagnet with broken sublattice space-inversion symmetry: (Mn2Au) 24
Néel spin-orbit torque in a single-layer antiferromagnet B(mT) (per 1 7 A/cm 2 ) B(mT) (per 1 7 A/cm 2 ).4.2 -.2 -.4.3.1 -.1 B x A B x B B y A B y B 45 9 135 18 Φ (Degrees) B z B B y B J x B y A B x B B x A -.3-9 -45 45 9 θ (Degrees) Antiferromagnet with broken sublattice space-inversion symmetry: (Mn 2 Au) B z A Zelezny, Gao, JS, Jungwirth, PRL (214) 25
How it works - kind of Frank Freimuth 26
!3 Néel SOT in CuMnAs Wadley et al, Science 216 CuMnAs" B" 8" 1" 2" 3" 4" 5" A"D" D Setting 3-7 3 ( '4 12 $ 22 2 P uls e (num be r Acm-2 C" 1 $ ( (!3 6 8 1 P uls e (num be r 4 6 8 P uls e )num be r + Figure"4""1 3 (A)"Transverse"resistance"using"orthogonal"probe"curr 2 (black)"and"3h7"(red)."(b)"dependence"of"the"change"in density"of"the"seung"pulse."the"dashed"line"is"a"guide 1 resistance"afer"current"pulses"alternately"along"ortho '1 1H6)"and"with"4.4"kOe"field"applied"(pulses"7H12)."(D)"M measured"by"squid"magnetometer." 5 6 7 8 9 1 44 6 6 8 81 1 12 14 16 S e tting +c urre nt+de ns ity+(ma /c m ) " be r $P uls e $num $ $ 3 Rashba field: 2 4 2 ΔR t+ (m Ω)!3 4 ( ΔR t((m Ω) ΔR t(m Ω) Setting 1-5 B" $ 3 ΔR t(m Ω) ΔR t((m Ω) 6" ( B ~ 3 mt per 4.4 )ko e )a pplie d '2 GaP" 17 ) ) ΔR t(m Ω) 7" B '1 6 8 1 12 14 16 $P uls e $num be r 2 A 1 4 N o)fie ld)a pplie d 4 CuMnAs C" 2 + A" C" 4 N o)fie ld)a pplie d ) 4.4 )ko e )a pplie d D" ( (.8.5 27
XMLD microscopy and spectroscopy J write [1] [1] 1 µm XMLD (a.u.) XMLD (%) 1-1 Experiment Theory 64 65 Photon energy 28
From prediction, to observation, to device in 1 one year!! Works like this but not done like this Electrical read/write antiferromagnetic memory Wadley, TJ et al. Science 16, TJ, Marti, Wadley, Wunderlich, Nature Nanotech. 16 29
How to use the Neel SOT? Gomonay, Jungwirth, JS PRL (216) M1 θ M2 Ω Speeds of ~ 5 km/sec!! x 3
Writing by Néel spin-orbit torque in a single-layer antiferromagnet 2D Antiferromagnet with Rashba SOC intrinsic Néel SOT can be much larger than FM SOTs!! BUT intrinsic Néel SOT 45 9 135 18 Φ (Degrees) extrinsic/rashba Néel SOT= B z A B z B.2 -.2 B(mT) (per.1 A/cm) Antiferromagnet with broken global space-inversion symmetry: 2D-AFM+Rashba B x B B z B B z A B x A -45 45 9 θ (Degrees).2 -.2 B(mT) (per.1 A/cm) 31
Writing by Néel spin-orbit torque in a single-layer antiferromagnet 2D Antiferromagnet with Rashba SOC intrinsic Néel SOT can be much larger than FM SOTs!! E(eV) E(eV) 15 1 5-5 -1 -X Γ X M Γ k 15 1 5-5 -1-15 -X Γ X M Γ k.2.2.1.1 DOS(states ev -1 nm -2 ) Antiferromagnet with broken global space-inversion symmetry: 2D-AFM+Rashba 32
Antiferromagnetic Spintronics: Neél spin-orbit torques to Diract fermions I. Spin-Orbit Torques in Ferromagnets: SHE and Inverse spin galvanic effect phenomenology Spin-Orbit Torques: Intrinsic SOT in GaMnAs SOT in NiMnSb Kurebayashi, et al., Nat. Nanot. (214) Ciccarelli, et al., Nat. Phys. (216) II. Antiferromagnetic Spintronics: Neél SOTs Active manipulation of Néel order by currents: Néel spin-orbit torque Zelezny, Gao, JS, Jungwirth PRL (214) Zelazny, Gao, et al. PRB (216) Gomonay, Jungwirth, Sinova PRL (216) III.Topological Dirac Fermion + Antiferromagnets + Neel SOTs I.Relativistic physics in solid state Smejkal, et al in prepration (216) Sinova,et al RMP (215) 33
216 Dirac/Weyl semimetals Néel SOT SOT 3D TI QSHE 2D TI graphene 23 SHE 34
Coexistence of Topological Dirac fermions and Néel SOT? E Relativistic fermions Topology? k Wan, PRB (211) Magnetic order Železný, JS, Jungwirth, PRL (214), arxiv (216) Wadley, Science (216) Γ X Z U Néel spin-orbit torques Libor Smejkal, et al (216) 35
Relativistic physics, topological semimetals and spinorbitronics effects 36
Dirac and Weyl fermions Relativistic quantum field theory = spinor fields + Lorentz invariant building blocks E E k k graphene http://phelafel.technion.ac.il/ ~tzipora/band_theory.html 37
Ab initio leading experiment: Topological Semimetal Dirac semimetals Na 3 Bi 212 1 /213 2 214 3 Weyl semimetal Y 2 Ir 2 O 7 Weyl semimetal TaAs 211 4 215 5,6 215 7-9 1 3D Dirac semimetals Young, Kane, Mele et al. PRL (212) 3 Liu et al. Science (214) 2 Na 3 Bi candidate Wang Na3Bi PRB (212) 38
Ab initio leading experiment: Topological Semimetal Dirac semimetals Na3Bi 2121/2132 2143 Weyl semimetal Y2Ir2O7 Weyl semimetal TaAs 2114 2155,6 2157-9 Symmetry breaking Time reversal broken Pyrochlore iridates Wan PRB (211) Noncentrosymmetric TaAs family: 5,7 Hasan group (214/15), 6Weng, Bernevig PRX(215), 8Lv PRX(215), 9 C. Felser group, Nat. Phys. (215) 39
Large mobilities Liang, Nature Materials (215) Ultrahigh mobility and giant magnetoresistance in Dirac semimetal Cd3As2 Bi nanowires Mechanism? Suppression of backscattering? 9 16 cm2 V 1 s 1 at 5 K Si 4
Can we control the relativistic fermions electrically? Libor Smejkal 41
Model of AFM topological semimetal B A δs B PT δs A [1] J [1] [1] 42
Quasi-2D variant (½ ) A U' A' B [1] PT (½ ) M [1] M' x Y M +i -i X' Г X -i +i 43
Dirac fermions in antiferromagnets CuMnX (X=As/P) tetra. ortho. Full potential ELK code DFT(FLAPW)+PBE+SOC Nonsymmorphic symmetry 44
Electrical control of Dirac fermions Demonstration of inplane Field like torque manipulation Demonstration of (1)! inplane Field like torque Nonsymmorphic symmetry: Screw axis+glide plane 45
Electrical control of phases Dirac semimetal SOC (1) Semiconductor SOC (11) 46
SUMMARY SHE and ISGE SOT in a single-layer ferromagnet Kurebayashi, et al., Nature Nanotech (214) ~ E JS,Valenzuela, Wunderlich, Back, Jungwirth RMP (215) Néel SOT in a singlelayer antiferromagnet J. Zelezny, et al, PRL (214) J. Zelezny, et al, PRB (216) O. Gomonay, et al, PRL (216) Wadley, Jungwirth et al Science (216) Bef f M eq Beff ~ M py Kurebayashi, et al., Nature Physics (216) Electrical control of Dirac fermions and topological phases Topological Dirac Semi Metal+ AFM (i) Neel SOT physics (ii) Libor Smejkal, et al (216) 47