Lecture I. Spin Orbitronics

Transcription

1 Lecture I Spin Orbitronics Alireza Qaiumzadeh Radboud University (RU) Institute for Molecules and Materials (IMM) Theory of Condensed Matter group (TCM)

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3 What We Talk About When We Talk About Spin Orbitronics Mott non-relativistic two-spin-channel model of ferromagnets Dirac relativistic spin-orbit coupling

4 What We Talk About When We Talk About Spin Orbitronics Anomalous Hall effect Spin Hall effect and inverse effect Spin galvanic effect and inverse effect Spin orbit torques and inverse effect Magnon Hall effect Topoligical insulators...

5 Outlook: 1.Rashba spin orbit interaction 2. Extraordinary Hall Effect 3. Spin transfer torques 4. Spin orbit torques

6 1. Rashba spin orbit interaction D. Bercioux and P. Lucignano, Rep. Prog. Phys. 78, (2015). A. Manchon, H. C. Koo, J. Nitta, S. M. Frolov, and R. A. Duine, Nat. Mater. 14, 871 (2015).

7 Spin orbit coupling (classic description) nucleus rest frame electron rest frame I Qv Q 0 I r r B 4 r 4 r 3 E 3 0 B 1 0 0v E 2 c v E H SO g B e S B mc S v E Lorentz transformation Thomas precession

8 Pauli equation Relativistic SOI

9 Intrinsic vs. Extrinsic SOI Time reversal symmetry: Inversion symmetry:

10 Intrinsic Spin Orbit Interaction k cubic Dresselhaus SOI: n doped 3D semiconductors with the bulk inversion asymmetry (BIA), III V and II VI zinc blende structures k linear Dresselhaus SOI: the electrons are conned to 2D, in semiconductors with BIA K linear Rashba SOI: n doped 3D semiconductors with the structure inversion asymmetry (SIA) K cubic Rashba SOI: Luttinger SOI: p doped GaAs

11 Rashbaterm wurtzite structure Rashba term 2D Confinement

12 (Quasi) 2D systems with structure inversion asymmetry 1. E. Rashba, Properties of semiconductors with an extremum loop. 1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys. Solid State 2, (1960). 2. F. T. Vas ko, Spin splitting in the spectrum of two dimensional electrons due to the surface potential. P. Zh. Eksp. Teor. Fiz. 30, (1979). 3. Y. A. Bychkov & E. I. Rasbha, Properties of a 2D electron gas with lifted spectral degeneracy. P. Zh. Eksp. Teor. Fiz. 39, (1984). 1. C. Ast, et al. Giant spin splitting through surface alloying. Phys. Rev. Lett. 98, (2007). 2. A. Manchon, et al. New perspectives for Rashba spin orbit coupling. Nat. Mater. 14, 871 (2015).

13 2. Extraordinary Hall Effect N. Nagaosa et al., Rev. Mod. Phys. 82, 1539 (2010). D. Xiao et al., Rev. Mod. Phys. 82, 1959 (2010). J. Sinova et al., Rev. Mod. Phys. 87, 1213 (2015). Sinova and Jungwirth presentations

14 Queen of solid state transport experiments Ordinary magnetoresistance: response to external magnetic field Acting via classical Lorentz force ordinary Hall effect (1879) B _ Extraordinary magnetoresistance F L I Extraordinary magnetoresistance: response to internal quantum-relativistic spin-orbit field anisotropic magnetoresistance (AMR) (1857) AMR s 1 ( ij 2 W. Thomson, Proc. Royal Soc. London 8, 546 (1857) ji ) (Lord Kelvin ( ) E. H. Hall, Amer. J. Math. 2, 287 (1879) V M _ F SO I V AHE A 1 ( ij 2 ji ) anomalous Hall effect (AHE) (1881) (Edwin Hall ) E. Hall, Phil. Mag. 12, 157 (1881)

15 Relativistic anisotropic magnetoresistance (AMR) Spintronic effect 150 years ahead of time M I e Kelvin, 1857 W. Thomson, Proc. Royal Soc. London 8, 546 (1857)

16 Read-out: relativistic anisotropic magnetoresistance (AMR) Spintronic effect 150 years ahead of time M I e Kelvin, 1857

17 Mechanisms which are responsible for spin orbitrnics

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19 Spin Swapping Principle Mott scattering B so ~k xk k k D yakonov & Perel, JETP Lett. 13, 467 (1971)

20 Intrinsic Anomalous Hall effect In systems with broken time reversal symmetry and SOI Nunner et al. Phys. Rev. B 76, (2007) Sinitsyn et al. Phys. Rev. B 75, (2007)

21 Intrinsic Anomalous Hall effect

22 a a a

23 Intrinsic Spin Hall Effect In systems with time reversal symmetry and SOI: z jy jx Disorder free limit P. Wang, Y Q. Li, and X. Zhao, PRB, 75, M.I. Dyakonov, Spin Hall Effect, Future Trends in Microelectronics, S. Luryi, J. Xu, and A. Zaslavsky (eds), Wiley 2010, p. 251

24 (Inverse) Spin Hall Effect Magnus effect: B. F. Miao, S.Y. Huang, D. Qu, and C. L. Chien, PRL 111, (2013)

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27 Edge polarized electro-luminescence Magneto-optical Kerr microscopy Extrinsic SHE Kato, Awschalom, et al., Intrinsic SHE Wunderlich, Kaestner, Sinova, Science 04 TJ, PRL 05

28 Inverse Spin Hall Effect Zhao, H. et al. Phys. Rev. Lett. 96, (2006).

29 3. Spin Transfer Torque (STT) D. C. Ralph and M. D. Stiles, JMMM, 320, 1190 (2008). A. Brataas, A. D. Kent, and H. Ohno, Nat. Mater. 11, 372 (2012).

30 What We Talk About When We Talk About Spin Orbitronics Anomalous Hall effect Spin Hall effect and inverse effect Spin galvanic effect and inverse effect Spin orbit torques and inverse effect Magnon Hall effect Topoligical insulators...

31 Landau Lifshtiz Gilbert (LLG) equation Non relativistic spin transfer torque: Spin polarized current driven switching J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996) (Antidamping torque) A. Brataas, A. D. Kent and H. Ohno, Nature Mat. 11, 372 (2012)

32 Writing by current: non relativistic spin transfer torque Spins injected from external polarizer in a non uniform magnetic structure M p M Berger PRB 96, Slonczewski JMMM 96 I e Sloncyewski, Berger, 1996 Buckley Prize at APS MM 2013 STT MRAM

33 MRAM: universal memory Write with magnetic field: on market since 2006 scales with current Write with current (STT MRAM): on market since 2013 scales with current density

34 Read-out: non-relativistic giant magnetoresistance (GMR) I e I e Fert, Grünberg, et al Nobel Prize 2007

35 Read-out: relativistic anisotropic magnetoresistance (AMR) Spintronic effect 150 years ahead of time M I e Kelvin, 1857

36 Read-out: relativistic anisotropic magnetoresistance (AMR) Spintronic effect 150 years ahead of time M I e Kelvin, 1857

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38 4. Spin orbit torques A. Q., R. A. Duine, and M. Titov, Phys. Rev. B 92, (2015)

39 Writing by current: relativistic spin orbit torque Spin current in a uniform magnetic structure with broken space inversion symmetry M Manchon & Zhang, PRB 08, Chernyshev et al. Nature Phys. 09, Miron et al. Nature Mater. 10, Fang, Ferguson, TJ et al. Nature Nanotech. 11 I e Zinc blende (Ga,Mn)As: broken bulk inversion symmetry In plane current switching Miron et al., Nature 11 Co/Pt: broken structural inversion symmetry

40 Writing by current: relativistic spin orbit torque Spin current in a uniform magnetic structure with broken space inversion symmetry M Manchon & Zhang, PRB 08, Chernyshev et al. Nature Phys. 09, Miron et al. Nature Mater. 10, Fang, Ferguson, TJ et al. Nature Nanotech. 11 I e Dirac Zinc blende (Ga,Mn)As: broken bulk inversion symmetry I I

41 Edelstein effect (inverse spin galvanic effect) V. M. Edelstein, Solid State Commun. 73, 233 (1990). me tr s 2 3 R E x yˆ Inverse Edelstein effect (spin galvanic effect) S. D. Ganichev et al., Nature, 417, 153 (2002).

42 Rashba spin orbit torques in ferromagnets Edelstein effect: 1 Field like 2 Single magnetic domain

43 Miron et al. Nature mater. 9, 230 (2010).

44 Spin Transfer Torque Generated by the Topological Insulator Our data suggest that topological insulators could enable very efficient electrical manipulation of magnetic materials at room temperature, for memory and logic applications. Nature, 511, 449 (2014)

45 1. Rashba spin orbit torques in ferromagnets Observation of magnetization reversal due to SOI In plane (Field like) and out of plane (Antidamping like) Spin orbit torques vs. spin Hall Effect Jairo Sinova?

46 SHE & STT switching SOT switching Ralph, Buhrman,et al., Science 12 Miron et al., Nature 11 We see (anti)damping like torque SOT is field like so we exclude it non relativistic STT in metals is dominated by the (anti)damping torque We also see (anti)damping like torque SOT is field like but maybe there is some (anti)damping like SOT as well and maybe we found it intrinsic SOT analogous to intrinsic SHE

47 Rashba spin orbit torques in ferromagnets

48 Rashba spin orbit torques in ferromagnets Y. Kim et al. IEEE Trans. Elect. Dev., 62, 561, (2015)

49 Rashba spin orbit torques in ferromagnets Microscopic derivation of SOTs based on Functional Formulation of the Keldysh Formalism:

50 Rashba spin orbit torques in ferromagnets

51 Rashba spin orbit torques in ferromagnets LLG equation: Gilbert damping: The SOT mechanism is based on the exchange of angular momentum between the crystal lattice and the local magnetization via spin orbit coupling.

52 H. Kurebayashi et al. Nat. Nano dm dt J ex M s Intrinsic SOT ~ M ([ E zˆ] M )