Spintronics: How spin can act on charge carriers and vice versa

1. Spintronics: How spin can act on charge carriers and vice versa TomasJungwirth Universityof Nottingham Institute of Physics Prague

2. Two paradigms for spintronics “Mott“ non-relativistic two-spin-channel model of ferromagnets I I Mott, 1936 “Dirac“ relativistic spin-orbit coupling I I Dirac, 1928

3. SHE & STT switching SOT switching Miron et al., Nature ‘11 Ralph, Buhrman,et al., Science ‘12 -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

4. Ohmic “Dirac“ device: AMR Kelvin, 1857 Magnetization-orientation-dependent scattering

5. Spin-orbit coupling

6. Spin-orbit coupling

7. V Extraordinary magnetoresistance: AMR, AHE, SHE, SOT..... Ordinary magnetoresistance: response to external magnetic field Acting via classical Lorentz force Extraordinary magnetoresistance: response to internalquantum-relativistic spin-orbit field anisotropic magnetoresistance B Lord Kelvin 1857 _ _ _ _ _ _ _ _ _ _ _ FL + + + + + + + + + + + + + I _ _ FSO M _ V I ordinary Hall effect 1879 anomalous Hall effect 1881

8. Classical Boltzmann equation Non-equilibrium distribution function Steady-state current in linear response to applied electric field Linear response: g linear in Ej

9. Steady-state solution for elastic (impurity) scattering

10. Steady-state solution for elastic (impurity) scattering if g(i,k)= Constant quasi-particle relaxation time solution

11. Steady-state solution for elastic (impurity) scattering is isotropic: depends on | - ’| if g(i,k)= Transport relaxation time solution: back-scattering dominates

12. Steady-state solution for elastic (impurity) scattering is anisotropic: depends on k, k’ if No relaxation time solution

13. AMR in Rashba 2D system Rashba Hamiltonian Eigenspinors

14. AMR in Rashba 2D system QM: 1st order Born approximation  isotropic anisotropic

15. AMR in Rashba 2D system Heuristic picture from back-scattering matrix elements current Rashba SOI Rashba SOI Back-scattering  high resistivity No back-scattering  low resistivity

16. Anomalous Hall effect in FMs 1881 Polarimetry of electrons in FMs Spin Hall effect in PMs jc Dyakonov and Perel 1971 Mott, N. F. Proc. R. Soc. Lond. A 1929 Kato,Awschalom, et al., Science‘04 Wunderlich, Kaestner, Sinova, TJ, PRL‘05 Electron spin-dependent scattering off Coulomb field of heavy atoms due to spin-orbit coupling Polarimetry of high-energy electron beams in accelerators Electron spin-dependent scattering off Coulomb field of dopands in a semiconductor due to spin-orbit coupling

17. Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect jc js Hirsch PRL‘99

18. Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect jc js - index Hirsch PNAS‘05

19. Theoretical proposal of intrinsic spin Hall effect Intrinsic anoumalous Hall effect in (Ga,Mn)As Non-magnetic GaAs FM (Ga,Mn)As Murakami, Nagaosa, & S.-C. Zhang, Science’03 Proposed detection by polarized electroluminescence Sinova, TJ, MacDonald, et al. PRL’04 Proposed detection by magneto-optical Kerr effect TJ, Niu, MacDonald, PRL’02

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

21. Optically generated spin current Optically detected charge accummulation due to iSHE fs pump-and-probe: iSHE generated before first scattering in the intrinsic GaAs  intrinsic iSHE Zhao et al., PRL‘06 Werake et al., PRL‘11

22. AHE and SHE

23. AHE and SHE

24. Skew scattering SHE

25. Mott (skew) scattering SHE SHE AMR

26. Skew scattering AHE (SHE) : not constant, not isotropic, not even symmetric  no relaxation time solution Approximation:

27. Skew scattering AHE (SHE)

28. Spin orbit torque M Ie

29. Field-like SOT Compare with AMR or skew-scattering SHE E=Exx ^

30. Field-like SOT (r)  isotropic E=Exx ^

31. Field-like SOT (r)  isotropic g(i,k)=

32. Field-like SOT E=Exx ^

33. Intrinsic spin Hall effect in PMs Intrinsic anoumalous Hall effect in FMs Non-magnetic GaAs FM (Ga,Mn)As Murakami, Nagaosa, & S.-C. Zhang, Science’03 Sinova, TJ, MacDonald, et al. PRL’04 TJ, Niu, MacDonald, PRL’02 Wunderlich, Kaestner, Sinova, TJ, PRL‘05 Werake et al., PRL‘11

34. Linear response I. Boltzmann theory : non-equilibrium distribution functionand equilibrium states

35. Linear response II. Perturbation theory: equilibrium distribution functionand non-equilibrium states

36. Linear response II. Perturbation theory: equilibrium distribution functionand non-equilibrium states

37. Linear response II. Perturbation theory: equilibrium distribution functionand non-equilibrium states Intrinsic SHE (AHE) 0 0

38. Heuristic picture: Bloch equations pz pz px py px py E=Exx ^

39. Field-like SOT Compare with AMR or skew-scattering SHE E=Exx ^

40. Intrinsic antidamping SOT from linear response II. 0 0 Compare with intrinsic SHE 0 0

41. pz pz Hex=0 px py px py pz Intrinsic SHE: transverse spin current Hex>> HR pz px py px py Intrinsic SOT: spin polarization

42. pz Intrinsic SHE: transverse spin current px py pz Intrinsic SOT: spin polarization px py

43. Intrinsic SOT is antidamping-like pz px py px py pz px py px py

44. SHE & STT switching SOT switching Miron et al., Nature ‘11 Ralph, Buhrman,et al., Science ‘12 -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