Spintronics: How spin can act on charge carriers and vice versa Tomas Jungwirth University of Nottingham Institute of Physics Prague

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

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

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

Spin-orbit coupling

Extraordinary magnetoresistance: AMR, AHE, SHE, SOT..... B V I _ _ _ _ _ _ FLFL Ordinary magnetoresistance: response to external magnetic field Acting via classical Lorentz force Extraordinary magnetoresistance: response to internal quantum-relativistic spin-orbit field ordinary Hall effect 1879 I _ F SO _ _ V anomalous Hall effect 1881 anisotropic magnetoresistance M Lord Kelvin 1857

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

Steady-state solution for elastic (impurity) scattering

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

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

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

AMR in Rashba 2D system Rashba Hamiltonian Eigenspinors

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

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

Mott, N. F. Proc. R. Soc. Lond. A 1929 Dyakonov and Perel 1971 Spin Hall effect in PMs 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 j c Anomalous Hall effect in FMs 1881 Polarimetry of electrons in FMs Kato, Awschalom, et al., Science‘04 Wunderlich, Kaestner, Sinova, TJ, PRL‘05

j c j s Hirsch PRL‘99 Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect

j c j s Proposal for electrical spin injection by the spin Hall effect and electrical detection by the inverse spin Hall effect Hirsch PNAS‘05 - index

Theoretical proposal of intrinsic spin Hall effect FM (Ga,Mn)As Non-magnetic GaAs TJ, Niu, MacDonald, PRL’02 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 Intrinsic anoumalous Hall effect in (Ga,Mn)As

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

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

AHE and SHE

Skew scattering SHE

Mott (skew) scattering SHE SHE AMR

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

Skew scattering AHE (SHE)

Spin orbit torque M IeIe

Field-like SOT Compare with AMR or skew-scattering SHE E=E x x ^

Field-like SOT E=E x x ^ isotropic   (r) (r)

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

Field-like SOT E=E x x ^

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

Boltzmann theory : non-equilibrium distribution function and equilibrium states Linear response I.

Perturbation theory: equilibrium distribution function and non-equilibrium states Linear response II.

Perturbation theory: equilibrium distribution function and non-equilibrium states Linear response II.

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

pzpz pxpx pypy pzpz pxpx pypy E=E x x ^ Heuristic picture: Bloch equations

Field-like SOT Compare with AMR or skew-scattering SHE E=E x x ^

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

pzpz pxpx pypy pzpz pxpx pypy pzpz pxpx pypy pzpz pxpx pypy Intrinsic SHE: transverse spin current Intrinsic SOT: spin polarization H ex =0 H ex >> H R

pzpz pxpx pypy pzpz Intrinsic SHE: transverse spin current Intrinsic SOT: spin polarization pxpx pypy

pzpz pxpx pypy pxpx pypy pzpz pxpx pypy pxpx pypy Intrinsic SOT is antidamping-like

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